Transient Dynamics Analysis of a Predator-Prey System with Square Root Functional Responses and Random Perturbation

Jianguo Tan (), Wenjuan Wang and Jianfeng Feng
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Jianguo Tan: School of Mathematical Sciences, Tiangong University, Tianjin 300387, China
Wenjuan Wang: School of Mathematical Sciences, Tiangong University, Tianjin 300387, China
Jianfeng Feng: Key Laboratory of Pollution Processes and Environmental Criteria, Ministry of Education, and Tianjin Key Laboratory of Environmental Remediation and Pollution Control, College of Environmental Science and Engineering, Nankai University, Tianjin 300071, China

Mathematics, 2022, vol. 10, issue 21, 1-12

Abstract: In this paper, we study the asymptotic and transient dynamics of a predator–prey model with square root functional responses and random perturbation. Firstly, the mean square stability matrix is obtained from the stability theory of stochastic systems, and three stability indexes (root-mean-square resilience, root-mean-square reactivity and root-mean-square amplification envelope) of the ecosystem response to stochastic disturbances are calculated. We find that: (1) no matter which population is disturbed, increasing the intensity of disturbance improves the ability of the system leaves steady state and thus decreases the stability. The root-mean-square amplification envelope rises with increasing disturbance intensity, (2) the system is more sensitive to the disturbance of the predator than disturbance to prey, (3) ρ m a x and t m a x are important indicators, which represent the intensity and time of maximum amplification by disturbance. These findings are helpful for managers to take corresponding management measures to reduce the disturbances, especially for predators, thereby avoiding the possible change of the structure and functions of the ecosystem.

Keywords: resilience; reactivity; amplification envelope; square root functional response; asymptotic and transient dynamics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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