Synchronization engineering: Theoretical framework and application to dynamical clustering
Abstract
A method for engineering the global behavior of populations of rhythmic elements is presented. The framework, which is based on phase models, allows a nonlinear time-delayed global feedback signal to be constructed which produces an interaction function corresponding to the desired behavior of the system. It is shown theoretically and confirmed in numerical simulations that a polynomial, delayed feedback is a versatile tool to tune synchronization patterns. Dynamical states consisting of one to four clusters were engineered to demonstrate the application of synchronization engineering in an experimental electrochemical system.
- Publication:
-
Chaos
- Pub Date:
- June 2008
- DOI:
- 10.1063/1.2927531
- arXiv:
- arXiv:0806.0705
- Bibcode:
- 2008Chaos..18b6111K
- Keywords:
-
- 05.45.Xt;
- 05.45.Pq;
- 02.60.-x;
- Synchronization;
- coupled oscillators;
- Numerical simulations of chaotic systems;
- Numerical approximation and analysis;
- Nonlinear Sciences - Adaptation and Self-Organizing Systems;
- Condensed Matter - Disordered Systems and Neural Networks;
- Nonlinear Sciences - Pattern Formation and Solitons;
- Physics - Chemical Physics
- E-Print:
- To appear in CHAOS