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In order to further understand a complex 3-D dynamical system proposed by Qi et al, showing four-wing chaotic attractors with very complicated topological structures over a large range of parameters, we study degenerate Hopf bifurcations in the system. It exhibits the result of a period-doubling cascade to chaos from a Hopf bifurcation point. The theoretical analysis and simulations demonstrate the rich dynamics of the system.
A fractional differential controller for incommensurate fractional unified chaotic system is described and proved by using the Gershgorin circle theorem in this paper. Also, based on the idea of a nonlinear observer, a new method for generalized synchronization (GS) of this system is proposed. Furthermore, the GS technique is applied in secure communication (SC), and a chaotic masking system is designed. Finally, the proposed fractional differential controller, GS and chaotic masking scheme are...
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