Construction of a class of chaos systems with Markov properties

Abstract

In this article, a kind of piecewise expanding linear system is constructed. It has a positive Lyapunov exponent as calculated. It is proved that the system has a uniform limit distribution The formula of the least period of the system is also presented. It is indicated that there is a contradictory relationship between the complexity and the least period of the system when the symbol entropy is applied to the system. The theoretical limit of the complexity of the system with changing parameters is presented. Simulation of the system shows that the sequence generated by the chaos is uniformly distributed. It also tells that the system can have higher complexity but longer least-period than the logistic system and the Tent-Map system. Experiments show that the system is suitable for constructing the cipher.