Work

Long-Term Behavior of Lotka–Volterra Model with Lévy Jump in Countable State-Dependent Environments

Year: 2025

Type: article

Abstract: In this study, we analyze a multi-species mutualistic Lotka–Volterra model with Lévy jumps and regime-switching. A defining feature of the work lies in modeling the random environment through state-dependent switching in an infinite countable state space. Our main objective is to establish the sufficient conditions of the extinction and stochastic permanence of the model. First, we analyze the existence and uniqueness of the model’s solution, followed by an examination of the solution’s stochastic ultimate boundedness. Moreover, the challenges arising from state-dependent switching are addressed using the stochastic comparison method. Due to the presence of the jump component, more complex conditions are required to achieve a finite partition of the countably infinite space. Furthermore, the M-matrix theory is also used to obtain the stochastic permanence property. Finally, two specific examples are provided to illustrate the conclusions in this paper.

Source: Mathematics

DOI: 10.3390/math13213566

Authors: Huijie Ji, Ping Yu, Hongxia Sun, Yuhang Zhen

Institutions: Shanxi Normal University, Zhejiang University of Water Resource and Electric Power

Language: English

Topic: Mathematical and Theoretical Epidemiology and Ecology Models

Subfield: Public Health, Environmental and Occupational Health

Field: Medicine

Domain: Health Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: National Natural Science Foundation of China