Complete global synchronization of van der Pol oscillators
POSTER
Abstract
Complete global synchronization of van der Pol oscillators
Seido Nagano
Department of Bioinformatics, Ritsumeilan University, Japan
https://sysbio-nagano.org/
Synchronization is a phenomenon in which the phase difference between oscillators disappears. Therefore, historically, the theory of synchronization has been constructed so as to follow changes in phase over time. Although adoption of the phase dynamics for the synchronization study is understandable mathematically, it is a formidable task for individual cells to know the phases of neighbor cells and the existence of such a biochemical system is not proved yet. This strongly suggests a different mechanism for synchronization in biology.
We propose a scheme to achieve complete synchronization between vdP oscillators using a superposition of oscillator variables ∑x_{i}. This may be a kind of paradigm shift in synchronization, but it meets the following three synchronization conditions.
(1)The synchronous state should match the solution of the vdP equation. That is, the effect of the introduced interaction term should vanish when synchronization is achieved.
(2) Only in-phase synchronization can be obtained.
(3) Achieving synchronization should not depend on initial values.
The prototype of our scheme was derived from research on multicellular systems about 20 years ago [1]. Although the synchronization itself was achieved, unfortunately the synchronization condition (1) could not be met.
References
[1] S. Nagano, “Receptors as a master key for synchronization of rhythms.” Phys. Rev. E67, 056215(2003).
[2] S. Nagano, "Complete global synchronization of van der Pol oscillators." to be submitted to Phys. Rev.E.
Seido Nagano
Department of Bioinformatics, Ritsumeilan University, Japan
https://sysbio-nagano.org/
Synchronization is a phenomenon in which the phase difference between oscillators disappears. Therefore, historically, the theory of synchronization has been constructed so as to follow changes in phase over time. Although adoption of the phase dynamics for the synchronization study is understandable mathematically, it is a formidable task for individual cells to know the phases of neighbor cells and the existence of such a biochemical system is not proved yet. This strongly suggests a different mechanism for synchronization in biology.
We propose a scheme to achieve complete synchronization between vdP oscillators using a superposition of oscillator variables ∑x_{i}. This may be a kind of paradigm shift in synchronization, but it meets the following three synchronization conditions.
(1)The synchronous state should match the solution of the vdP equation. That is, the effect of the introduced interaction term should vanish when synchronization is achieved.
(2) Only in-phase synchronization can be obtained.
(3) Achieving synchronization should not depend on initial values.
The prototype of our scheme was derived from research on multicellular systems about 20 years ago [1]. Although the synchronization itself was achieved, unfortunately the synchronization condition (1) could not be met.
References
[1] S. Nagano, “Receptors as a master key for synchronization of rhythms.” Phys. Rev. E67, 056215(2003).
[2] S. Nagano, "Complete global synchronization of van der Pol oscillators." to be submitted to Phys. Rev.E.
Presenters
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Seido Nagano
Ritsumeikan University
Authors
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Seido Nagano
Ritsumeikan University