Analysis of global dynamics in an unusual 3D chaotic system

In order to further understand a complex three-dimensional (3D) dynamical system showing strange chaotic attractors with two stable node-foci as its only equilibria, we analyze dynamics at infinity of the system. First, we give the complete description of the phase portrait of the system at infinity, and perform a numerical study on how the solutions reach the infinity, depending on the parameter values. Then, combining analytical and numerical techniques, we find that for the parameter value b=0, the system presents an infinite set of singularly degenerate heteroclinic cycles. It is hoped that these global study can give a contribution in understanding of this unusual chaotic system, and will shed some light leading to final revealing the true geometrical structure and the essence of chaos for the chaotic attractor.

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