Determination and Properties Analysis of a Cubic Polynomial Chaotic Map

This paper provides the sufficient conditions for topological conjugation between the general cubic polynomial maps and a piecewise linear chaotic map, then provides indirectly the sufficient conditions that make the cubic polynomial maps be chaotic. This paper analyzes further the uniformity, structural complexity and randomness of the piecewise linear map and cubic polynomial maps of topological conjugation. The results show that the uniformity of the piecewise linear map is better than the polynomial maps while the randomness of the polynomial maps is superior to the piecewise linear map. As for the structural complexity, there is no significant difference between the two kinds of systems, but it should be noted that the quantitative method makes a significant impact on the structure complexity of the systems.