An exponential chaotic oscillator design and its dynamic analysis

Abstract

After years of development, chaotic circuits have possessed many different mathematic forms and multiple realization methods. However, in most of the existing chaotic systems, the nonlinear units are composed of the product terms. In this paper, in order to obtain a chaotic oscillator with higher nonlinearity and complexity to meet the needs of utilization, we discuss a novel chaotic system whose nonlinear term is realized by an exponential term. The new exponential chaotic oscillator is constructed by adding an exponential term to the classical Lu system. To further investigate the dynamic characteristics of the oscillator, classical theoretical analyses have been performed, such as phase diagrams, equilibrium points, stabilities of the system, Poincare mappings, Lyapunov exponent spectrums, and bifurcation diagrams. Then through the National Institute of Standards and Technology &#x0028 NIST &#x0029 statistical test, it is proved that the chaotic sequence generated by the exponential chaotic oscillator is more random than that produced by the Lu system. In order to further verify the practicability of this chaotic oscillator, by applying the improved modular design method, the system equivalent circuit has been realized and proved by the Multisim simulation. The theoretical analysis and the Multisim simulation results are in good agreement.