A universal method for constructing n-dimensional polynomial hyperchaotic systems with any desired positive Lyapunov exponents

Abstract

Most existing chaotic maps have many defects in engineering applications, such as discontinuous parameter range, uneven output of chaotic sequences and dynamic degradation. Based on this, a generalized n-dimensional polynomial chaotic map is proposed in this paper. By setting the coefficient of the linear term and the order of the highest order term of the polynomial, a series of n-dimensional polynomial chaotic maps of specific Lyapunov exponents can be obtained. The system solves the defects of the above system well, in addition, one can get the desired number of positive Lyapunov exponents, and one can get the desired value of positive Lyapunov exponents. Then, the effectiveness of the map is verified by a specific numerical example, and its dynamic analysis shows that the map has complex dynamic behavior. Finally, the map is applied to secure communication technology. Compared with other chaotic maps of the same dimension, the maps can obtain a smaller bit error rate, indicating that the chaotic map is more suitable for chaotic secure communication applications.