Ultimate boundedness and estimation of tick population system with non-linear delayed Gamma-Ricker function and stochastic perturbation

Stochastically ultimate boundedness and Lyapunov exponent estimation are fundamental in the analysis of stochastic models. These properties are particularly crucial for addressing stochastic biological models that incorporate delays, necessitating the application of advanced mathematical techniques....

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Bibliographic Details
Published in:Chaos, solitons and fractals solitons and fractals, 2025-02, Vol.191, p.115824, Article 115824
Main Author: Chen, Xingzhi
Format: Article
Language:English
Subjects:
Gamma-Ricker function
Stochastic perturbation
Stochastically ultimate boundedness
Tick population model
Time-delay
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Summary:Stochastically ultimate boundedness and Lyapunov exponent estimation are fundamental in the analysis of stochastic models. These properties are particularly crucial for addressing stochastic biological models that incorporate delays, necessitating the application of advanced mathematical techniques. In this paper, a stochastic tick population model incorporating non-linear delayed Gamma-Ricker function is proposed and examined. Then, several critical issues related to the stochastic model are investigated, including the global nonnegative solution and the ultimately bounded solution, and Lyapunov exponent estimation. Finally, a numerical simulation is presented to confirm the mathematical findings and illustrate the practical applicability of the analysis.
ISSN:0960-0779
DOI:10.1016/j.chaos.2024.115824