Dynamical Analysis of a Delayed Diffusive Predator–Prey Model with Additional Food Provided and Anti-Predator Behavior

Abstract

We studied a delayed predator–prey model with diffusion and anti-predator behavior. Assume that additional food is provided for predator population. Then the stability of the positive equilibrium is considered. The existence of Hopf bifurcation is also discussed based on the Hopf bifurcation theory. The property of Hopf bifurcation is derived through the theory of center manifold and normal form method. Finally, we analyze the effect of time delay on the model through numerical simulations.

Bifurcation analysis of delayed predator–prey system with fear effect, additional food for predator, prey refuge and predator age structure

“…In the complex and diverse natural world, besides the factors currently considered in this paper, as part of future research, we suggest including non-linear mortality caused by anti-predator activities and stochastic environmental factors into the model to enhance its realism. Additionally, we believe there will be interesting findings when applying the reaction-diffusion model [38][39][40] and infectious disease model [41][42][43]. However, these aspects will be left for further exploration in our future work.…”

Stage structured prey-predator model incorporating mortal peril consequential to inefficiency and habitat complexity in juvenile hunting

“…At the period-doubling bifurcation point r = r pd , the fixed point E 3 undergoes destabilisation, resulting in the emergence of two points that constitute the period-2 solution. The characteristic polynomial of J e3 with r = r pd , µ = 0.59977 and the other parameters as stated previously, λ 3 + 0.992639λ 2 − 0.951366λ − 0.944005 = 0 (8) here, p 1 = 0.992639, p 2 = −0.951366, and p 3 = −0.944005.…”

“…The predator-prey model has garnered significant attention from researchers in the field of ecology, following the groundbreaking contributions of Lotka [1] and Volterra [2] to the field. Subsequent to that, numerous kinds of enhancements for the predator-prey model have been suggested [3][4][5][6][7][8].…”

Analisis Dinamik Model Predator-prey dengan Perilaku Anti Predator serta Efek Allee pada Prey

“…Besides altering its response functions, the predatorprey model is also adapted by incorporating additional factors such as the Allee effect [3,5,9], and anti-predator behavior [4,6,8]. The Allee effect represents a phenomenon illustrating how the growth or reproduction of individuals within a population can be impeded or even halted when the population density drops below a certain threshold known as the Allee threshold.…”