Global analysis of a stage-structured model with population diffusion

Abstract

The population diffusions are incorporated into the prey–predator model with the stage structure for predators. The threshold is established above which the predators are permanent and below which the predators become extinct. The necessary and sufficient conditions for the local stability of the positive steady state are obtained by analysing eigenvalues. With the Lyapunov direct method, explicit conditions for the global stability of the positive equilibrium are derived.

Keywords:

• permanence
• extinction
• stability
• eigenvalue
• Lyapunov

AMS Subject Classifications::

• 35B35
• 35B40

Acknowledgements

This research was supported by the National Science Fund of P.R. China (10871162), partially supported by the University of Catania under a local contract and by Gruppo Nazionale della Fisica Matematica of the Istituto Nazionale di Alta Matematica.