Dynamic analysis and control of a new hyperchaotic finance system

Abstract

In this paper, a new hyperchaotic finance system which is constructed based on a chaotic finance system by adding an additional state variable is presented. The basic dynamical behaviors of this hyperchaotic finance system are investigated, such as the equilibrium, stability, hyperchaotic attractor, Lyapunov exponents, and bifurcation analysis. Furthermore, effective speed feedback controllers and linear feedback controllers are designed for stabilizing hyperchaos to unstable equilibrium points. Numerical simulations are given to illustrate and verify the results.

Impulsive stabilization and synchronization of uncertain financial hyperchaotic systems

“…In this section, some preliminaries including the novel hyperchaotic system model ( [28]), some necessary definitions and lemmas are presented, which are used throughout this paper.…”

“…Let ε 1 = 1. In ( [28]) typical phase portraits of this system are shown. It is also shown that in hyperchaotic region of parameters, this system is a forced dissipative system with bounded states (M ≤ 4) as t → ∞.…”

“…As we all know, in nonlinear areas, researchers are striving to utilize the theory of nonlinear dynamics, especially the chaos theory, to study the complexity of economic and financial systems in recent years ( [1,3,4,8,9,14,20,21,28,30,32]). Since Strotz et al ([21]).…”

“…Since Strotz et al ([21]). has done the pioneering work in this area, various economics chaotic models have been proposed, such as the Kaldorian model ( [20]), the IS-LM model ( [9]), the hyperchaotic finance systems ( [8,28]). Economic chaotic systems are inevitably influenced by external disturbances stemmed from environmental interference ( [30]), external disturbances may lead to the destabilization of economic and financial chaotic systems and cause undesirable results.…”

Recursive Backstepping Nonlinear Control and Sliding Mode Control of a Novel Hyperchaotic Finance System

“…Therefore, more and more scholars improve it by adding an additional state variable [4,5]. Recently, a novel financial hyperchaotic system was brought up [6] on the ground of global economic crisis arousing from 2007. The dynamical behaviors of the new system are more complex.…”