Dynamical analysis of a new autonomous 3-D chaotic system only with stable equilibria. (English) Zbl 1213.37061

The authors introduce a new chaotic system described by a system of three ordinary differential equations with six terms, one of which is nonlinear (exponential function). They study its properties with the goal to compare the topological structure of a new system with that of a Lorenz system and some other known Lorenz-like chaotic systems. The existence of singularly degenerate heteroclinic cycles, periodic solutions and chaotic attractors are investigated. It is shown that in the case when all equilibria of a new system are stable, the system gives rise to a double-scroll chaotic attractor which does not satisfy the conditions of the Sil’nikov homoclinic theorem. The results of numerical simulations are also provided.


37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C28 Complex behavior and chaotic systems of ordinary differential equations
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