Abstract: 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.

Key words: Hamilton energy; Discrete memristor; Self-adaptive regulation; Digital signal process (DSP) implementation

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