Dynamics of a new Lorenz-like chaotic system.(English)Zbl 1202.34083

Authors’ abstract: The present work is devoted to giving new insights into a new Lorenz-like chaotic system. The local dynamical entities, such as the number of equilibria, the stability of the hyperbolic equilibria and the stability of the non-hyperbolic equilibrium obtained by using the center manifold theorem, the pitchfork bifurcation and the degenerate pitchfork bifurcation, Hopf bifurcations and the local manifold character, are all analyzed when the parameters are varied in the space of parameters. The existence of homoclinic and heteroclinic orbits of the system is also rigorously studied. More exactly, for $$b\geq 2a>0$$ and $$c>0$$, we prove that the system has no homoclinic orbit but has two and only two heteroclinic orbits.

MSC:

 34C28 Complex behavior and chaotic systems of ordinary differential equations
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References:

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