Quantifying the synchronizability of externally driven oscillators.
This paper is focused on the problem of complete synchronization in arrays of externally driven identical or slightly different oscillators. These oscillators are coupled by common driving which makes an occurrence of generalized synchronization between a driving signal and response oscillators possible. Therefore, the phenomenon of generalized synchronization is also analyzed here. The research is concentrated on the cases of an irregular (chaotic or stochastic) driving signal acting on continuous-time (Duffing systems) and discrete-time (Henon maps) response oscillators. As a tool for quantifying the robustness of the synchronized state, response (conditional) Lyapunov exponents are applied. The most significant result presented in this paper is a novel method of estimation of the largest response Lyapunov exponent. This approach is based on the complete synchronization of two twin response subsystems via additional master-slave coupling between them. Examples of the method application and its comparison with the classical algorithm for calculation of Lyapunov exponents are widely demonstrated. Finally, the idea of effective response Lyapunov exponents, which allows us to quantify the synchronizability in case of slightly different response oscillators, is introduced.
Stefański
Andrzej
A
Division of Dynamics, Technical University of Lodz, Stefanowskiego 1/15, 90-924 Lodz, Poland.
D000465:Algorithms; D001683:Biological Clocks; D003198:Computer Simulation; D005246:Feedback / Q000502:physiology*; D008954:Models, Biological; D017711:Nonlinear Dynamics