Permanence of a single-species dispersal system and predator survival

Authors:
Jing'an Cui;Yasuhiro Takeuchi
Affiliations:
Department of Mathematics, Nanjing Normal University, Nanjing 210097, P.R. China;Department of Systems Engineering, Faculty of Engineering, Shizuoka University, Hamamatsu 432-8561, Japan
Venue:
Journal of Computational and Applied Mathematics
Year:
2005

Citing 3
Cited 0

Global stability and predator dynamics in a model of prey dispersal in a patchy environment

Non-Linear Analysis
Permanence and extinction of periodic predator-prey systems in a patchy environment with delay

Nonlinear Analysis: Real World Applications
The qualitative analysis of n-species Lotka-Volterra periodic competition systems

Mathematical and Computer Modelling: An International Journal

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Abstract

This paper considers permanence of a single-species dispersal periodic system with the possibility of the loss for the species during their dispersion among patches. The condition obtained for permanence generalizes the known condition on the system without loss for the species in the process of movement. Next, we add predators into every patch and consider the survival possibility of the predator. It is shown that the total amount of the predators can remain positive, if the single-species (prey) dispersal system has a positive periodic solution and the quantity of prey in each patch is enough for survival of the predator.