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

Xingzhi Chen

Chaos, Solitons & Fractals, 2025, vol. 191, issue C

Abstract: 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.

Keywords: Tick population model; Stochastic perturbation; Time-delay; Gamma-Ricker function; Stochastically ultimate boundedness (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:191:y:2025:i:c:s0960077924013766

DOI: 10.1016/j.chaos.2024.115824

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