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Recent field experiments have shown that predators influence the prey population not only by direct consumption but also by stimulating various defensive strategies. The cost of these defensive strategies can include energetic investment in defensive structures, reduced energy income, lower mating success, and emigration which ultimately reduces the reproduction of prey. To explore the effect of these defensive strategies (anti‐predator behaviors), a modified Leslie–Gower predator–prey model with the cost of fear has been considered. Gestation delay is also incorporated in the system for a more realistic formulation. Boundedness, equilibria and stability analysis are performed for the temporal system. By considering gestation delay as a bifurcation parameter, the existence of Hopf‐bifurcation around the interior equilibrium point is discussed together with the direction, stability, and period of bifurcating solutions arising through Hopf‐bifurcation. The spatial extension of the proposed model incorporating density‐dependent cross‐diffusion is also investigated and the conditions for diffusion‐driven instability are obtained. To illustrate the analytical findings, detailed numerical simulations are performed. Biologically realistic Turing patterns such as spots, spots and stripes mixture, and labyrinthine type patterns are identified. It is found that the fear level has a stabilizing impact on delay induced destabilization and both stabilizing and destabilizing effects on Turing instability. [ABSTRACT FROM AUTHOR]

In this paper, we have formulated an e-epidemic energy efficient susceptible-infected--terminally infected-recovered (SITR) model to analyse the attacking behaviour of worms in wireless sensor network (WSN) using cyrtoid type functional response. In this model, once a sensor node has been attacked by the worms, the terminally infected node spreads the worms to its neighbouring nodes using normal communications, which further spread it to their neighbouring nodes and the process continues. To tackle this issue, we proposed an SITR model by considering the sleep mode concept of WSN in which the operational capabilities and power consumption of the motes decreases. Boundedness, existence of equilibrium points, stability and bifurcation analysis are analysed for the proposed model system. Stability and direction of Hopf-bifurcation are also obtained for endemic equilibrium point using center manifold theorem. Finally, numerical simulations are carried out that supports the analytical findings. The impact of the control parameters like transmission rate (β), inter-nodes interference coefficient (θ1) and intrinsic growth rate (r1) on the dynamics of the model system are investigated. [ABSTRACT FROM AUTHOR]

We have proposed a three-species hybrid food chain model with multiple time delays. The interaction between the prey and the middle predator follows Holling type (HT) II functional response, while the interaction between the top predator and its only food, the middle predator, is taken as a general functional response with the mutual interference schemes, such as Crowley–Martin (CM), Beddington–DeAngelis (BD) and Hassell–Varley (HV) functional responses. We analyse the model system which employs HT II and CM functional responses, and discuss the local and global stability analyses of the coexisting equilibrium solution. The effect of gestation delay on both the middle and top predator has been studied. The dynamics of model systems are affected by both factors: gestation delay and the form of functional responses considered. The theoretical results are supported by appropriate numerical simulations, and bifurcation diagrams are obtained for biologically feasible parameter values. It is interesting from the application point of view to show how an individual delay changes the dynamics of the model system depending on the form of functional response. [ABSTRACT FROM AUTHOR]

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]

In this paper, an eco-epidemiological model in which both species diffuse along a spatial gradient has been shown to exhibit temporal chaos at a fixed point in space. The proposed model is a modification of the model recently presented by Upadhyay and Roy [2014]. The spatial interactions among the species have been represented in the form of reaction-diffusion equations. The model incorporates the intrinsic growth rate of fish population which varies linearly with the depth of water. Numerical results show that diffusion can drive otherwise stable system into aperiodic behavior with sensitivity to initial conditions. We show that spatially induced chaos plays an important role in spatial pattern formation in heterogeneous environment. Spatiotemporal distributions of species have been simulated using the diffusivity assumptions realistic for natural eco-epidemic systems. We found that in heterogeneous environment, the temporal dynamics of both the species are drastically different and show chaotic behavior. It was also found that the instability observed in the model is due to spatial heterogeneity and diffusion-driven. Cumulative death rate of predator has an appreciable effect on model dynamics as the spatial distribution of all constituent populations exhibit significant changes when this model parameter is changed and it acts as a regularizing factor. [ABSTRACT FROM AUTHOR]

• 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]

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]