Nonparametric bifurcation mechanism in 2-D hyperchaotic discrete memristor-based map

• Published in: Nonlinear dynamics Vol. 104; no. 4; pp. 4601 - 4614
• Main Authors: Deng, Yue, Li, Yuxia
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.06.2021; Springer Nature B.V
• Subjects: Automotive Engineering; Bifurcations; Classical Mechanics; Control; Digital mapping; Digital signal processors; Dynamical Systems; Engineering; Liapunov exponents; Mathematical analysis; Mathematical models; Mechanical Engineering; Memristors; Microprocessors; Nonparametric statistics; Original Paper; Phase diagrams; Sequences; Signal processing; Two dimensional models; Vibration; Nonparametric bifurcation; Discrete memristor; Hyperchaos
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-021-06544-7

Compared with continuous-time memristor (CM), discrete memristor (DM) has not been received adequate attention. In this paper, a new n- dimensional generalized DM model is proposed based on the discrete theory. Two 2-D discrete mathematical models satisfying the three fingerprints characteristics of memristors are designed. Applying the mathematical model into the Sine map yields a new hyperchaotic map called discrete memristor-based Sine (DM-S) map. The DM-S map has a line of fixed points, and its dynamical behaviors including nonparametric bifurcation and hyperchaos are explored by phase diagrams, bifurcation diagrams, and Lyapunov exponent spectrums. The i – v characteristics of the DM and the attractors of the DM-S map are implemented by digital signal processor. In addition, the sequences of map are tested by using SP800-22 NIST software.