Controlled generation of switching dynamics among metastable states in pulse-coupled oscillator networks

Hai-Lin Zou, Yuichi Katori, Zi-Chen Deng, Kazuyuki Aihara, Ying-Cheng Lai

Research output: Contribution to journalArticle

5 Citations (Scopus)
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Abstract

Switching dynamics among saddles in a network of nonlinear oscillators can be exploited for information encoding and processing (hence computing), but stable attractors in the system can terminate the switching behavior. An effective control strategy is presented to sustain switching dynamics in networks of pulse-coupled oscillators. The support for the switching behavior is a set of saddles, or unstable invariant sets in the phase space. We thus identify saddles with a common property, localize the system in the vicinity of them, and then guide the system from one metastable state to another to generate desired switching dynamics. We demonstrate that the control method successfully generates persistent switching trajectories and prevents the system from entering stable attractors. In addition, there exists correspondence between the network structure and the switching dynamics, providing fundamental insights on the development of a computing paradigm based on the switching dynamics.
Original languageEnglish
Article number103109
JournalChaos
Volume25
Issue number10
Early online date16 Sep 2015
DOIs
Publication statusPublished - 2015

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Metastable States
Coupled Oscillators
metastable state
oscillators
pulses
saddles
Saddle
Attractor
Computing
Nonlinear Oscillator
Terminate
Invariant Set
Network Structure
Control Strategy
Phase Space
coding
Encoding
Correspondence
Unstable
Paradigm

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Controlled generation of switching dynamics among metastable states in pulse-coupled oscillator networks. / Zou, Hai-Lin; Katori, Yuichi; Deng, Zi-Chen; Aihara, Kazuyuki; Lai, Ying-Cheng.

In: Chaos, Vol. 25, No. 10, 103109, 2015.

Research output: Contribution to journalArticle

Zou, Hai-Lin ; Katori, Yuichi ; Deng, Zi-Chen ; Aihara, Kazuyuki ; Lai, Ying-Cheng. / Controlled generation of switching dynamics among metastable states in pulse-coupled oscillator networks. In: Chaos. 2015 ; Vol. 25, No. 10.
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abstract = "Switching dynamics among saddles in a network of nonlinear oscillators can be exploited for information encoding and processing (hence computing), but stable attractors in the system can terminate the switching behavior. An effective control strategy is presented to sustain switching dynamics in networks of pulse-coupled oscillators. The support for the switching behavior is a set of saddles, or unstable invariant sets in the phase space. We thus identify saddles with a common property, localize the system in the vicinity of them, and then guide the system from one metastable state to another to generate desired switching dynamics. We demonstrate that the control method successfully generates persistent switching trajectories and prevents the system from entering stable attractors. In addition, there exists correspondence between the network structure and the switching dynamics, providing fundamental insights on the development of a computing paradigm based on the switching dynamics.",
author = "Hai-Lin Zou and Yuichi Katori and Zi-Chen Deng and Kazuyuki Aihara and Ying-Cheng Lai",
note = "This research was supported by the Aihara Project, the FIRST program from JSPS, initiated by CSTP, and CREST, JST. Y.C.L. was supported by ARO under Grant No. W911NF-14-1-0504. Z.C.D. was supported by the National Natural Science Foundation of China (No. 11432010). H.L.Z. was supported by “The Fundamental Research Funds for the Central Universities” (No. 3102014JCQ01036), and by the National Natural Science Foundation of China (No. 11502200). We also thank anonymous reviewers for their insightful and useful comments.",
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