A New Three-Dimensional Chaotic System with Constant Exponent Spectrum: Analysis, Synchronization and Circuit Implementation

Abstract

Abstract:A new chaotic system with constant Lyapunov exponent spectrum is presented, two system parameters of which remain constant exponent characteristics. The basic dynamic properties of the new system are analyzed by Poincar section, Lyapunov exponent and dimension and the signal power spectrum. Based on the Lyapunov exponent spectrum, bifurcation diagrams and state variable amplitude with respect to system parameters show that the new system has two parameters with globally nonlinear modulation characteristic. Based on the Lyapunov stability theory and the improvement of the traditional method, through constructing a Lyapunov function with containing a positive constant that the complete synchronization with single controllers are achieved by means of nonlinear active feedback, adaptive, backstepping and passive control theory, respectively. And the designed single controllers are verified via numerical simulation. Because of single controller, synchronous switch circuit consists of four synchronization schemes is implemented, which further validate the correctness and practicability of the single controllers.

Constructing multiwing attractors from a robust chaotic system with non-hyperbolic equilibrium points

“…based on the relation of the system parameter and the mathematical expression of the nonzero equilibrium point [52]. Thus, system (1) is degenerated to the normalized system about parameter k, as below ⎧ ⎨ ⎩ẋ…”

“…These investigations only concern the robust chaos feature over a limited parameter range. Recently, we found that there exists robust chaos in the continuous chaotic system over infinite parameter range, and these parameters can regularly control the signal amplitude (which is called amplitude modulation for the convenience), yet the Lyapunov exponents keep invariable [50][51][52][53][54]. Therefore, it is a promising type of system in the practical application of image encryption, signal processing, synchronization and chaotic communication [53,54].…”

Dynamics Feature and Synchronization of a Robust Fractional‐Order Chaotic System

“…The investigation of chaos has benefited the exploration of the complex behavior, intrinsic nonlinear structure of natural system, and the construction of chaotic system, as well as practical applications such as secure communications and signal detection [5][6][7][8][9]. Robust chaotic system can usually provide signal-amplitude modulation by controlling one or some of the parameters in the dynamical equations yet keep the Lyapunov exponents and power spectral density invariable [10][11][12][13][14]. Therefore, it is a type of chaotic system with potential applications in synchronization, signal processing, image encryption, chaotic radar, and chaotic communication [10,12].…”