Circuit realization of chaotic systems with quadratic nonlinearity using AD633 based generic topology

Abstract

This paper presents the systematic realization of chaotic systems, with cross product or quadratic type non-linearities, using only one type of active building block, namely AD633, which is a commercially available Integrated Circuit (IC) of Analog Multiplier (AM), and few off the shelf passive components, namely resistors and capacitors. The number of AD633s required in the proposed scheme is equal to the dimension of the system. This reduces the requirement of summation/ subtraction circuits involving voltage and current mode active building blocks, thus reducing the component count significantly and make the design of chaotic circuits simple and cost effective. The simulations have been performed in LTspice design environment, and the results in the form of phase space diagrams have been presented for two chaotic systems: Rabinovich chaotic system and Lorenz chaotic system. The shape of the phase space plots, also known as attractors confirms the feasibility of the proposed approach.