Abstract
In this paper, a three species reaction-diffusion food-chain system with nonlocal delays is investigated. Sufficient conditions are derived for the global stability of a positive steady state and boundary steady states of the system by using the energy function method. Numerical simulations are carried out to illustrate the theoretical results.
Highlights
The classical Lotka–Volterra type systems are very important in the models of multi-species populations interactions
Three-species food chain models have been studied by many authors
Motivated by the work of Lin [8] and Gourley and So [6], in this paper, we study the following reaction-diffusion food-chain model with nonlocal delays
Summary
The classical Lotka–Volterra type systems are very important in the models of multi-species populations interactions. Three-species food chain models have been studied by many authors (see, for example, [3, 8, 9, 11, 15, 16]). In [8], Lin studied the following three-species food-chain system with time delays. In many realistic ecological models, any delays should be spatially inhomogeneous, that is, the delays affect both the temporal and spatial variables This is due to the fact that any given individual may not necessarily have been at the same spatial location at previous times. +∞ 0 k(t) dt Motivated by the work of Lin [8] and Gourley and So [6], in this paper, we study the following reaction-diffusion food-chain model with nonlocal delays. Some numerical simulations are given to illustrate the main theoretical results
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