Dynamics of a predator-prey system with fear and group defense

Cross-Diffusion-Driven Instability in a Predator-Prey System with Fear and Group Defense

“…Stability conditions for all the equilibria of the ODEs model (1) and investigations on the possible occurrence of a Hopf bifurcation at the interior equilibrium E * can be found in [18]. Based on their findings, we report that, in the case of two solutions of (7), the bigger one always results in an unstable equilibrium; for the smaller one conditions are found to characterize the stability region.…”

“…To incorporate these effects into predator-prey interactions, many predator-prey models have been proposed (e.g., [12][13][14][15][16][17], just to mention a few). Recently, in [18], the authors have considered a model describing the predator-prey interaction, introducing the group defense of prey through the Holling type IV functional response and the reduction of prey growth rate, represented as a fear factor, in the presence of group defense through Monod-Haldane type functional response. In this formulation there is an interesting link between the cost due to fear and the benefit due to group defense through the parameter α describing the predator-taxis sensitivity.…”

“…where x, y are the density of prey and predator population respectively, r is the birth rate of prey, η the level of fear, α the predator-taxis sensitivity, d 1 the natural death rate of prey, d 2 death due to intra-prey competition, β rate of predation, a half-saturation constant, b tolerance limit of predation, c conversion efficiency of biomass, m natural death rate of predator. Details on both the derivation of (1) and the biological meaning of parameters can be found in [18]. In the present paper we have extended [18], introducing self-and cross-diffusion terms.…”

“…Details on both the derivation of (1) and the biological meaning of parameters can be found in [18]. In the present paper we have extended [18], introducing self-and cross-diffusion terms. The spatial diffusion plays an important role in the process of population evolution, not only in ecology but also in many other fields of applied mathematics such as biochemistry or economics and the effect of self-and cross-diffusion on the population dynamics has been widely investigated theoretically by many mathematicians ( [19][20][21][22][23][24] and references therein).…”

Impact of predator fear on two competing prey species

“…Wang and Zou [28] investigated a predator-prey model with the cost of fear and adaptive avoidance of predators and established that both strong adaption of adult prey and the large cost of fear induces destabilizing effect while large population of predators stabilize the system. Sasmal and Takeuchi [22] discussed the dynamics of a prey-predator model incorporating two facts: fear effect and group defense. Mondal et al [16] analyzed the predator-prey model considering both the effects of fear and additional food and showed stability of equilibrium points and Hopf bifurcation.…”