Simulation Experiment Research on the Chaotic Characteristics of the Simple Unary Polynomial Transformation

Abstract

To enhance the complexity of the chaos, improve the characteristics of chaos, and increase the number of chaotic types, a simple method is put forward in this paper. This method does not need to change the existing chaotic system, but just makes a nonlinear transformation to the chaotic signal by a unary polynomial. The nonlinear transformation has the characteristic that its physical circuit is easy to implement. Therefore, after a systematic consideration, a simple unary polynomial is chosen in this paper and a series of simulation experiments are conducted from the aspects of Lyapunov exponent, power spectrum, phase diagram and the sensitivity to initial conditions. The results show that this method is effective and feasible.