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

Astakhov, Vladimir; Shabunin, Alexey; Klimshin, Alexander; Anishchenko, Vadim

Discrete Dyn. Nat. Soc. 7, No. 4, 215-229 (2002).

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.

Reviewer: Sergiy Yanchuk (Berlin)

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

Keywords:

antisynchronization; complete synchronization; coupled cubic maps