Dynamical analysis of a new autonomous 3-D chaotic system only with stable equilibria (Q611220)

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.