PARTIAL PERMANENCE AND STATIONARY DISTRIBUTION OF A DELAYED STOCHASTIC FACULTATIVE MUTUALISM MODEL WITH FEEDBACK CONTROLS

Xiaojie He; Zhijun Liu; Qinglong Wang

doi:10.11948/20220405

2024 Volume 14 Issue 2

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Xiaojie He, Zhijun Liu, Qinglong Wang. PARTIAL PERMANENCE AND STATIONARY DISTRIBUTION OF A DELAYED STOCHASTIC FACULTATIVE MUTUALISM MODEL WITH FEEDBACK CONTROLS[J]. Journal of Applied Analysis & Computation, 2024, 14(2): 657-681. doi: 10.11948/20220405

Citation:

Xiaojie He, Zhijun Liu, Qinglong Wang. PARTIAL PERMANENCE AND STATIONARY DISTRIBUTION OF A DELAYED STOCHASTIC FACULTATIVE MUTUALISM MODEL WITH FEEDBACK CONTROLS[J]. Journal of Applied Analysis & Computation, 2024, 14(2): 657-681. doi: 10.11948/20220405

PARTIAL PERMANENCE AND STATIONARY DISTRIBUTION OF A DELAYED STOCHASTIC FACULTATIVE MUTUALISM MODEL WITH FEEDBACK CONTROLS

1.
School of Mathematics and Statistics, Hubei Minzu University, Enshi, Hubei 445000, China

Author Bio: Email: xiaojiehe_math@163.com(X. He); Email: wangqinglong125@163.com(Q. Wang)
Corresponding author: Email: zjliu@hbmzu.edu.cn(Z. Liu)
Fund Project: The authors were supported by National Natural Science Foundation of China (Nos. 12101211, 11871201)

Abstract

Abstract

This paper characterizes a facultative mutualism model with feedback controls by using delayed stochastic differential equations, in which each interspecific mutualism term contains saturation effects and distributed delays with strong kernels. Firstly, we transform the stochastic facultative mutualism model with strong kernels into an equivalent eight-dimensional stochastic model by a linear chain technique. After that, sufficient criteria for partial permanence of both species and the existence of a unique stationary distribution are established, respectively. Finally, illustrative examples and corresponding numerical simulations are carried out to support our theoretical results.
- Delayed stochastic mutualism model /
- feedback controls /
- partial permanence /
- stationary distribution
MSC: 92D25, 60H10

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References

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