abstract

• Multi-scroll Unstable Dissipative Systems (UDS) in R3 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. © 2017 World Scientific Publishing Company.

authors

• Lozoya-Ponce R.E.
• Ontañon García Pimentel Luis Javier

publication date

• 2017-01-01

funding provided via

• Universidad Autónoma de San Luis Potosí, UASLP: C16- FAI-09-46.46, MSU0011E-21  Grant

published in

• International Journal of Bifurcation and Chaos  Journal

keywords

• analog electronics; chaos; multi-scroll; Piecewise linear systems; unstable dissipative systems Chaos theory; Energy dissipation; Linear systems; Operational amplifiers; Piecewise linear techniques; Switching systems; Analog electronics; Dissipative systems; Electronic implementations; Mathematical expressions; Multi-scroll attractors; Multi-scrolls; Piece-wise linear systems; Stability indices; Eigenvalues and eigenfunctions

Digital Object Identifier (DOI)

• 10.1142/S0218127417500936

start page

end page

volume

• 27

issue

• 6