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The simplest 4-D chaotic system with line of equilibria, chaotic 2-torus and 3-torus behaviour

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Abstract

The paper reports the simplest 4-D dissipative autonomous chaotic system with line of equilibria and many unique properties. The dynamics of the new system contains a total of eight terms with one nonlinear term. It has one bifurcation parameter. Therefore, the proposed chaotic system is the simplest compared with the other similar 4-D systems. The Jacobian matrix of the new system has rank less than four. However, the proposed system exhibits four distinct Lyapunov exponents with \((+, 0, -, -)\) sign for some values of parameter and thus confirms the presence of chaos. Further, the system shows chaotic 2-torus \((+,0,0,-)\), quasi-periodic \([(0,0,-,-), (0,0,0,-)]\) and multistability behaviour. Bifurcation diagram, Lyapunov spectrum, phase portrait, instantaneous phase plot, Poincaré map, frequency spectrum, recurrence analysis, 0–1 test, sensitivity to initial conditions and circuit simulation are used to analyse and describe the complex and rich dynamic behaviour of the proposed system. The hardware circuit realisation of the new system validates the MATLAB simulation results. The new system is developed from the well-known Rossler type-IV 3-D chaotic system.

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Author thanks editor and anonymous reviewers for their valuable suggestions that helped to improve the standard of the paper.

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  1. National Institute of Technology Silchar, Silchar, India

    Jay Prakash Singh & B. K. Roy

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  1. Jay Prakash Singh
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Singh, J.P., Roy, B.K. The simplest 4-D chaotic system with line of equilibria, chaotic 2-torus and 3-torus behaviour. Nonlinear Dyn 89, 1845–1862 (2017). https://doi.org/10.1007/s11071-017-3556-4

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