Synergetic Approach to the Phenomena of Mode-Locking in Nonlinear Systems

Aizawa, Yōji

doi:10.1143/ptp.56.703

Cited by 55 publications

(11 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The earlier attempt due to Winfree is based on aphase description (Winfree, 1967). Approaches not based on a phase description also exist (Aizawa, 1976;Yamaguchi et al, 1981). Approaches not based on a phase description also exist (Aizawa, 1976;Yamaguchi et al, 1981).…”

Section: Synchronization As a Mode Of Self-organizationmentioning

confidence: 99%

Chemical Oscillations, Waves, and Turbulence

Kuramoto

1984

Springer Series in Synergetics

6,241

6,896

View full text Add to dashboard Cite

Section: Synchronization As a Mode Of Self-organizationmentioning

confidence: 99%

Chemical Oscillations, Waves, and Turbulence

Kuramoto

1984

Springer Series in Synergetics

6,241

6,896

View full text Add to dashboard Cite

“…Mutual synchronization of a system occurs when interacting oscillators affect their phases so as to spontaneously lock on to a particular frequency or phase (Pikovsky et al 2003). In the works of Aizawa (1976) and Mirollo & Strogatz (1990), the oscillator phase interactions are generalized to incorporate amplitude variation effects. Amplitude and phase coupling between oscillators result in a variety of interesting physical phenomena.…”

Section: Introductionmentioning

confidence: 99%

Networked-oscillator-based modeling and control of unsteady wake flows

2018

View full text Add to dashboard Cite

A networked-oscillator-based analysis is performed to examine and control the transfer of kinetic energy for periodic bluff body flows. The dynamics of energy fluctuations in the flow field are described by a set of oscillators defined by conjugate pairs of spatial proper orthogonal decomposition (POD) modes. To extract the network of interactions among oscillators, impulse responses of the oscillators to amplitude and phase perturbations are tracked. Tracking small energy inputs and using linear regression, a networked-oscillator model is constructed that reveals energy exchange among the modes. The model captures the nonlinear interactions among the modal oscillators through a linear approximation. A large collection of system responses is aggregated to capture the general network structure of oscillator interactions. The present networked-oscillator model describes the modal perturbation dynamics more accurately than the empirical Galerkin reduced-order model. The linear network model for nonlinear dynamics is subsequently utilized to design a model-based feedback controller. The controller suppresses the modal amplitudes that result in wake unsteadiness leading to drag reduction. The strength of the proposed approach is demonstrated for a canonical example of two-dimensional unsteady flow over a circular cylinder. The present formulation enables the characterization of modal interactions to control fundamental energy transfers in unsteady bluff body flows.

show abstract

“…Synchronization effects in ensembles of selfsustained oscillators and phase oscillators with local coupling have been studied in [172,217,218,[278][279][280][281][282][283] and in many other papers and monographs. Synchronization effects in ensembles of selfsustained oscillators and phase oscillators with local coupling have been studied in [172,217,218,[278][279][280][281][282][283] and in many other papers and monographs.…”

Section: Introductionmentioning

confidence: 99%