Analog Electronic Implementation of Unstable Dissipative Systems of Type I with Multi-Scrolls Displaced Along Space

Abstract

Multi-scroll Unstable Dissipative Systems (UDS) in [Formula: see text] which consist of piecewise linear systems are implemented electronically by means of analog computing. The scrolling behavior of the systems can be designed to oscillate along a specific axis or into space depending on the unstable and stable manifolds. In order for a multi-scroll attractor, this switching system must present at least two unstable hyperbolic focus-saddle equilibria with the same stability index, a negative real eigenvalue and a pair of complex conjugated eigenvalues with positive real part. Then, to displace the scrolls among the axes and space different switching control laws must be designed. By taking into consideration the mathematical expressions of the switching systems, the electronic implementations are carried out by means of operational amplifiers representing the real analog physical solution of the systems, from which the voltage is measured representing the states solution.