Dynamic analysis of stochastic delay mutualistic system of leaf-cutter ants with stage structure and their fungus garden

Abstract

In this paper, we propose a stochastic delay mutualistic model of leaf-cutter ants with stage structure and their fungus garden, in which we explore how the discrete delay and white noise affect the dynamic of the population system. The existence and uniqueness of global positive solution are proved, and the asymptotic behaviours of the stochastic model around the positive equilibrium point of the deterministic model are also investigated. Furthermore, the sufficient conditions for the persistence of the population are established. Finally, some numerical simulations are performed to show the effect of random environmental fluctuation on the model.

Keywords:

• Stochastic mutualistic system
• discrete delay
• Lyapunov function
• stability

Acknowledgments

We are grateful to the editor and reviewers for their valuable comments and suggestions that greatly improved the presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by National Natural Sciences Foundation of China (11971405, 22072057).