A construction method of N-dimensional non-degenerate discrete memristive hyperchaotic map

Abstract

In this paper, a discrete memristor model with periodic memristive function is proposed, and a construction method of N-dimensional non-degenerate discrete hyperchaotic map based on the new memristors is further proposed. This method only needs simple operation steps to construct a non-degenerate hyperchaotic map with dimension-tunable and the map designed by this method has very concise structure, but this map still has complex dynamic behaviors, such as initial-boosting behaviors, state transition phenomena, large Lyapunov exponent and ultra-wide non-degenerate hyperchaotic parameter range. The construction method proposed has a seed function and by selecting different seed function, the method can construct almost infinite kinds of non-degeneracy hyperchaotic maps in any-dimension. Then we give the structure diagram of any-dimensional map and the mathematical proof for the existence of non-degeneracy hyperchaotic state of N-dimensional simplest maps. We use this method to construct three sub-maps of different dimensions and analyze their dynamic behaviors. We perform a noise robustness verification experiment on the memristor and the map, and analyze the impact of noise on critical states. We also describe the SE complexity and carry out the NIST test to show that the submaps have higher SE complexity and better pseudo-randomness. Finally the sub-maps through DSP hardware platform are implemented and the results are the same with the simulations.