Stability Analysis of a Differential Model for Quasi-Periodic Plasma Perturbations

This paper deals with the stability of a differential model for quasi-periodic plasma perturbations. First, we derive the linear stability conditions on the parameters of the differential model by using symbolic computation of solving semi-algebraic systems. Then, we analyze the Jacobi stability of the quasi-periodic plasma perturbations by using the Kosambi–Cartan–Chern (KCC) theory. We reformulate the differential model as a set of two second-order nonlinear differential equations and explicitly obtain the geometric invariants, as well as the deviation curvature tensor. The Jacobi stability of the fixed points of the system is detected by using computer algebra methods. Furthermore, the dynamic behavior of the components of the deviation vector near the fixed points is also discussed. The obtained results show that all the fixed points of the differential model are always Jacobi unstable, while the linear stability of the fixed points depends on the values of the parameters. Some examples and numerical simulations are presented to verify the established results.