## In-phase and antiphase complete chaotic synchronization in symmetrically coupled discrete maps.(English)Zbl 1026.37037

The authors consider the system of coupled cubic maps $$x_{n+1}=f(x_n) +\gamma (f(y_n) -f(x_n))$$, $$y_{n+1}=f(y_n) +\gamma (f(x_n) -f(y_n))$$, where $$f(x)=(a-1)x-ax^3$$. Two synchronization regimes are possible in this system: $$x=y$$ and $$x=-y$$. The authors call them complete in-phase and antiphase synchronization, respectively. The main purpose of the paper is to give a detailed study of the bifurcational mechanisms involved in appearance of both types of synchronization. Feedback control method is also used to achieve antiphase synchronization.

### MSC:

 37E99 Low-dimensional dynamical systems 34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations 93B52 Feedback control 37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems 37E05 Dynamical systems involving maps of the interval
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