Abstract
In this paper, a chaotic three dimansional dynamical system is proposed, that is a modification of the system in Volos et al. (2017). The new system has two hyperbolic sine nonlinear terms, as opposed to the original system that only included one, in order to optimize system’s chaotic behavior, which is confirmed by the calculation of the maximal Lyapunov exponents and Kaplan-Yorke dimension. The system is experimentally realized, using Bi-color LEDs to emulate the hyperbolic sine functions. An extended dynamical analysis is then performed, by computing numerically the system’s bifurcation and continuation diagrams, Lyapunov exponents and phase portraits, and comparing the numerical simulations with the circuit simulations. A series of interesting phenomena are unmasked, like period doubling route to chaos, coexisting attractors and antimonotonicity, which are all verified from the circuit realization of the system. Hence, the circuit setup accurately emulates the chaotic dynamics of the proposed system.
Highlights
During the last six decades, the theory of chaotic systems has been a prominent field of study for physicists, mathematicians, and analog circuit design engineers
Chaos has so far been observed in systems related to mechanics, physics, chemistry, biology, circuits, economics and more, and the chaotic behavior has been verified via well-known theoretical and numerical tools, such as the bifurcation diagrams and the algorithm for calculating the Lyapunov Exponents (LEs)
The present paper extends the results of [27], with a more detailed dynamical analysis and a plethora of new simulations performed
Summary
During the last six decades, the theory of chaotic systems has been a prominent field of study for physicists, mathematicians, and analog circuit design engineers. Technologies 2021, 9, 15 working on developing new chaotic systems with rich dynamics. This is often done by considering existing systems and enriching their dynamics by modifying the differential/difference equations that describe them. Many chaotic circuits with a hyperbolic sine term as a nonlinearity, have been developed [14,21,22,23,24,25,26]. Due to the nature of the i − v characteristic of this term, phenomena like a period doubling route to chaos, coexisting attractors, antimonotonicity and intermittency have been observed in the above systems. Calculation of the bifurcation diagrams, Lyapunov exponents diagram and phase portraits unmask interesting phenomena for the system, like period doubling route to chaos, antimonotonicity, coexisting attractors and a higher.
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