Dynamics of the Lü System on the Invariant Algebraic Surface and at infinity

Firstly, the dynamics of the Lu system having an invariant algebraic surface are analyzed. Secondly, by using the Poincare compactification in ℝ3, a global analysis of the system is presented, including the complete description of its dynamic behavior on the sphere at infinity. Lastly, combining analytical and numerical techniques, it is shown that for the parameter value b = 0, the system presents an infinite set of singularly degenerate heteroclinic cycles. The chaotic attractors for the Lu system in the case of small b > 0 are found numerically, hence the singularly degenerate heteroclinic cycles.

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