Leon Chua's Local Activity theory quantitatively relates the compact model of an isolated nonlinear circuit element, such as a memristor, to its potential for desired dynamical behaviors when externally coupled to passive elements in a circuit. However, the theory's use has often been limited to potentially unphysical toy models and analyses of small-signal linear circuits containing pseudo-elements (resistors, capacitors, and inductors), which provide little insight into required physical, material, and device properties. Furthermore, the Local Activity concept relies on a local analysis and must be complemented by examining dynamical behavior far away from the steady-states of a circuit. In this work, we review and study a class of generic and extended one-dimensional electro-thermal memristors (i.e., temperature is the sole state variable), re-framing the analysis in terms of physically motivated definitions and visualizations to derive intuitive compact models and simulate their dynamical behavior in terms of experimentally measurable properties, such as electrical and thermal conductance and capacitance and their derivatives with respect to voltage and temperature. Within this unified framework, we connect steady-state phenomena, such as negative differential resistance, and dynamical behaviors, such as instability, oscillations, and bifurcations, through a set of dimensionless nonlinearity parameters. In particular, we reveal that the reactance associated with electro-thermal memristors is the result of a phase shift between oscillating current and voltage induced by the dynamical delay and coupling between the electrical and thermal variables. We thus, demonstrate both the utility and limitations of local analyses to understand non-local dynamical behavior. Critically for future experimentation, the analyses show that external coupling of a memristor to impedances within modern sourcing and measurement instruments can dominate the response of the total circuit, making it impossible to characterize the response of an uncoupled circuit element for which a compact model is desired. However, these effects can be minimized by proper understanding of the Local Activity theory to design and utilize purpose-built instruments.

中文翻译：

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基于物理的电热忆阻器紧凑建模：负微分电阻、局部活动和非局部动态分岔

Leon Chua 的局部活动理论定量地将隔离非线性电路元件（例如忆阻器）的紧凑模型与外部耦合到电路中的无源元件时所需的动态行为的潜力联系起来。然而，该理论的用途通常仅限于潜在的非物理玩具模型和对包含伪元件（电阻器、电容器和电感器）的小信号线性电路的分析，这几乎无法深入了解所需的物理、材料和器件特性。此外，局部活动概念依赖于局部分析，并且必须通过检查远离电路稳态的动态行为来补充。在这项工作中，我们回顾和研究了一类通用和扩展的一维电热忆阻器（即，温度是唯一的状态变量），根据物理动机的定义和可视化重新构建分析，以得出直观的紧凑模型，并根据实验可测量的特性（例如电导和热导和电容及其导数）模拟它们的动态行为关于电压和温度。在这个统一的框架内，我们通过一组无量纲非线性参数将稳态现象（例如负微分阻力）和动态行为（例如不稳定性、振荡和分叉）联系起来。特别是，我们揭示了与电热忆阻器相关的电抗是由电和热变量之间的动态延迟和耦合引起的振荡电流和电压之间的相移的结果。因此，我们证明了局部分析在理解非局部动力学行为方面的实用性和局限性。对于未来的实验至关重要，分析表明，忆阻器与现代采购和测量仪器中的阻抗的外部耦合可能会主导整个电路的响应，因此无法表征需要紧凑模型的非耦合电路元件的响应. 然而，这些影响可以通过正确理解局部活动理论来设计和使用专用仪器来最小化。证明了局部分析的实用性和局限性，以了解非局部动态行为。对于未来的实验至关重要，分析表明，忆阻器与现代采购和测量仪器中的阻抗的外部耦合可能会主导整个电路的响应，因此无法表征需要紧凑模型的非耦合电路元件的响应. 然而，这些影响可以通过正确理解局部活动理论来设计和使用专用仪器来最小化。证明了局部分析的实用性和局限性，以了解非局部动态行为。对于未来的实验至关重要，分析表明，忆阻器与现代采购和测量仪器中的阻抗的外部耦合可能会主导整个电路的响应，因此无法表征需要紧凑模型的非耦合电路元件的响应. 然而，这些影响可以通过正确理解局部活动理论来设计和使用专用仪器来最小化。分析表明，忆阻器与现代采购和测量仪器中的阻抗的外部耦合可能会主导整个电路的响应，因此无法表征需要紧凑模型的非耦合电路元件的响应。然而，这些影响可以通过正确理解局部活动理论来设计和使用专用仪器来最小化。分析表明，忆阻器与现代采购和测量仪器中的阻抗的外部耦合可能会主导整个电路的响应，因此无法表征需要紧凑模型的非耦合电路元件的响应。然而，这些影响可以通过正确理解局部活动理论来设计和使用专用仪器来最小化。