Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

A Study of the Jacobi Stability of the Rosenzweig–MacArthur Predator–prey System by the KCC Geometric Theory

Version 1 : Received: 30 July 2022 / Approved: 8 August 2022 / Online: 8 August 2022 (03:58:14 CEST)

A peer-reviewed article of this Preprint also exists.

Munteanu, F. A Study of the Jacobi Stability of the Rosenzweig–MacArthur Predator–Prey System through the KCC Geometric Theory. Symmetry 2022, 14, 1815. Munteanu, F. A Study of the Jacobi Stability of the Rosenzweig–MacArthur Predator–Prey System through the KCC Geometric Theory. Symmetry 2022, 14, 1815.

Journal reference: Symmetry 2022, 14, 1815
DOI: 10.3390/sym14091815

Abstract

In this paper, we will consider an autonomous two-dimensional ODE Kolmogorov type 1 system with three parameters, which is a particular system of the general predator–prey systems with 2 a Holling type II. By reformulating this system as a set of two second order differential equations, we 3 will investigate the nonlinear dynamics of the system from the Jacobi stability point of view, using 4 the Kosambi-Cartan-Chern (KCC) geometric theory. We will determine the nonlinear connection, the 5 Berwald connection and the five KCC-invariants which express the intrinsic geometric properties 6 of the system, including the deviation curvature tensor. Furthermore, we will obtain necessary and 7 sufficient conditions on the parameters of the system in order to have the Jacobi stability near the 8 equilibrium points and we will point out these on a few examples.

Keywords

predator–prey systems; Kolmogorov systems; KCC-theory; the deviation curvature tensor; Jacobi stability

Subject

MATHEMATICS & COMPUTER SCIENCE, Applied Mathematics

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