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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]