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A new 5D hyperchaotic system based on modified generalized Lorenz system

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Abstract

This paper reports a new five-dimensional (5D) hyperchaotic system with three positive Lyapunov exponents, which is generated by adding a linear controller to the second equation of a 4D system that is obtained by coupling of a 1D linear system and a 3D modified generalized Lorenz system. This hyperchaotic system has very simple algebraic structure but can exhibit complex dynamical behaviors. Of particular interest are the observations that the hyperchaotic system has a hyperchaotic attractor with three positive Lyapunov exponents under a unique equilibrium, three or infinite equilibria, and there are three types of coexisting attractors of this new 5D hyperchaotic system. Numerical analysis of phase trajectories, Lyapunov exponents, bifurcation, Poincaré projections and power spectrum verifies the existence of the hyperchaotic and chaotic attractors. Moreover, stability of hyperbolic or non-hyperbolic equilibria and two complete mathematical characterization for 5D Hopf bifurcation are rigorously studied. Finally, some electronic circuits are designed to implement the 5D hyperchaotic system.

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Acknowledgements

This work was partly supported by the National Natural Science Foundation of China (Nos. 11271139, 11671149) and the Natural Science Foundation of Guangdong Province (No. 2014A030313256).

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  1. School of Mathematical Sciences, South China University of Technology, Guangzhou, 510640, People’s Republic of China

    Qigui Yang & Meili Bai

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  1. Qigui Yang
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  2. Meili Bai
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Correspondence to Qigui Yang.

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Yang, Q., Bai, M. A new 5D hyperchaotic system based on modified generalized Lorenz system. Nonlinear Dyn 88, 189–221 (2017). https://doi.org/10.1007/s11071-016-3238-7

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