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Predator–prey interactions do not solely depend on biotic factors: rather, they depend on many other abiotic factors also. One such abiotic factor is wind speed, which can crucially change the predation efficiency of the predator population. In this article, the impact of wind speed along with seasonality on various parameters has been investigated. Here, we present two continuous-time models with specialist and generalist type predators incorporating the effect of wind and the seasonality on the model parameters. It has been observed that wind speed plays a significant role in controlling the system dynamics for both systems. It makes the systems stable for both of the seasonally unperturbed systems. However, it controls the chaotic dynamics that occur in case of no wind for the seasonally perturbed system with the predator as a specialist. On the other hand, for the seasonally perturbed system with a generalist predator, it controls period-four oscillations (which occur considering no wind speed) to simple limit-cycle oscillations. Furthermore, the wind parameter has a huge impact on the survival of predator species. The survival of predator species may be achieved by ensuring a suitable range of wind speeds in the ecosystem. Therefore, we observe that seasonality introduces chaos, but wind reduces it. These results may be very useful for adopting necessary management for the conservation of endangered species that are massively affected by wind speed in an ecosystem. [ABSTRACT FROM AUTHOR]

The anti-predator element because of fear from predator population in prey–predator models has an excellent significance and it is able to lessen the duplicate of prey population to a positive degree. In this paper, a delayed prey–predator model including fear effect and predator-taxis sensitivity is studied. Local stability and occurrence of Hopf bifurcation are analyzed by fixing the time delay as the bifurcating parameter. Then, a series of sufficient criteria for global stability is established by designing a suitable Lyapunov function. Furthermore, direction and stability of the Hopf bifurcation are studied. Lastly, numerical simulation outcomes are performed to confirm our theoretical findings. [ABSTRACT FROM AUTHOR]

In this study, we present a delayed predator–prey model with cannibalism including a prey, a juvenile predator and an adult predator. The adult predator hunts not only the prey but also the juvenile predator. The alternative resource is considered to reduce cannibalism in predator species. The main results are demonstrated by local stability and Hopf bifurcation. Sufficient criteria for local stability of the interior equilibrium point and the exhibition of a Hopf bifurcation are derived. Global stability is analyzed via designing a suitable Lyapunov function. Additionally, stability of the Hopf bifurcation is explored. Finally, numerical simulations are executed to validate the obtained results. [ABSTRACT FROM AUTHOR]

Smoking poses an enormous threat to public health in the globe and continues to be one of the main cause of health problems. In this paper, a delayed smoking model with reversion class is proposed. Local stability of the smoking equilibrium and Hopf bifurcation is analyzed by taking the time delay as the bifurcation parameter. In particular, global exponential stability is proved by using the linear matrix inequality method. The theoretical results obtained are validated numerically and graphically. [ABSTRACT FROM AUTHOR]

• 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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In this paper, an e-epidemic Susceptible–Infected–Vaccinated ( S I V ) model has been proposed to analyze the effect of node immunization and worms attacking dynamics in wireless sensor network. A modified nonlinear incidence rate with cyrtoid type functional response has been considered using sleep and active mode approach. Detailed stability analysis and the sufficient criteria for the persistence of the model system have been established. We also established different types of bifurcation analysis for different equilibria at different critical points of the control parameters. We performed a detailed Hopf bifurcation analysis and determine the direction and stability of the bifurcating periodic solutions using center manifold theorem. Numerical simulations are carried out to confirm the theoretical results. The impact of the control parameters on the dynamics of the model system has been investigated and malicious chaotic signals are detected. Finally, we have analyzed the effect of time delay on the dynamics of the model system. [ABSTRACT FROM AUTHOR]

In earlier literature, a version of a classical three-species food chain model, with modified Holling type IV functional response, is proposed. Results on the global boundedness of solutions to the model system under certain parametric restrictions are derived, and chaotic dynamics is shown. We prove that in fact the model possesses explosive instability, and solutions can explode/blow up in finite time, for certain initial conditions, even under the parametric restrictions of the literature. Furthermore, we derive the Hopf bifurcation criterion, route to chaos, and Turing bifurcation in case of the spatially explicit model. Lastly, we propose, analyze, and simulate a version of the model, incorporating gestation effect, via an appropriate time delay. The delayed model is shown to possess globally bounded solutions, for any initial condition. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In present paper, a delayed SEIR model of malware propagation on mobile wireless sensor networks is formulated. Basic reproduction number of the model is calculated by employing the next generation matrix method and impact of the time delay due to incubation period of malware is discussed with the help of eigenvalue method. What is more, properties of the Hopf bifurcation are derived by using center manifold method. To minimize number of the infectious nodes and the cost related with detoxication, an optimal control strategy is presented by constructing a suitable Hamiltonian function. Numerical calculations are performed to justify the obtained theoretical findings. • A delayed SEIR model of malware propagation on mobile wireless sensor networks is formulated. • Existence and properties of Hopf bifurcation of the model are analyzed. • Optimal control of the model is solved. [ABSTRACT FROM AUTHOR]

In this paper, we have proposed and analyzed a simple model of Influenza spread with an asymptotic transmission rate. Existence and uniqueness of solutions are established and shown to be uniformly bounded for all non-negative initial values. We have also found a sufficient condition which ensures the persistence of the model system. This implies that both susceptible and infected will always coexist at any location of the inhabited domain. This coexistence is independent of values of the diffusivity constants for two subpopulations. The global stability of the endemic equilibrium is established by constructing a Lyapunov function. By linearizing the system at the positive constant steady-state solution and analyzing the associated characteristic equation, conditions for Hopf and Turing bifurcations are obtained. We have also studied the criteria for diffusion-driven instability caused by local random movements of both susceptible and infective subpopulations. Turing patterns selected by the reaction-diffusion system under zero flux boundary conditions have been explored. Numerical simulations show that contact rate, β which is related to the reproduction number , plays an important role in spatial pattern formation. It was found that diffusion has appreciable influence on spatial spread of epidemics. The wave of chaos appears to be a dominant mode of disease dispersal. This suggests a bidirectional spread for influenza epidemics. The epidemic propagates in the form of nonchaotic and chaotic waves as observed in H1N1 incidence data of positive tests in 2009 in the United States. We have conducted numerical simulations to confirm the analytic work and observed interesting behaviors. This suggests that influenza has a complex dynamics of spatial spread which evolves with time. [ABSTRACT FROM AUTHOR]

The main objective of the present paper is to consider the dynamical analysis of a three dimensional prey-predator model within deterministic environment and the influence of environmental driving forces on the dynamics of the model system. For the deterministic model we have obtained the local asymptotic stability criteria of various equilibrium points and derived the condition for the existence of small amplitude periodic solution bifurcating from interior equilibrium point through Hopf bifurcation. We have obtained the parametric domain within which the model system exhibit chaotic oscillation and determined the route to chaos. Finally, we have shown that chaotic oscillation disappears in presence of environmental driving forces which actually affect the deterministic growth rates. These driving forces are unable to drive the system from a regime of deterministic chaos towards a stochastically stable situation. The stochastic stability results are discussed in terms of the stability of first and second order moments. Exhaustive numerical simulations are carried out to validate the analytical findings. [ABSTRACT FROM AUTHOR]

Abstract: A model food chain involving a specialist and a generalist predator is proposed and studied. One of the salient features of this model food chain is that it combines both the schemes (Volterra and Leslie) of modeling predator–prey interaction in one system in such a way that the demerits of these individual formulations are suppressed and the resulting model system represents a common unit of real world food webs. The stability analysis of the proposed model is carried out. The Hopf bifurcation conditions of the positive equilibrium point are established. Our numerical computations show that chaotic dynamics is sensitive to changes in values of parameters measuring attributes of either interacting populations or their environments. Two dimensional parameter scans suggest that the model food chain displays short-term recurrent chaos. This can be regarded as a plausible explanation for why it has been so difficult to detect deterministic chaos in natural populations. [Copyright &y& Elsevier]

Most of the infectious diseases associated with human population are still a threat to become epidemic in the globe. Mathematical models have been an important tool to study the complex behavior of infectious diseases. In this paper a deterministic SVIRS epidemic model with Holling type II incidence rate and treatment rate including three delays is investigated. Local stability of disease equilibrium and existence of Hopf bifurcation are discussed explicitly. Then, direction and stability of the bifurcated periodic solutions are determined. Finally, with the suitable choices of the parameters, numerical simulations are presented in order to verify effectiveness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

Tobacco epidemic which is the primary risk factor for noncommunicable diseases such as cardiovascular, cancers, diabetes and hear diseases, has been one of the most serious public health problems in the globe. It is of vital significance to control tobacco epidemic and reduce smoking rate in order to protect our health and life. For this purpose, a delayed giving up smoking model considering relapse is proposed in this research work. Local stability and existence of Hopf bifurcation are performed through taking different combinations of the two delays as bifurcation parameters. Specially, global exponential stability is proved with aid of LMI techniques. Finally, the theoretical results are verified numerically and graphically. [ABSTRACT FROM AUTHOR]

A delayed SEIRS worm propagation model with the inclusion of a finite communication radius and node density for wireless sensor networks is investigated in this paper. By using different combinations of the three delays as bifurcating parameter and analyzing distribution of roots of the corresponding characteristic equation, sufficient conditions are derived for local stability of the endemic equilibrium and the existence of a Hopf bifurcation at the endemic equilibrium are addressed. By constructing a suitable Lyapunov function, sufficient conditions for global stability of the endemic equilibrium are determined. Finally, numerical simulations for a set of parameter values are performed to illustrate the analytical findings. [ABSTRACT FROM AUTHOR]

We propose an e-epidemic time-delay Susceptible-Latent-Breaking out-Susceptible (S L B S ) model to study delay dynamics appearing due to antivirus software, which takes time to clean the viruses from latent and breaking-out computers. We perform nonlinear stability analysis, Hopf bifurcation analysis, and its direction and stability. Numerical simulation results (time series analysis and bifurcation diagram) give useful insights for delay dynamics. We investigate the effect of the control parameters like rate of infection of all the classes and cure rates on the model system. Our results suggest that time delay is responsible for destabilizing the system dynamics. For smooth functionality of a computer system, our results suggest the minimum use of removable storage devices like smart phones, optical discs, memory cards, external hard disk, digital cameras, and so on and use of effective antivirus softwares. [ABSTRACT FROM AUTHOR]

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]