Stability of a three-dimensional diffusive Lotka–Volterra system of type-K with delays

Abstract

A three-dimensional diffusive Lotka–Volterra system of type-K with delays is investigated. We give a stability analysis in detail for all equilibria of the system and obtain some threshold conditions for linear instability and linear asymptotic stability of each equilibrium. We develop the analytical method for stability analysis of reaction–diffusion equations with multi-delays.

Keywords:

• stability
• diffusive system of type-K
• delay
• Rouche's theorem
• auxiliary equation

AMS Subject Classifications::

• 35K57
• 35Q80
• 92D25

Acknowledgements

This research is supported by the NSF of China (11171120), the Doctoral Program of Higher Education of China (20094407110001) and NSF of Guangdong Province (10151063101000003). We thank the reviewers for their helpful suggestions which has improved the quality of this article.