45 results on '"UPADHYAY, RANJIT KUMAR"'
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2. Analysis of interval-valued model for interaction between plankton-fish population in marine ecosystem
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Renu, Upadhyay, Ranjit Kumar, Tiwari, S.P., and Yadav, R.P.
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- 2023
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3. Modelling and analysis of delayed tumour–immune system with hunting T-cells
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Dehingia, Kaushik, Das, Parthasakha, Upadhyay, Ranjit Kumar, Misra, Arvind Kumar, Rihan, Fathalla A., and Hosseini, Kamyar
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- 2023
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4. Cross diffusion induced spatiotemporal pattern in diffusive nutrient–plankton model with nutrient recycling
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Kumari, Sarita, Tiwari, Satish Kumar, and Upadhyay, Ranjit Kumar
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- 2022
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5. Hopf bifurcation and optimal control of a delayed malware propagation model on mobile wireless sensor networks
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Zhang, Hu, Upadhyay, Ranjit Kumar, Liu, Guiyun, and Zhang, Zizhen
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- 2022
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6. Exploring the behavior of malware propagation on mobile wireless sensor networks: Stability and control analysis
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Kumari, Sangeeta and Upadhyay, Ranjit Kumar
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- 2021
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7. An analytical scheme on complete integrability of 2D biophysical excitable systems
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Mondal, Argha, Mistri, Kshitish Ch., Aziz-Alaoui, M.A., and Upadhyay, Ranjit Kumar
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- 2021
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8. Dynamical analysis for a deterministic SVIRS epidemic model with Holling type II incidence rate and multiple delays
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Zhang, Zizhen and Upadhyay, Ranjit Kumar
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- 2021
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9. Stability and Hopf bifurcation of a delayed giving up smoking model with harmonic mean type incidence rate and relapse
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Zhang, Zizhen, Zou, Junchen, and Upadhyay, Ranjit Kumar
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- 2020
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10. An epidemic model with multiple delays for the propagation of worms in wireless sensor networks
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Zhang, Zizhen, Zou, Junchen, Upadhyay, Ranjit Kumar, and Rahman, Ghaus ur
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- 2020
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11. Emergence of spiral and antispiral patterns and its CGLE analysis in leech-heart interneuron model with electromagnetic induction.
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Upadhyay, Ranjit Kumar, Pradhan, Debasish, Sharma, Sanjeev Kumar, and Mondal, Arnab
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ELECTROMAGNETIC induction , *INTERNEURONS , *MEMBRANE potential , *COMPUTATIONAL electromagnetics , *MAGNETIC flux , *HOPF bifurcations - Abstract
Neurons can exhibit various rhythmic activities such as bursting, spiking, and quiescent states when exposed to external input current stimulus. In this paper, a model of medicinal leech's heart (LH) interneuron is considered to describe the dynamics of neurons with a varied range of electrical activities. The crucial insights into the model's dynamics are explored in three different parameter regimes: phasic spiking, regular spiking, and bursting, based upon the codimension-one bifurcation of the model by considering V K 2 s h i f t as a bifurcation parameter. The spatiotemporal dynamics of the model are explored by allowing 1D and 2D diffusion in the membrane voltage. The 1D diffusive system produces irregular bursting dynamics for the intermediate value of diffusion coefficients, whereas, at higher values, it shows synchronized oscillations. In the presence of 2D diffusion, the emergence of different types of spiral patterns is observed in the system. Furthermore, the system is extended by incorporating electromagnetic induction in the membrane voltage to explore the effect of induction on the various dynamics of neural model. By varying its intensities, the membrane voltage in the extended model produces a variety of discharge modes, such as periodic spiking, fast-spiking, resting, and spike-adding phenomena. In addition, the emergence of anti-spiral patterns in the extended model near subcritical Hopf bifurcation is analytically verified using the complex Ginzburg-Landau equation (CGLE). These findings demonstrate that the firing patterns vary based on the control parameters, and these variations contribute to our understanding of how the brain system transmits and processes the signals. • A slow-fast neuron model of Leech's heart interneuron is considered. • The model is improved by adding EMI to study the impact of magnetic flux. • Bifurcation scenarios and different firing activities of both models are performed. • These systems with diffusion display irregular firing and multi-arm spiral patterns. • CGLE analysis in the system with EMI confirms anti-spiral patterns occurrence. [ABSTRACT FROM AUTHOR]
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- 2024
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12. Modeling and control of computer virus attack on a targeted network
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Upadhyay, Ranjit Kumar and Singh, Prerna
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- 2020
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13. Virus dynamics of a distributed attack on a targeted network: Effect of firewall and optimal control
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Kumari, Sangeeta, Singh, Prerna, and Upadhyay, Ranjit Kumar
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- 2019
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14. Viral dynamic model with cellular immune response: A case study of HIV-1 infected humanized mice
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Dhar, Mausumi, Samaddar, Shilpa, Bhattacharya, Paritosh, and Upadhyay, Ranjit Kumar
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- 2019
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15. Spiking and bursting patterns of fractional-order Izhikevich model
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Teka, Wondimu W., Upadhyay, Ranjit Kumar, and Mondal, Argha
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- 2018
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16. Detecting malicious chaotic signals in wireless sensor network
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Upadhyay, Ranjit Kumar and Kumari, Sangeeta
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- 2018
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17. Dynamics of a modified Hindmarsh–Rose neural model with random perturbations: Moment analysis and firing activities
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Mondal, Argha and Upadhyay, Ranjit Kumar
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- 2017
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18. Predator interference effects on biological control: The “paradox” of the generalist predator revisited
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Parshad, Rana D., Bhowmick, Suman, Quansah, Emmanuel, Basheer, Aladeen, and Upadhyay, Ranjit Kumar
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- 2016
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19. Spread of a disease and its effect on population dynamics in an eco-epidemiological system
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Upadhyay, Ranjit Kumar and Roy, Parimita
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- 2014
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20. Emergence of hidden dynamics in different neuronal network architecture with injected electromagnetic induction.
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Upadhyay, Ranjit Kumar, Sharma, Sanjeev Kumar, Mondal, Arnab, and Mondal, Argha
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ELECTROMAGNETIC induction , *NEURAL circuitry , *HOPF bifurcations , *REDUCED-order models , *PHASE velocity , *GROUP velocity , *FUZZY neural networks , *HOPFIELD networks - Abstract
• An attempt has been made to understand the effect of electromagnetic induction on the network of neurons. • An excitable slow-fast memristive model has been studied with its various intrinsic dynamics. • We analytically establish the existence and stability of Hopf bifurcation with bifurcating periodic solutions. • We investigate the emergence of multi-arm antispiral waves in the system with proper analytical justification. • A random network architecture is used to study the dynamics of coupled network that generates MMOs and bursting patterns. The diverse firing responses in a single neuron model as well as in a neuronal network play a major role in understanding the collective neuronal dynamics. In this paper, we consider an excitable slow-fast memristive model and study its various intrinsic dynamics by allowing a periodic external stimulus. The single model exhibits various types of spiking, bursting, mixed-mode oscillations (MMOs), and mixed-mode bursting oscillations (MMBOs) depending on the amplitude and frequency of the periodic injected current. Corresponding bifurcation analysis reveals the existence of supercritical and subcritical Hopf bifurcations in the system depending on the major predominant parameters that establish the scenarios of the neuronal responses. We have verified analytically the existence and stability of Hopf bifurcations. The memristive system can produce cascade of period doubling bifurcations for particular parameter regimes. Next, we investigate the emergence of multi-arm antispiral waves in the diffusively coupled system with proper analytical justification. We have also computed the group and phase velocities to discern the spiral and antispiral waves near the Hopf instability. A transition from target wave to multi-arm antispiral wave is observed in the diffusive system. Moreover, we use a random network architecture different from the diffusive network to study the dynamics of the coupled network for certain firing activities. It is observed that the network of heterogeneous desynchronized neurons with higher electrical couplings, can generate MMOs, MMBOs, and bursting for different external stimuli. However, the uncoupled systems cannot reveal such typical dynamics for particular parameters. Further, we introduce a reduced-order model to summarize the complete dynamics of the larger random network and report the findings. [ABSTRACT FROM AUTHOR]
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- 2022
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21. Discrete and data packet delays as determinants of switching stability in wireless sensor networks.
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Upadhyay, Ranjit Kumar and Kumari, Sangeeta
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WIRELESS sensor networks , *HOPF bifurcations , *DATA transmission systems , *DATA packeting , *SENSOR networks , *SECURITY systems - Abstract
• To understand transmission dynamics of malicious signals in WSN, an energy efficient e-epidemic delay model is proposed. • Malicious signals can be controlled, system stabilizes with small delay and exhibits oscillatory behavior for large delay. • Data packet and discrete delays are responsible for stability switching and occurrence of chaotic dynamics respectively. • Occurrence of double Hopf bifurcation indicates about regular functionality and robust security of sensor network. • We examine how the stability regions and bifurcation scenario changes with the transmission rate. An attempt has been made to understand the transmission dynamics of malicious signals in wireless sensor networks. An energy efficient e-epidemic model with data packet transmission delay has been considered. Linear stability analysis is performed for all the equilibrium points, whose characteristic equations involve the time delay. Global stability and Hopf bifurcation analyses are carried out for the endemic equilibrium point of the delay system. Attention has been paid to the direction of Hopf bifurcation and the stability of the resulting periodic solutions. Numerical study exhibits double Hopf bifurcation dynamics and it causes stability switching i.e., instability to stability and back to instability or the reverse transition of the solution of the considered system. Finally, numerical simulations provide useful observations for different delays and they show an interesting bifurcation scenario. The impact of the control parameters β and τ on the system dynamics have been investigated. Our results suggest that the data packet delay and discrete delay are responsible for the stability switching and the occurrence of chaotic dynamics respectively. The presence of chaotic dynamics indicates fragile security system of the network. Looking into the simulation results, we have indicated the most effective control measures to control the propagation of malicious signals. [ABSTRACT FROM AUTHOR]
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- 2019
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22. Explosive tritrophic food chain models with interference: A comparative study.
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Jana, Debaldev, Upadhyay, Ranjit Kumar, Agrawal, Rashmi, Parshad, Rana D., and Basheer, Aladeen
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TOP predators , *COMPARATIVE studies , *DYNAMICAL systems , *PREY availability , *PREGNANCY , *COMPUTER simulation , *FOOD chains - Abstract
• The effect of top predator interference on the dynamics of a tritrophic food chain model is the principal goal to study general framework for three species food chain models in which intermediate and top predators are specialist and generalist types respectively where the top predator grows by sexual reproduction. • This concept is used to design five different models in this paper by five different combinations of functional responses of specialist intermediate predator (food uptake process follows either prey dependent, Holling type III/IV or prey-predator dependent, BD-functional response) and sexually reproductive generalist top predator (food uptake follows strictly prey-predator dependent, BD/CM functional response) respectively assuming the fact that the growth of intermediate predator is mediated by gestation delay. • Stability of each equilibria of the non-delayed counterpart of each model and the existence of Hopf-bifurcation for the coexisting equilibrium point of all delayed systems are established. • The delayed and non-delayed models can blow-up in finite time under sufficient conditions on the initial data. Furthermore, some dynamic behaviors of the systems are clarified by some numerical tests. The numerical simulations show that the gestation delay can act as a damping mechanism and prevent blow-up in certain critical range of gestation period. • Ecological implications of this phenomenon are discussed. Depending upon the choice of food, availability of resource and growth structure, food uptake process of higher trophic level species are significantly complicated and gives interesting dynamical impacts on community food chain. The effect of top predator interference on the dynamics of a tritrophic food chain model is the principal goal to study general framework for three species food chain models in which intermediate and top predators are specialist and generalist types respectively where the top predator grows by sexual reproduction. This concept is used to design five different models in this paper by five different combinations of functional responses of specialist intermediate predator (food uptake process follows either prey dependent, Holling type III/IV or prey-predator dependent, Beddington-DeAngelis (BD)-functional response) and sexually reproductive generalist top predator (food uptake follows strictly prey-predator dependent, BD/Crowley–Martin (CM) functional response) respectively assuming the fact that the growth of intermediate predator is mediated by gestation delay. We establish the stability of each equilibrium point of the non-delayed counterpart of each model and investigate the existence of Hopf-bifurcation for the coexistence equilibrium point of all delayed systems. We also show that both the delayed and non delayed models can blow-up in finite time under sufficient conditions on the initial data. Furthermore, some dynamic behaviors of the systems are clarified by some numerical tests. The numerical simulations show that the gestation delay can act as a damping mechanism and prevent blow-up in certain critical range of gestation period. Ecological implications of this phenomenon are discussed. [ABSTRACT FROM AUTHOR]
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- 2020
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23. Estimation of biophysical parameters in a neuron model under random fluctuations.
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Upadhyay, Ranjit Kumar, Paul, Chinmoy, Mondal, Argha, and Vishwakarma, Gajendra K.
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NOISE (Work environment) , *NEURONS , *RANDOM noise theory , *MEMBRANE potential , *ALGORITHMS - Abstract
In this paper, an attempt has been made to estimate the biophysical parameters in an improved version of Morris–Lecar (M–L) neuron model in a noisy environment. To observe the influence of noisy stimulation in estimation procedure, a Gaussian white noise has been added to the membrane voltage of the model system. Estimation of the parameters has been investigated by a proposed algorithm. The denoising technique (local projection method) has been applied to reduce the influence of noisy stimuli and the effectiveness of the method is reported. The proposed scheme performs well for an excitable neuron model and provides good estimates between the estimated parameters and the actual values in a reasonable way. This approach can be used for parameter estimation for other nonlinear dynamical systems. [ABSTRACT FROM AUTHOR]
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- 2018
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24. Conservation of degraded wetland system of Keoladeo National Park, Bharatpur, India.
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Tiwari, S.K. and Upadhyay, Ranjit Kumar
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WETLAND conservation ,WATER shortages ,BIODIVERSITY ,URBANIZATION - Abstract
The most common threats to wetlands and the Keoladeo National Park are water scarcity, changing biodiversity, increasing rate of contamination, uncontrolled growth of grass, urbanization and human intervention. In this paper, an attempt has been made to study the degradation and conservation of biotic part of the park through a reaction diffusion modeling. The biotic part of wetland is divided into three categories good biomass, bad biomass, and bird population. Good biomasses are those species that provide food for bird population and contain floating vegetation, fishses, waterfowl and useful species. Bad biomasses contain Paspalum distichum and its family that affect the growth of good biomass. The interaction between good biomass and bird population is considered to be Crowley–Martin type functional response. We have presented the theoretical analysis of stability and Turing instability. With the help of numerical simulations, we have observed spatial patterns for the wetland model system. This study demonstrates that spatial heterogeneity, diffusion coefficients and per capita availability of water to bad biomass play an important role on the dynamical behavior of the model system. Also, we have pointed out the parameters that are responsible for the bad health of wetland ecosystem and suggested enhancing the water supply, decontamination and optimizing the land use structure for sustaining ecological balance and socio-economic stability of a region. [ABSTRACT FROM AUTHOR]
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- 2017
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25. Fractional-order leaky integrate-and-fire model with long-term memory and power law dynamics.
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Teka, Wondimu W., Upadhyay, Ranjit Kumar, and Mondal, Argha
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PYRAMIDAL neurons , *POWER law (Mathematics) , *FRACTIONAL calculus , *COMPUTER storage devices , *ELECTRIC potential - Abstract
Pyramidal neurons produce different spiking patterns to process information, communicate with each other and transform information. These spiking patterns have complex and multiple time scale dynamics that have been described with the fractional-order leaky integrate-and-Fire (FLIF) model. Models with fractional (non-integer) order differentiation that generalize power law dynamics can be used to describe complex temporal voltage dynamics. The main characteristic of FLIF model is that it depends on all past values of the voltage that causes long-term memory. The model produces spikes with high interspike interval variability and displays several spiking properties such as upward spike-frequency adaptation and long spike latency in response to a constant stimulus. We show that the subthreshold voltage and the firing rate of the fractional-order model make transitions from exponential to power law dynamics when the fractional order α decreases from 1 to smaller values. The firing rate displays different types of spike timing adaptation caused by changes on initial values. We also show that the voltage-memory trace and fractional coefficient are the causes of these different types of spiking properties. The voltage-memory trace that represents the long-term memory has a feedback regulatory mechanism and affects spiking activity. The results suggest that fractional-order models might be appropriate for understanding multiple time scale neuronal dynamics. Overall, a neuron with fractional dynamics displays history dependent activities that might be very useful and powerful for effective information processing. [ABSTRACT FROM AUTHOR]
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- 2017
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26. Synchronization analysis through coupling mechanism in realistic neural models.
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Upadhyay, Ranjit Kumar, Mondal, Argha, and Aziz-Alaoui, M.A.
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SYNCHRONIZATION , *ARTIFICIAL neural networks , *MAGNETIC coupling , *ELECTRIC oscillators , *CLOSED loop systems - Abstract
Synchronization which relates to the system’s stability is important to many engineering and neural applications. In this paper, an attempt has been made to implement response synchronization using coupling mechanism for a class of nonlinear neural systems. We propose an OPCL (open-plus-closed-loop) coupling method to investigate the synchronization state of driver-response neural systems, and to understand how the behavior of these coupled systems depend on their inner dynamics. We have investigated a general method of coupling for generalized synchronization (GS) in 3D modified spiking and bursting Morris–Lecar (M-L) neural models. We have also presented the synchronized behavior of a network of four bursting Hindmarsh–Rose (H-R) neural oscillators using a bidirectional coupling mechanism. We can extend the coupling scheme to a network of N neural oscillators to reach the desired synchronous state. To make the investigations more promising, we consider another coupling method to a network of H-R oscillators using bidirectional ring type connections and present the effectiveness of the coupling scheme. [ABSTRACT FROM AUTHOR]
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- 2017
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27. Assessment of rabbit hemorrhagic disease in controlling the population of red fox: A measure to preserve endangered species in Australia.
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Roy, Parimita and Upadhyay, Ranjit Kumar
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RABBIT calicivirus disease ,RED fox ,WILDLIFE management ,PREDATION ,EPIDEMIOLOGY ,COMPUTER simulation - Abstract
Predator's management requires a detailed understanding of the ecological circumstances associated with predation. Predation by foxes has been a significant contributor to the Australian native animal reduction. This paper mainly focuses on the dissemination of rabbit hemorrhagic disease in the rabbit population and its subsequences on red fox ( Vulpes vulpes ) population, by qualitative and quantitative analyses of a designed eco-epidemiological model with simple law of mass action and sigmoid functional response. Existence of solution has been analyzed and shown to be uniformly bounded. The basic reproduction number ( R 0 ) is obtained and the occurrence of a backward bifurcation at R 0 = 1 is shown to be possible using central manifold theory. Global stability of endemic equilibrium is established by geometric approach. Criteria for diffusion-driven ecological instability caused by local random movements of European rabbits and red fox are obtained. Detailed analyses of Turing patterns formation selected by reaction-diffusion system under zero flux boundary conditions are presented. We found that transmission rate, self and cross-diffusion coefficients have appreciable influence on spatial spread of epidemics. Numerical simulation results confirm the analytical finding and generate patterns which indicate that population of red foxes might be controlled if rabbit hemorrhagic disease (RHD) is introduced into the rabbit population and thus ecological balance can be maintained. [ABSTRACT FROM AUTHOR]
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- 2016
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28. Synchronization of bursting neurons with a slowly varying d. c. current.
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Upadhyay, Ranjit Kumar and Mondal, Argha
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ACTION potentials , *DIRECT currents , *SYNAPSES , *INFORMATION processing , *LYAPUNOV exponents , *NEUROLOGICAL disorders - Abstract
Bursting of neuronal firing is an interesting dynamical consequences depending on fast/slow dynamics. Certain cells in different brain regions produce spike-burst activity. We study such firing activity and its transitions to synchronization using identical as well as non-identical coupled bursting Morris-Lecar (M-L) neurons. Synchronization of different firing activity is a multi-time-scale phenomenon and burst synchronization presents the precursor to spike synchronization. Chemical synapses are one of the dynamical means of information processing between neurons. Electrical synapses play a major role for synchronous activity in a certain network of neurons. Synaptically coupled neural cells exhibit different types of synchronization such as in phase or anti-phase depending on the nature and strength of coupling functions and the synchronization regimes are analyzed by similarity functions. The sequential transitions to synchronization regime are examined by the maximum transverse Lyapunov exponents. Synchronization of voltage traces of two types of planar bursting mechanisms is explored for both kind of synapses under realistic conditions. The noisy influence effects on the transmission of signals and strongly acts to the firing activity (such as periodic firing and bursting) and integration of signals for a network. It has been examined using the mean interspike interval analysis. The transition to synchronization states of coupled and a network of bursting neurons may be useful for further research in information processing and even the origins of certain neurological disorders. [ABSTRACT FROM AUTHOR]
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- 2017
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29. Wave of chaos in a spatial eco-epidemiological system: Generating realistic patterns of patchiness in rabbit–lynx dynamics.
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Upadhyay, Ranjit Kumar, Roy, Parimita, Venkataraman, C., and Madzvamuse, A.
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ANALYTICAL mechanics , *DYNAMICS , *FORCE & energy , *EPIDEMIOLOGY , *DIFFUSION - Abstract
In the present paper, we propose and analyze an eco-epidemiological model with diffusion to study the dynamics of rabbit populations which are consumed by lynx populations. Existence, boundedness, stability and bifurcation analyses of solutions for the proposed rabbit–lynx model are performed. Results show that in the presence of diffusion the model has the potential of exhibiting Turing instability. Numerical results (finite difference and finite element methods) reveal the existence of the wave of chaos and this appears to be a dominant mode of disease dispersal. We also show the mechanism of spatiotemporal pattern formation resulting from the Hopf bifurcation analysis, which can be a potential candidate for understanding the complex spatiotemporal dynamics of eco-epidemiological systems. Implications of the asymptotic transmission rate on disease eradication among rabbit population which in turn enhances the survival of Iberian lynx are discussed. [ABSTRACT FROM AUTHOR]
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- 2016
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30. Emergence of Turing patterns and dynamic visualization in excitable neuron model.
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Mondal, Arnab, Upadhyay, Ranjit Kumar, Mondal, Argha, and Sharma, Sanjeev Kumar
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VISUALIZATION , *NEURONS - Published
- 2022
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31. Conserving Iberian Lynx in Europe: Issues and challenges.
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Roy, Parimita and Upadhyay, Ranjit Kumar
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LYNX populations ,HEMORRHAGIC fever ,CLASSIFICATION of mammals ,MAMMAL reproduction ,QUALITATIVE research - Abstract
The world's most endangered feline species; the Iberian Lynx has suffered severe population decline and is now on the verge of extinction despite recovery plans. In this paper, an attempt has been made to understand the extinction dynamics of this endangered cat species. The paper focuses on the spread of rabbit haemorrhagic disease in the European rabbit population and its effect on the survival of the Iberian Lynx. A qualitative analysis of an eco-epidemiological model with simple law of mass action and Holling type II functional response is carried out. Existence and uniqueness of solutions are established and shown to be uniformly bounded. The basic reproduction number R 0 is obtained and the occurrence of a backward bifurcation at R 0 = 1 is shown to be possible using central manifold theory. The global stability of endemic equilibrium is established using a geometric approach. Criteria for diffusion-driven instability caused by local random movements of European rabbits and Iberian Lynx are obtained. Detailed analysis of Turing patterns formation selected by the reaction-diffusion system under zero flux boundary conditions is presented. We found that diffusion coefficients and transmission rate have appreciable influence on spatial spread of the epidemic. Numerical simulation results confirm the analytical finding and generate beautiful patterns that are consistent with the field observations and suggest that Iberian Lynx might have become extinct from Portugal and neighbouring countries. Suggestions for disease eradication and its control which in turn may increase the population of Iberian Lynx are discussed. [ABSTRACT FROM AUTHOR]
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- 2015
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32. Dynamics and patterns of species abundance in ocean: A mathematical modeling study.
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Kumari, Sarita, Upadhyay, Ranjit Kumar, Kumar, Pramod, and Rai, Vikas
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MATHEMATICAL models , *FICK'S laws of diffusion , *SPATIAL systems , *PLANT size , *OCEAN , *PLANT competition - Abstract
In the complex and competitive world of oceans, different size of plants and animals exist. All of them compete for the limited resources; e.g., nutrients, sunlight, minerals etc. Size-specific and intraspecific predation is common among zooplankton. We design a model food chain and explore dynamics, and patterns of species abundance in ocean. The proposed mathematical model is based on a parameter; exponent of closure, m. A value of m less than 1 represents both size-specific and intraspecific predation among zooplankton. The mathematical model has been extended to include random movements of all the constituent populations by adding Fickian diffusion. Eigenvalues and amplitude equations are used to figure out relevant parameter spaces for numerical exploration. An analysis of the spatial system in the neighborhood of a critical parameter is performed using amplitude equation. Choosing appropriate control parameter from the Turing space, existence conditions for stable patterns are derived. Equal density contours were plotted for all the constituents of the model food chain. Epidemiological significance of these spatial patterns is provided. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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33. Strategies for the existence of spatial patterns in predator–prey communities generated by cross-diffusion.
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Mishra, Swati and Upadhyay, Ranjit Kumar
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MULTIPLE scale method , *PREDATION , *BIFURCATION diagrams , *DIFFUSION control , *LINEAR statistical models , *SIMULATION methods & models , *STABLE isotopes - Abstract
Fear of predators is an important drive for predator–prey interactions, which increases survival probability but cost the overall population size of the prey. In this paper, we have extended our previous work spatiotemporal dynamics of predator–prey interactions with fear effect by introducing the cross-diffusion. The conditions for cross-diffusion-driven instability are obtained using the linear stability analysis. The standard multiple scale analysis is used to derive the amplitude equations for the excited modes near Turing bifurcation threshold by taking the cross-diffusion coefficient as a bifurcation parameter. From the stability analysis of amplitude equations, the conditions for the emergence of various ecologically realistic Turing patterns such as spot, stripe, and mixture of spots and stripes are identified. Analytical results are verified with the help of numerical simulations. Turing bifurcation diagrams are plotted taking diffusion coefficients as control parameters. The effect of the cross-diffusion coefficients on the homogeneous steady state and pattern structures of the self-diffusive model is illustrated using the simulation techniques. It is also observed that the level of fear has stabilizing effect on the cross-diffusion induced instability and spot patterns change to stripe, then a mixture of spots and stripes and finally to the labyrinthine type of patterns with an increase in the level of fear. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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34. Spatial distribution of microalgae in marine systems: A reaction–diffusion model.
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Upadhyay, Ranjit Kumar, Kumari, Sarita, Kumar, Pramod, and Rai, Vikas
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MARINE zooplankton ,ZOOPLANKTON ,PARTIAL differential equations ,SPATIAL behavior ,SPATIAL systems ,COLOR codes ,CLEAN energy - Abstract
• A reaction–diffusion model is presented to guide exploration and harvesting microalgae for bio-diesel production. • Biotic components are assumed to be diffusing in turbulent conditions of marine systems. • Knowledge of temporal variations of this biotic constituent of the model system is equally important for fixing time of harvesting efforts. • Simulation experiments and computed densities suggest that the spatial distribution of microalgae is complex. • Harvesting of microalgae in marine systems for bio-diesel production is a challenging problem. In this paper, we have proposed a reaction–diffusion system of partial differential equations which model the plankton-nutrient interaction mediated by a toxin-determined functional response. It has been established that microalgae, a clean and green source of energy, can be potentially used for carbon capture and sequestration. The common biofuels (bio-diesel and ethanol) are efficiently extracted from microalgae of different shapes and sizes. A spatio-temporal model has been presented to guide exploration and harvesting of microalgae (e.g., dinoflagellates, cilliates, chlorella, etc.). The spatial distribution of the phytoplankton (microalgae) is determined by growth pattern of the biotic subsystem (phytoplankton and zooplankton); e.g., whether it is oscillatory or aperiodic. The model incorporates a toxin-determined functional response of the zooplankton, which can be parametrized for specific phytoplankton–zooplankton combinations in different aquatic bodies such as ponds, seas, and oceans. The present model does not take into account higher zooplankton's role in maintaining the core subsystem. The temporal model is analytically investigated in terms of the existence criteria and stability analysis (both linear and nonlinear) of the possible equilibria and the spatio-temporal model is studied in terms of global stability, Turing instability and existence of Hopf-bifurcation which help us to explore the dynamical behavior of the spatial model system. Numerical simulations are carried out to support the obtained theoretical results. Simulation experiments and computed densities thereof (equal densities are codes by same color) suggest that the spatial distribution of microalgae is complex; e.g., spatial density of microalgae varies chaotically for certain parameter sets. Harvesting schedule can be designed based on information thus derived. It should be implemented carefully in case the spatial density distribution is chaotic. The sustainability of the marine system for future use has been the prime concern. Parameters of harvesting strategy (time, intensity and technology) are determined in such a way that exploitation causes minimal damage to the environment and the yield of the harvest is maximal. Future studies would consider larger carnivorous fishes (e.g., Squids, Dolphins) on system's dynamics. The effect of oceanic noise and colloidal swarming of zooplankton in the presence of bacteria will also be incorporated. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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35. Predator–prey interaction system with mutually interfering predator: role of feedback control.
- Author
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Tiwari, Vandana, Tripathi, Jai Prakash, Upadhyay, Ranjit Kumar, Wu, Yong-Ping, Wang, Jin-Shan, and Sun, Gui-Quan
- Subjects
- *
PREDATION , *PARTIAL differential equations , *ORDINARY differential equations , *ECOLOGICAL disturbances , *LYAPUNOV functions , *AGRICULTURAL ecology , *COEXISTENCE of species - Abstract
• We construct a Leslie-Gower type prey-predator system with feedback. • We systematically analyze the effects of feedback controls on the dynamics of ecosystems. • Pattern transition emerges as feedback intensity varies. In this study, we investigate the global dynamics of non-autonomous and autonomous systems based on the Leslie–Gower type model using the Beddington–DeAngelis functional response (BDFR) with time-independent and time-dependent model parameters. Unpredictable disturbances are introduced in the forms of feedback control variables. BDFR explains the feeding rate of the predator as functions of both the predator and prey densities. The global stability of the unique positive equilibrium solution of the autonomous model is determined by defining an appropriate Lyapunov function. The condition obtained for the global stability of the interior equilibrium ensures that the global stability is free from control variables, which is also a significant issue in the ecological balance control procedure. The autonomous system exhibits complex dynamics via bifurcation scenarios, such as period doubling bifurcation. We prove the existence of a globally stable almost periodic solution of the associated non-autonomous model. The different coefficients of the system are taken as almost periodic functions by generalizing periodic assumptions. The permanence of the non-autonomous system is established by defining upper and lower averages of a function. Our results also explain how the important hypothesis in ecology known as the "intermediate disturbance hypothesis" applies in predator–prey interactions. We show that moderate feedback intensity can make both the ordinary differential equation system and partial differential equation system more robust. The results obtained provide new insights into the protection of populations, where moderate feedback intensity can promote the coexistence of species and adjusting the intensity of the feedback in appropriate regions can control the population biomass while maintaining the stability of the system. Finally, the results obtained from extensive numerical simulations support the analytical results as well as the usefulness of the present study in terms of ecological balance and bio-control problems in agro-ecosystems. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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36. Bifurcation and bio-economic analysis of a prey-generalist predator model with Holling type IV functional response and nonlinear age-selective prey harvesting.
- Author
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Datta, Jyotiska, Jana, Debaldev, and Upadhyay, Ranjit Kumar
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- *
HARVESTING , *NONLINEAR functional analysis , *PONTRYAGIN'S minimum principle , *BIFURCATION theory , *HOPF bifurcations - Abstract
• Dynamical behaviour of a Leslie–Gower model with Holling type-IV functional response and nonlinear age-selective prey harvesting has been studied. • Qualitative analysis, bifurcation theory, bionomic equilibrium, MSY and optimal harvesting policy has been analyzed. • The age-selective harvesting system under goes a Hopf bifurcation with respect to the maturation delay. • Conditions for the MSY and existence of bionomic equilibrium are analyzed and Pontryagin's maximum principle has been used to find the path of a singular control and Pontryagin's maximum principle has been used to find the path of a singular control. In this paper, we have studied the dynamical behaviour of a Leslie-Gower model with Holling type-IV functional response and nonlinear prey harvesting where target prey for harvesting are above a particular age which is called maturation delay. The model system has been studied using qualitative analysis, bifurcation theory, bionomic equilibrium, MSY and optimal harvesting policy. We explain that the interior equilibrium is delay dependent and locally asymptotically stable. The age-selective harvesting system under goes a Hopf-bifurcation with respect to the maturation delay. Conditions for the MSY and existence of bionomic equilibrium are analyzed and Pontryagin's maximum principle has been used to find the path of a singular control. Difficult analytical results are featured by numerical examples to better understand the system in a simple way. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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- View/download PDF
37. Dynamics of generalist predator in a stochastic environment: Effect of delayed growth and prey refuge.
- Author
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Jana, Debaldev, Agrawal, Rashmi, and Upadhyay, Ranjit Kumar
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- *
DYNAMICS , *PREDATION , *STOCHASTIC analysis , *REFUGE (Predation) , *PREGNANCY in animals - Abstract
In this paper, an attempt has been made to understand the dynamics of a prey–predator system with multiple time delays where the predator population is regarded as a generalist type. In this regard, we consider a modified Holling–Tanner prey–predator system where a constant time delay is incorporated in the logistic growth of the prey to represent a delayed density dependent feedback mechanism and the second time delay is considered to account for the length of the gestation period of the predator. Predator’s interference in prey–predator relationship provides better descriptions of predator’s feeding over a range of prey–predator abundances, so the predator’s functional response is considered to be Type II ratio-dependent and foraging efficiency of predator largely varies with the refuge strategy of prey population. In accordance with previous studies, it is observed that delay destabilizes the system, in general and stability loss occurs via Hopf-bifurcation. In particular, we show that there exists critical values of the delay parameters below which the coexistence equilibrium is stable and above which it is unstable. Hopf bifurcation occurs when the delay parameters cross their critical values. Also, environmental stochasticity in the form of Gaussian white-noise plays a significant role to describe the system and its values. Numerical computation is also performed to validate and visualize different theoretical results presented. The analysis and results in this work are interesting both in mathematical and biological point of views. [ABSTRACT FROM AUTHOR]
- Published
- 2015
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38. Ecological dynamics of age selective harvesting of fish population: Maximum sustainable yield and its control strategy.
- Author
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Jana, Debaldev, Agrawal, Rashmi, Upadhyay, Ranjit Kumar, and Samanta, G.P.
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- *
ECOSYSTEM dynamics , *FISH populations , *MAXIMUM sustainable yield (Population ecology) , *EMPIRICAL research , *ECOLOGICAL impact , *ECOSYSTEMS - Abstract
Life history of ecological resource management and empirical studies are increasingly documenting the impact of selective harvesting process on the evolutionary stable strategy of both aquatic and terrestrial ecosystems. In the present study, the interaction between population and their independent and combined selective harvesting are framed by a multi-delayed prey-predator system. Depending upon the age selection strategy, system experiences stable coexistence to oscillatory mode and vice versa via Hopf-bifurcation. Economic evolution of the system which is mainly featured by maximum sustainable yield (MSY), bionomic equilibrium and optimal harvesting vary largely with the commensurate age selections of both population because equilibrium population abundance becomes age-selection dependent. Our study indicates that balance between harvesting delays and harvesting intensities should be maintained for better ecosystem management. Numerical examples support the analytical findings. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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39. Top-predator interference and gestation delay as determinants of the dynamics of a realistic model food chain.
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Jana, Debaldev, Agrawal, Rashmi, and Upadhyay, Ranjit Kumar
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- *
FOOD chains , *PREDATORY animals , *GESTATIONAL age , *VOLTERRA equations , *BIFURCATION theory , *COMPUTER simulation , *PARAMETER estimation - Abstract
An attempt has been made to understand the role of top predator interference and gestation delay on the dynamics of a three species food chain model involving intermediate and top predator populations. Interaction between the prey and an intermediate predator follows the Volterra scheme (with Holling type IV functional response), while that between the top predator and its prey depends on Beddington–DeAngelis type functional response. Stability switches and Hopf-bifurcation occurs when the delay crosses some critical value. Model system exhibits irregular behavior when the interference is high or gestation period is larger than its critical value. Furthermore, the direction of Hopf-bifurcation and the stability of the bifurcating periodic solutions are determined using the center manifold theorem and normal form theory. Computer simulations have been carried out to illustrate the analytical findings. Different diagnostic tests, like, initial sensitivity, Lyapunov exponent, recurrence plot tests ensure the complex dynamical behavior of the model system. Finally, we observed the subcritical Hopf-bifurcation phenomena in the designed model system and the bifurcating periodic solution is unstable for the considered set of parameter values. [ABSTRACT FROM AUTHOR]
- Published
- 2014
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40. Diffusion driven finite time blow-up and pattern formation in a mutualistic preys-sexually reproductive predator system: A comparative study.
- Author
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Batabyal, Saikat, Jana, Debaldev, and Upadhyay, Ranjit Kumar
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- *
GENITALIA , *FINITE, The , *NONLINEAR analysis , *PREDATION , *STRUCTURAL models , *PREY availability - Abstract
• To establish a control strategy that decreases the harmful population to healthy levels. • Five different diffusive models have been introduced associated to their functional responses. • Blow up phenomenon at finite time in spatial cases have been discussed for all model systems. • Theoretical analysis of the patterns formations has been described by using amplitude equations. Species have the general tendency to sustain their own survival chance in the ecology. In this paper, we design different diffusive model systems in which two prey populations make mutualistic relationship in which they are getting benefited from each other with their usual growth rate and sexually reproductive generalist predator preys upon the prey according to their functional responses. In the absence of generalist predator, there is no sign of mutualism between two prey. Sometimes environment may turn favourable for the invasive species, causing the growth of their population to outbreak. Biological control is an adopted strategy to limit harmful populations. To establish a control strategy that decreases the harmful population to healthy levels as opposed to high and risky levels, five different diffusive models have been introduced associated to their functional responses which are either prey dependent (Holling type-III and IV) or predator dependent (Beddington–DeAngelis, Crowley–Martin and and Hassel–Varley). The blow up phenomenon at finite time in spatial cases have been discussed for all the model systems. For each model system, mathematical conditions are established under which species can blow up at finite time. Spatio-temporal dynamics and weakly nonlinear analysis have been thoroughly studied. Stability analysis of these model systems have been investigated and concentrated on discussing the Turing patterns. Theoretical analysis of the patterns formations has been described by using amplitude equations and the results are validated by numerical simulations. Mathematical computations of the structural models have been studied and explored their blow up phenomena under the effects of diffusion with the pattern formation of preys and predator populations in the spatiotemporal domain.The best chance of survival of the species upon diffusion has been discussed elaborately. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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- View/download PDF
41. Optimal treatment strategies for delayed cancer-immune system with multiple therapeutic approach.
- Author
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Das, Parthasakha, Das, Samhita, Upadhyay, Ranjit Kumar, and Das, Pritha
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- *
PONTRYAGIN'S minimum principle , *ALTERNATIVE medicine , *OPTIMAL control theory , *COST analysis - Abstract
In this article, we propose and analyze an optimal control problem of a delayed tumor-immune model in presence of a multi immuno-chemotherapeutic drug. Local dynamics of drug-free steady states are studied and Hopf-bifurcation is observed with delay bifurcation parameter. By formulating a quadratic control based functional, an optimal control problem is constructed with treatments as control variables. The formulation of the functional is aimed at minimizing the proliferation rate of tumor cells and the detrimental effects of injected drugs. Additionally, maximizing the effector cells and maintaining an attributed level of normal cells are also a priority. By applying Pontryagin's maximum principle, the sufficient and necessary conditions of optimality system are established. The sensitivity analysis of cost functional is performed with different combinations of control variables. The cost-effectiveness analysis is carried out to determine the most cost-effective strategy. The numerical results verify analytical findings and demonstrate that a multi-therapeutic treatment protocol can alleviate tumor burden within a few months of drug administration. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
42. Long time dynamics of a three-species food chain model with Allee effect in the top predator.
- Author
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Parshad, Rana D., Quansah, Emmanuel, Black, Kelly, Upadhyay, Ranjit Kumar, Tiwari, S.K., and Kumari, Nitu
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- *
DYNAMICS , *FOOD chains , *ALLEE effect , *TOP predators , *POPULATION biology - Abstract
The Allee effect is an important phenomenon in population biology characterized by positive density dependence, that is a positive correlation between population density and individual fitness. However, the effect is not well studied in multi-level trophic food chains. We consider a ratio dependent spatially explicit three species food chain model, where the top predator is subjected to a strong Allee effect. We show the existence of a global attractor for the model, that is upper semicontinuous in the Allee threshold parameter m . Next, we numerically investigate the decay rate to a target attractor, that is when m = 0 , in terms of m . We find decay estimates that are O ( m γ ) , where γ is found explicitly. Furthermore, we prove various overexploitation theorems for the food chain model, showing that overexploitation has to be driven by the middle predator. In particular overexploitation is not possible without an Allee effect in place. We also uncover a rich class of Turing patterns in the model which depend significantly on the Allee threshold parameter m . Our results have potential applications to trophic cascade control, conservation efforts in food chains, as well as Allee mediated biological control. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
43. Emergence of Canard induced mixed mode oscillations in a slow–fast dynamics of a biophysical excitable model.
- Author
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Sharma, Sanjeev Kumar, Mondal, Arnab, Mondal, Argha, Aziz-Alaoui, M.A., Upadhyay, Ranjit Kumar, and Ma, Jun
- Subjects
- *
OSCILLATIONS , *LYAPUNOV functions , *STELLAR oscillations - Abstract
We study the dynamics of a biophysically motivated slow–fast FitzHugh–Rinzel (FHR) model neurons in understanding the complex dynamical behavior of neural computation. We discuss the mathematical frameworks of diverse excitabilities and repetitive firing responses due to the applied stimulus using the slow–fast system. The results focus on the multiple time scale dynamics that include canard phenomenon induced mixed mode oscillations (MMOs) and mixed mode bursting oscillations (MMBOs). The bifurcation structure of the system is examined with injected current stimulus as the relevant parameter. We use the folded node theory to study the canards near the fold points. Further, we demonstrate the homoclinic bifurcation and the transition route to chaos through MMOs. It helps us in understanding the fundamentals of such complex rich neuronal responses. To show the chaotic nature in certain parameter regime, we compute the Lyapunov spectrum as a function of time and predominant parameter, I , that establishes our findings. Finally, we conclude that our observed results may have major significance and discuss the potential applications of MMOs in neural dynamics. • The dynamics of slow-fast FHR neurons are explored for various parameter sets. • The results focus on canard phenomenon induced MMOs and MMBOs. • Bifurcation structure is examined with external current as a bifurcation parameter. • We use the folded node theory to study the canards near the fold points. • The homoclinic bifurcation and transition route to chaos through MMOs are explored. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
44. Modeling the fear effect and stability of non-equilibrium patterns in mutually interfering predator–prey systems.
- Author
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Tiwari, Vandana, Tripathi, Jai Prakash, Mishra, Swati, and Upadhyay, Ranjit Kumar
- Subjects
- *
PREDATION , *SPATIAL systems , *PHYSIOLOGICAL stress , *FEAR , *SYSTEM dynamics - Abstract
Recent demographic experiments have demonstrated that both birth and survival in free-living animals are essentially affected due to having sufficient exposure to predators and further leaving physiological stress effects. In this paper, we have proposed and analyzed a predator–prey interaction model with Beddington–DeAngelis functional response (BDFR) and incorporating the cost of fear into prey reproduction. Stability analysis and the existence of transcritical bifurcation are studied. For the spatial system, the Hopf-bifurcation around the interior equilibrium, stability of homogeneous steady state, direction and stability of spatially homogeneous periodic orbits have been established. Using Normal form of the steady state bifurcation, the possibility of pitchfork bifurcation has been established. The impact of the level of fear and mutual interference on the stability and Turing patterns of the spatiotemporal system have been discussed in detail. Simulation results ensure that the fear of predator stabilizes the system dynamics and cost the overall population size of the species. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
45. An investigation of delay induced stability transition in nutrient-plankton systems.
- Author
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Thakur, Nilesh Kumar, Ojha, Archana, Tiwari, Pankaj Kumar, and Upadhyay, Ranjit Kumar
- Subjects
- *
LYAPUNOV exponents , *LIMIT cycles , *STABILITY criterion , *BIFURCATION diagrams , *TIME series analysis , *PLANKTON , *MARINE zooplankton , *TOXINS - Abstract
In this paper, a nutrient-plankton interaction model is proposed to explore the characteristic of plankton system in the presence of toxic phytoplankton and discrete time delay. Anti-predator efforts of phytoplankton by toxin liberation act as a prominent role on plankton dynamics. Toxicity controls the system dynamics and reduces the grazing rate of zooplankton. The toxic substance released by phytoplankton is not an instantaneous process, it requires some time for maturity. So, a discrete time delay is incorporated in the toxin liberation by the phytoplankton. The choice of functional response is important to understand the toxin liberation and it depends on the nonlinearity of the system, which follows the Monod-Haldane type functional response. Theoretically, we have studied the boundedness condition along with all the feasible equilibria analysis and stability criteria of delay free system. We have explored the local stability conditions of delayed system. The existence criterion for stability and direction of Hopf-bifurcation are also derived by using the theory of normal form and center manifold arguments. The essential features of time delay are studied by time series, phase portrait and bifurcation diagram. We perform a global sensitivity analysis to identify the important parameters of the model having a significant impact on zooplankton. Our numerical investigation reveals that the toxin liberation delay switches the stability of the system from stable to limit cycle and after a certain interval chaotic dynamics is observed. High rate of toxic substances production shows extinction of zooplankton. Further, the negative and positive impacts of other control parameters are studied. Moreover, to support the occurrence of chaos, the Poincaré map is drawn and the maximum Lyapunov exponents are also computed. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
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