A gallery of chaotic systems with an infinite number of equilibrium points. (December 2016)

• Record Type: Journal Article
• Authors: Pham, Viet–Thanh; Jafari, Sajad; Volos, Christos; Kapitaniak, Tomasz
• Is Part Of: Chaos, solitons and fractals. Volume 93(2016)
• Page Start: 58
• Page End: 63
• Publication Date: 2016-12
• Subjects: Chaos -- Hidden attractor -- Equilibrium -- Phase portrait -- Bifurcation diagram -- Lyapunov exponent; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2016.10.002
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: In this work, a systematic search for finding chaotic systems with infinite equilibria is described. As a result, we obtained a gallery of chaotic systems with various shapes of equilibrium points such as a line, two parallel lines, a piece–wise linear curve, a parabola, a hyperbola, or a circle. Interestingly, such novel systems exhibit "hidden attractors", which play vital roles in nonlinear theory and practical engineering issues.