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Abstract
This paper is concerned with a multi-delay three-species predator-prey model with feedback controls and prey diffusion. By developing some new analysis techniques and using the comparison principle of differential equations, we obtained some new sufficient conditions which ensure the system to be permanent.
Highlights
It is important to obtain the conditions which ensure all species in multi-species community are permanent and global attractive
Diffusion often occurs in an ecological environment, that is to say, species can diffuse between patches
As a prey species which grows in weak environment, spread to an advantageous environment is conducive to maintaining the permanence and global attractive of the species
Summary
It is important to obtain the conditions which ensure all species in multi-species community are permanent and global attractive. In [9], Zhou, Shi and Song considered the following nonautonomous predator-prey model with nonlinear diffusion and time-delays They obtained some sufficient conditions for the permanence and global stability of the model. In [16], Chen et al proposed the following Lotka-volterra predator-prey system with feedback controls x1 (t )(a1 They by constructing two suitable Lyapunov functions, sufficient conditions which guarantee the global attractivity of the positive equilibrium and boundary equilibrium are obtained. They results show that enough large feedback controls could lead to the extinction of the predator species. Based on system (4) and motivated by the above works, in this paper, we propose and investigate the following three-species Lotka-Volterra multi-delay predator-prey system with feedback controls and prey diffusions. By developing a new analysis technique, the sufficient conditions are established for the permanence of the predator-prey model in this paper
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