A minimum five-component five-term single-nonlinearity chaotic jerk circuit based on a twin-jerk single-op-amp technique

摘要

A minimum 5-component 5-term single-nonlinearity chaotic jerk circuit is presented as the first simplest chaotic jerk circuit in a category that a single op-amp is employed. Such a simplest circuit displays 5 simultaneous advantages of (1) 5 minimum basic electronic components, (2) 5 minimum algebraic terms in a set of 3 coupled first-order ordinary differential equations (ODEs), (3) a single minimum term of nonlinearity in the ODEs, (4) a simple passive component for nonlinearity, and (5) a single op-amp. The proposed 5-term single-nonlinearity chaotic jerk circuit and a slightly modified version of an existing 6-term 2-nonlinearity chaotic jerk circuit form mirrored images of each other. Although both mirrored circuits yield 2 different sets of the ODEs, both sets however can be recast into a pair of twin jerk equations. Both mirrored circuits are therefore algebraically twin 5-component chaotic jerk circuits, leading to a twin-jerk single-op-amp approach to the proposed minimum chaotic jerk circuit. Two cross verifications of trajectories of both circuits are illustrated through numerical and experimental results. Dynamical properties are also presented.