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New Chaotic Dynamical System with a Conic-Shaped Equilibrium Located on the Plane Structure

Department of Radio Electronics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technicka 3082/12, Brno 61600, Czech Republic
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Appl. Sci. 2017, 7(10), 976; https://doi.org/10.3390/app7100976
Received: 25 August 2017 / Revised: 11 September 2017 / Accepted: 20 September 2017 / Published: 22 September 2017
This paper presents a new autonomous deterministic dynamical system with equilibrium degenerated into a plane-oriented hyperbolic geometrical structure. It is demonstrated via numerical analysis and laboratory experiments that the discovered system has both a structurally stable strange attractor and experimentally measurable chaotic behavior. It is shown that the evolution of complex dynamics can be associated with a single parameter of a mathematical model and, due to one-to-one correspondence, to a single circuit parameter. Two-dimensional high resolution plots of the largest Lyapunov exponent and basins of attraction expressed in terms of final state energy are calculated and put into the context of the discovered third-order mathematical model and real chaotic oscillator. Both voltage- and current-mode analog chaotic oscillators are presented and verified by visualization of the typical chaotic attractor in a different fashion. View Full-Text
Keywords: analog oscillator; autonomous deterministic system; circuit synthesis; chaos; nonlinear dynamics; strange attractor analog oscillator; autonomous deterministic system; circuit synthesis; chaos; nonlinear dynamics; strange attractor
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Petrzela, J.; Gotthans, T. New Chaotic Dynamical System with a Conic-Shaped Equilibrium Located on the Plane Structure. Appl. Sci. 2017, 7, 976.

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