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

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.