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.
概要
目的
从物理角度论证忆阻型映射设计的方法和可靠性判据, 给出能量函数并表达其自适应调控的机理。
创新点
1. 设计两种不同忆阻型映射并论证忆阻型映射的物理可靠性;2. 给出忆阻映射的能量函数定义方法;3. 提出自适应调控忆阻映射的能力机理。
方法
1. 以两类忆阻器分别耦合电感型和电容型器件, 设计两类忆阻电路和忆阻振子;2. 利用两种方法分别计算忆阻振子的能量函数;3. 对忆阻振子的变量和参数进行线性变换得到对应的忆阻映射和能量函数;4. 引入阶跃函数和取整函数来表达参数自适应调整, 忆阻振子能量超过一定阈值则促进参数进一步增长。
结论
1. 非线性电路和振子的构造需要最基本的电感型、电容性器件和非线性器件(变量和函数);2. 能量决定着振子和映射的振荡模态;3. 包含时间标度的线性变换可以把非线性振子转换为等效的非线性映射;4. 随机性刺激可诱发忆阻映射产生相干共振;5. 准确的能量定义有利于判断非线性振子的物理意义和可靠性。
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Acknowledgments
This work is supported by the National Natural Science Foundation of China (No. 12072139).
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Feifei YANG: methodology, software, numerical calculation, and writing-original draft. Lujie REN: numerical calculation and DSP implementation. Jun MA and Zhigang ZHU: methodology, supervision, and writing-final version.
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Jun MA is an Editorial Board member of this journal, and is NOT involved in the editorial review or the decision to publish this article. Feifei YANG, Lujie REN, Jun MA, and Zhigang ZHU declare that they have no conflict of interest.
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Yang, F., Ren, L., Ma, J. et al. Two simple memristive maps with adaptive energy regulation and digital signal process verification. J. Zhejiang Univ. Sci. A (2024). https://doi.org/10.1631/jzus.A2300651
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DOI: https://doi.org/10.1631/jzus.A2300651
Key words
- Hamilton energy
- Discrete memristor
- Self-adaptive regulation
- Digital signal process (DSP) implementation