A 3D nonlinear chaotic system, called the T system, is analyzed in this paper. Horseshoe chaos is investigated via the heteroclinic Shilnikov method constructing a heteroclinic connections between the saddle equilibrium points of the system. Partially numerical computations are carried out to support the analytical results.

No abstract

Degenerate Chenciner bifurcation in generic discrete-time dynamical systems is studied in this work. While the nondegenerate Chenciner bifurcation can be described by two bifurcation diagrams, the degeneracy we studied in this work gives rise to 32 different bifurcation diagrams.

No abstract

Generic results for degenerate Chenciner (generalized Neimark–Sacker) bifurcation are obtained in the present work. The bifurcation arises from two-dimensional discrete-time systems with two independent parameters. We define in this work a new transformation of parameters, which enables the study of the bifurcation when degeneracy occurs. By the four bifurcation diagrams we obtained, new behaviors hidden by the degeneracy are brought to light.