Abstract:Background and Objectives: In this paper we consider the peculiarity that arises during the generalized chaotic synchronization regime detection in systems with a complex attractor topology having internal symmetry. Materials and Methods: As the system under study we consider two modified Guckenheimer – Holmes discrete maps coupled unidirectionally. To detect the presence of generalized synchronization we calculate the spectrum of Lyapunov exponents and propose the modification of auxiliary system approach. Results: Considering that the symmetry in the dynamics of the autonomous response system can lead to multistability due to the drive system signal, the correct detection of generalized synchronization with the help of the auxiliary system approach may be complicated. Modification of the generalized synchronization criterion, which allows increasing the reliability of the method in such cases, has been proposed. Conclusion: The results obtained with the help of modified auxiliary system approach are in a good agreement with the calculation of Lyapunov exponents.
Fulltext:
PDF file (838 kB)