Designing torus-doubling solutions to discrete time systems by hybrid projective synchronization

• Report a novel method for designing torus-doubling solution with desired property.
• The method is entirely different from the conventional anti-control of bifurcation.
• It can completely solve possible physical meaning conflict of the created solution.
• New interdisciplinary between chaos synchronization & anti-control of bifurcation.

Doubling of torus occurs in high dimensional nonlinear systems, which is related to a certain kind of typical second bifurcations. It is a nontrivial task to create a torus-doubling solution with desired dynamical properties based on the classical bifurcation theories. In this paper, dead-beat hybrid projective synchronization is employed to build a novel method for designing stable torus-doubling solutions into discrete time systems with proper properties to achieve the purpose of utilizing bifurcation solutions as well as avoiding the possible conflict of physical meaning of the created solution. Although anti-controls of bifurcation and chaos synchronizations are two different topics in nonlinear dynamics and control, the results imply that it is possible to develop some new interdisciplinary methods between chaos synchronization and anti-controls of bifurcations.