Analysis, Control and Circuit Simulation of a Novel 3-D Finance Chaotic System

Abstract

There is a growing interest in developing nonlinear dynamical systems for economic models displaying chaotic behaviour. In this work, we describe an eight-term novel 3-D finance chaotic system consisting of two nonlinearities (one quadratic and one quartic). The phase portraits of the novel 3-D finance chaotic system are depicted using MATLAB. We give a dynamic analysis of the novel 3-D finance chaotic system. The novel chaotic system has three equilibrium points of which one equilibrium point on the \(x_2\) axis is a saddle point, while the other two equilibrium points are saddle-foci. The novel finance chaotic system has rotation symmetry about the \(x_2\) axis. The Lyapunov exponents of the novel finance chaotic system are obtained as \(L_1 = 0.1209\), \(L_2 = 0\) and \(L_3 = -0.4321\), while the Kaplan–Yorke dimension of the novel finance chaotic system is obtained as \(D_{KY} = 2.2798\). Since the sum of the Lyapunov exponents is negative, the novel chaotic system is dissipative. Next, we derive new results for the global chaos control of the novel finance chaotic system with unknown parameters using adaptive control method. The chaos control problem aims to regulate the states of the novel finance chaotic system to desired constant values. The main adaptive control result for the novel finance chaotic system is established using Lyapunov stability theory. Finally, an electronic circuit realization of the novel finance chaotic system using Spice is presented in detail to confirm the feasibility of the theoretical model.