A modified Rössler prototype-4 system based on Chua's diode nonlinearity : Dynamics, multistability, multiscroll generation and FPGA implementation. (November 2020)

• Record Type: Journal Article
• Authors: Kuate, Paul Didier Kamdem; Tchendjeu, Achille Ecladore Tchahou; Fotsin, Hilaire
• Is Part Of: Chaos, solitons and fractals. Volume 140(2020)
• Publication Date: 2020-11
• Subjects: Multistability -- Multiscroll generation -- Antimonotonicity -- Chua's diode -- Rössler system -- FPGA Implementation; 00–01; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2020.110213
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: The process of designing a new 3D system from Rössler prototype-4 equations and Chua's diode nonlinearity is detailed. A variety of features are highlighted: multiplier-free, variable-boostable, total amplitude control. Its complex dynamics is numerically demonstrated using bifurcation diagrams, Lyapunov exponents spectra and basins of attraction. A simple approach of multiscroll generation and a rare case of up to eight coexisting attractors are demonstrated. Analog circuit and FPGA implementation are designed and presented. Abstract: Since the introduction of chaos theory, the design of simple chaotic systems exhibiting complex dynamics has always been a hot research topic. Multistability and multiscroll generation are studied and applied in several domains like cryptography and engineering. This paper aims to construct a new three-dimensional chaotic system with up to eight coexisting attractors, inspired from one of the first prototype equations introduced by Rössler in 1976. The proposed system is multiplier-free, variable boostable and exclusively based on the Chua's diode nonlinearity. The use of familiar tools such as bifurcation diagrams, Lyapunov exponents spectra, basins of attraction, frequency power spectra as well as Poincaré map help to demonstrate its richer and complex dynamics. Chaos, antimonotonicity, total amplitude control, multistability as well as the multiscroll generation are investigated. Finally, an FPGA-based implementation is presented to confirm its feasibility.