Stability Analysis of the Chaotic Reverse Butterfly-Shaped Dynamical System Represented in State Variable form Using Hurwitz Polynomials

The stability of a dynamic system of a differential equations in state variable form describes how it responds to significantly small perturbations. This qualitative behavior a of system of differential equations is studied using Lyapunov or Hurwitz polynomials. The latter reduces the problem of stability of equilibrium points of nonlinear systems to an algebraic linearized system, providing necessary and sufficient criteria in terms of Hurwitz determinant or Routh - Hurwitz Array for which the system is stable. In this paper, the stability analysis of the chaotic reverse butterfly-shaped dynamical system is presented using Hurwitz polynomials. The proposed procedure has been illustrated lucidly and validated with numerical simulations in MAPLE software.