Approximate Equivalence of Higher-Order Feedback and Its Application in Chaotic Systems

Yikai Gao, Chunbiao Li, Irene Moroz, Haiyan Fu, Tengfei Lei
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Abstract

Based on the feature of piecewise linear (PWL) functions, a nonlinear feedback of a higher-order system can be transformed to an approximately equivalent PWL function so as to ease system implementation in engineering. As an example, a cubic feedback term can be approximately equivalently transformed to be a PWL function. Since the PWL function can be expressed by many simple functions such as signum function and absolute-valued function, the cubic term can be approximately equivalently replaced with these functions. Consequently, the method of approximate equivalence is employed in the JCS-08-13-2022 (JCS) chaotic system for simple circuit design and implementation. In this approach, the widely used multipliers are avoided and the circuits become more economical and also more robust. In this paper, the cubic Chua’s resistor is equivalently approximately replaced by a PWL function. To show the effectiveness of the approximate equivalence, numerical simulations are demonstrated and verified by circuit implementation.
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高阶反馈的近似等效性及其在混沌系统中的应用
根据分片线性(PWL)函数的特点,可以将高阶系统的非线性反馈转化为近似等效的 PWL 函数,从而简化工程中的系统实施。例如,立方反馈项可以近似等效地转换为 PWL 函数。由于 PWL 函数可以用许多简单的函数来表示,如符号函数和绝对值函数,因此立方项可以近似等价地替换为这些函数。因此,JCS-08-13-2022(JCS)混沌系统中采用了近似等价的方法来进行简单的电路设计和实现。在这种方法中,避免了广泛使用的乘法器,电路变得更经济、更稳健。在本文中,立方蔡氏电阻被 PWL 函数近似等效替代。为了证明近似等效的有效性,本文进行了数值模拟演示,并通过电路实现进行了验证。
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