Abstract
We introduce a reaction–diffusion system with modified nonlinear functional responses. We first discuss the large-time behavior of positive solutions for the system. And then, for the corresponding steady-state system, we are concerned with the priori estimate, the existence of the nonconstant positive solutions as well as the bifurcations emitting from the positive constant equilibrium solution. Finally, we present some numerical examples to test the theoretical and computational analysis results. Meanwhile, we depict the trajectory graphs and spatiotemporal patterns to simulate the dynamics for the system. The numerical computations and simulated graphs imply that the available food resource for consumer is very likely not single.
Highlights
Many ecological phenomena among different populations can be characterized or simulated by various mathematical models
By analyzing different kinds of mathematical models people may give scientific predictions and explanations on the dynamics of these models, and further, put forward reasonable projects corresponding to some ecological problems
Since the classical Lotka–Volterra ecological model [13] was introduced into investigations, the predator–prey-type models received extensively attentions
Summary
Many ecological phenomena among different populations can be characterized or simulated by various mathematical models. Since in actual ecological systems, the carrying capacity set by environmental resources is proportional to prey abundance and the predators always try to survive by catching other preys when their conventional food is short seriously, in such situations, the growth rate of the predator would be affected For this reason, Aziz-Alaoui [2] modified the logistic form and proposed the Leslie–Gower-type functional response hx/(a + y), where a is a positive constant and measures the environmental protection for predator. It is worth mentioning that the numerical simulated graphs imply that the available food resource for predator may not single if the system parameters are controlled properly
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