混沌NOR门和置位/复位触发器的定性模型与实验研究
Qualitative models and experimental investigation of chaotic NOR gates and set/reset flip-flops
摘要：
通过实验和SPICE模拟观察到，基于蔡氏电路的逻辑电路具有复杂的动力学行为。这种行为可以用来设计更复杂的逻辑系列的模拟，并且某些特性可以用于电子应用。这些电路中的一些已经被建模为常微分方程系统。然而，随着新电路中组件数量的增加，复杂性也随之增加。这使得连续动态系统模型不切实际，需要新的建模技术。近年来，一些离散的动力学模型已被开发使用各种简化的假设。为了建立一个强大的建模框架，混沌逻辑电路，我们开发了确定性和随机离散动力学模型，利用自然递归行为，两个混沌NOR门和混沌置位/复位触发器（RSFF）。本文对逻辑电路进行了完整的应用数学研究。对我们自己设计的上述电路的实验进行了建模，并对模型进行了严格的分析和模拟，结果与实验结果惊人地接近。此外，模型的设计，以适应类似设计的电路的动态。这将使研究人员能够用一个简单的建模框架开发出更复杂的混沌逻辑电路。
英文摘要：
It has been observed through experiments and SPICE simulations that logical circuits based upon Chua's circuit exhibit complex dynamical behavior. This behavior can be used to design analogs of more complex logic families and some properties can be exploited for electronics applications. Some of these circuits have been modeled as systems of ordinary differential equations. However, as the number of components in newer circuits increases so does the complexity. This renders continuous dynamical systems models impractical and necessitates new modeling techniques. In recent years some discrete dynamical models have been developed using various simplifying assumptions. To create a robust modeling framework for chaotic logical circuits, we developed both deterministic and stochastic discrete dynamical models, which exploit the natural recurrence behavior, for two chaotic NOR gates and a chaotic set/reset flip-flop (RSFF). This work presents a complete applied mathematical investigation of logical circuits. Experiments on our own designs of the above circuits are modeled and the models are rigorously analyzed and simulated showing surprisingly close qualitative agreement with the experiments. Furthermore, the models are designed to accommodate dynamics of similarly designed circuits. This will allow researchers to develop ever more complex chaotic logical circuits with a simple modeling framework.
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