Abstract
In the chaos literature, there is currently significant interest in the discovery of new chaotic systems with hidden chaotic attractors. A new 4-D chaotic system with only two quadratic nonlinearities is investigated in this work. First, we derive a no-equilibrium chaotic system and show that the new chaotic system exhibits hidden attractor. Properties of the new chaotic system are analyzed by means of phase portraits, Lyapunov chaos exponents, and Kaplan-Yorke dimension. Then an electronic circuit realization is shown to validate the chaotic behavior of the new 4-D chaotic system. Finally, the physical circuit experimental results of the 4-D chaotic system show agreement with numerical simulations.
Highlights
Chaos theory deals with nonlinear dynamical systems that are highly sensitive to initial conditions
We propose a new 4-D chaotic system with two quadratic nonlinearities given by
We show that the system (1) displays chaotic behaviour and hidden attractor when a = 4, b = 40 (2)
Summary
Chaos theory deals with nonlinear dynamical systems that are highly sensitive to initial conditions. Such nonlinear systems are characterized by the existence of a positive Lyapunov exponent. A self-excited attractor has a basin of attraction which is excited from unstable equilibrium points. A hidden attractor has a basin of attraction which does not contain neighbourhoods of equilibrium points. Some recent examples of self-excited attractors are Vaidyanathan systems ([36]-[37]), Zhu system [38], Sprott system [39], etc. The main contribution of this work is the finding of a new 4-D chaotic system with hidden attractor.
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