The purpose of the present paper is to study the stability of a prey–predator model using KCC theory. The KCC theory is based on the assumption that the second-order dynamical system and geodesics equation, in associated Finsler space, are topologically equivalent. The stability (Jacobi stability) based on KCC theory and linear stability of the model are discussed in detail. Further, the effect of parameters on stability and the presence of chaos in the model are investigated. The critical values of bifurcation parameters are found and their effects on the model are investigated. The numerical examples of particular interest are compared to the results of Jacobi stability and linear stability and it is found that Jacobi stability on the basis of KCC theory is global than the linear stability.

中文翻译：

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捕食者模型的稳定性和分岔分析

本文的目的是利用 KCC 理论研究捕食者模型的稳定性。KCC 理论基于这样的假设，即相关 Finsler 空间中的二阶动力系统和测地线方程是拓扑等价的。详细讨论了基于KCC理论的稳定性（Jacobi稳定性）和模型的线性稳定性。此外，还研究了参数对稳定性的影响以及模型中是否存在混沌。找到了分岔参数的临界值，并研究了它们对模型的影响。将特别感兴趣的数值例子与雅可比稳定性和线性稳定性的结果进行比较，发现基于KCC理论的雅可比稳定性比线性稳定性更具有全局性。