Hyperchaotic maps of a discrete memristor coupled to trigonometric function

Abstract

Abstract In this paper, a new chaotic map coupled with a memristor is constructed. Based on the proposed discrete maps of sine and cosine functions, the discrete memristor is introduced and used as input to enhance their chaotic performance. Then Lyapunov exponents spectra (LEs), bifurcation diagram, and other methods are used to evaluate their chaotic behaviors. Firstly, the fixed point of the new mapping is solved, and the stability of the fixed point is analyzed with different system parameters. The distinguishing feature of the discrete graph is the coexistence of multiple types such as chaos, quasi-periodic oscillation, and discrete periodic points. In particular, the coexistence of multiple chaotic and hyperchaotic attractors has been discovered, and the initial value can be adjusted to control the shift of the chaotic attractor. In addition, state transition phenomena such as chaos degeneration and the transformation of chaos into hyperchaos have been discovered. Finally, we designed and implemented the discrete map on the DSP platform. The research results provide guidance for the application and teaching of the chaotic map coupled discrete memristor.