Analysis and simulation on dynamics of a partial differential system with nonlinear functional responses
Articles
Yunfeng Jia
Shaanxi Normal University
Published 2021-03-01
https://doi.org/10.15388/namc.2021.26.22356
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Keywords

reaction–diffusion system
large-time behavior
positive solution
bifurcation
numerical and graphical analysis

How to Cite

Jia, Y. (2021) “Analysis and simulation on dynamics of a partial differential system with nonlinear functional responses”, Nonlinear Analysis: Modelling and Control, 26(2), pp. 293–314. doi:10.15388/namc.2021.26.22356.

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.

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