Synchronization engineering: theoretical framework and application to dynamical clustering.
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.
Kori
Hiroshi
H
Department of Mathematics, Hokkaido University, Sapporo, Hokkaido 060-0810, Japan. kori.hiroshi@ocha.ac.jp
Rusin
Craig G
CG
Kiss
István Z
IZ
Hudson
John L
JL
D000465:Algorithms; D000818:Animals; D001703:Biophysics / Q000379:methods*; D016000:Cluster Analysis; D004563:Electrochemistry / Q000379:methods*; D025461:Feedback, Physiological; D005583:Fourier Analysis; D006801:Humans; D008962:Models, Theoretical; D009474:Neurons / Q000378:metabolism; D009991:Oscillometry; D010300:Parkinson Disease / Q000378:metabolism; D015398:Signal Transduction; D013997:Time Factors