A Study of the Jacobi Stability of the Rosenzweig–MacArthur Predator–Prey System through the KCC Geometric Theory

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