Two simple memristive maps with adaptive energy regulation and digital signal process verification

• Published in: Journal of Zhejiang University. A. Science Vol. 25; no. 5; pp. 382 - 394
• Main Authors: Yang, Feifei, Ren, Lujie, Ma, Jun, Zhu, Zhigang
• Format: Journal Article
• Language: English
• Published: Hangzhou Zhejiang University Press 01.05.2024; Springer Nature B.V; Department of Physics,Lanzhou University of Technology,Lanzhou 730050,China%Department of Physics,Lanzhou University of Technology,Lanzhou 730050,China; College of Electrical and Information Engineering,Lanzhou University of Technology,Lanzhou 730050,China%School of Information Science and Engineering,Dalian Polytechnic University,Dalian 116034,China%College of Electrical and Information Engineering,Lanzhou University of Technology,Lanzhou 730050,China
• Subjects: Circuits; Civil Engineering; Classical and Continuum Physics; Digital mapping; Energy; Energy flow; Engineering; Inductors; Industrial Chemistry/Chemical Engineering; Linear transformations; Mathematical models; Mechanical Engineering; Memory devices; Memristors; Neural networks; Nonlinear systems; Oscillators; Parameters; Research Article; Signal processing; 数字电路实现; 自适应调控; Hamilton energy; Discrete memristor; Self-adaptive regulation; 离散忆阻器; Digital signal process (DSP) implementation; 哈密顿能量; Digital signal process(DSP)implementation
• ISSN: 1673-565X; 1862-1775
• DOI: 10.1631/jzus.A2300651

Mathematical models can produce desired dynamics and statistical properties with the insertion of suitable nonlinear terms, while energy characteristics are crucial for practical application because any hardware realizations of nonlinear systems are relative to energy flow. The involvement of memristive terms relative to memristors enables multistability and initial-dependent property in memristive systems. In this study, two kinds of memristors are used to couple a capacitor or an inductor, along with a nonlinear resistor, to build different neural circuits. The corresponding circuit equations are derived to develop two different types of memristive oscillators, which are further converted into two kinds of memristive maps after linear transformation. The Hamilton energy function for memristive oscillators is obtained by applying the Helmholz theorem or by mapping from the field energy of the memristive circuits. The Hamilton energy functions for both memristive maps are obtained by replacing the gains and discrete variables for the memristive oscillator with the corresponding parameters and variables. The two memristive maps have rich dynamic behaviors including coherence resonance under noisy excitation, and an adaptive growth law for parameters is presented to express the self-adaptive property of the memristive maps. A digital signal process (DSP) platform is used to verify these results. Our scheme will provide a theoretical basis and experimental guidance for oscillator-to-map transformation and discrete map-energy calculation.