Synchronization of infinitely many coupled limit-cycle type oscillators

Shiino, Mastoshi; Frankowicz, Marek

doi:10.1016/0375-9601(89)90187-4

Cited by 69 publications

(33 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In particular, it was established that a fairly general class of such systems can exhibit amplitude death in case the individual oscillator frequencies are sufficiently different and the coupling is diffusive. In a similar vein, it was shown that a network of limit cycle oscillators can experience amplitude death if there is a distribution in frequencies [26][27][28].…”

Section: Introductionmentioning

confidence: 93%

See 1 more Smart Citation

Total and partial amplitude death in networks of diffusively coupled oscillators

Atay

2003

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

Networks of weakly nonlinear oscillators are considered with diffusive and timedelayed coupling. Averaging theory is used to determine parameter ranges for which the network experiences amplitude death, whereby oscillations are quenched and the equilibrium solution has a large domain of attraction. The amplitude death is shown to be a common phenomenon, which can be observed regardless of the precise nature of the nonlinearities and under very general coupling conditions. In addition, when the network consists of dissimilar oscillators, there exist parameter values for which only parts of the network are suppressed. Sufficient conditions are derived for total and partial amplitude death in arbitrary network topologies with general nonlinearities, coupling coefficients, and connection delays.

show abstract

Section: Introductionmentioning

confidence: 93%

“…Recalling that K ii = 0, and using (26) and (41), the divergence of the vector field defined by the right hand side is calculated as…”

Section: Network Of Oscillatorsmentioning

confidence: 99%

Total and partial amplitude death in networks of diffusively coupled oscillators

Atay

2003

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

show abstract

“…Most of the works related to collective synchronization in the last decade studied populations of stable limit cycle oscillators described by ordinary differential equations continuously coupled in time [18,19,20,21,22,23,24,25,26,27]. Much theoretical understanding has been obtained for such systems, as well on models where the phases are the only relevant dynamical parameters [18,19,20,21,22,23,24,25,28,29,30] or on models where phase and amplitude can vary [26,31,27], and for populations of identical or almost similar oscillators.…”

Section: Introductionmentioning

confidence: 99%

Synchronization of integrate and fire oscillators with global coupling

Bottani

1996

Phys. Rev. E

View full text Add to dashboard Cite

In this article we study the behavior of globally coupled assemblies of a large number of Integrate and Fire oscillators with excitatory pulse-like interactions. On some simple models we show that the additive effects of pulses on the state of Integrate and Fire oscillators are sufficient for the synchronization of the relaxations of all the oscillators. This synchronization occurs in two forms depending on the system: either the oscillators evolve "en bloc" at the same phase and therefore relax together or the oscillators do not remain in phase but their relaxations occur always in stable avalanches. We prove that synchronization can occur independently of the convexity or concavity of the oscillators evolution function. Furthermore the presence of disorder, up to some level, is not only compatible with synchronization, but removes some possible degeneracy of identical systems and allows new mechanisms towards this state.

show abstract

“…All the previous studies show that the mean-field coupling in oscillators can induce AD only [15][16][17]. Only in Refs.…”

Section: Introductionmentioning

confidence: 99%

“…In the above mentioned studies the role of mean-field diffusive coupling on the occurrence of OD, and the AD-OD transition is not considered; mean-field coupling is one of the most widely studied topics because of its presence in many natural phenomena in the field of biology, physics, and engineering [15][16][17][18]. All the previous studies show that the mean-field coupling in oscillators can induce AD only [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Transition from amplitude to oscillation death under mean-field diffusive coupling

Banerjee

Ghosh

2014

Phys. Rev. E

View full text Add to dashboard Cite

We study the transition from amplitude death (AD) to oscillation death (OD) state in limit-cycle oscillators coupled through mean-field diffusion. We show that this coupling scheme can induce an important transition from AD to OD even in identical limit cycle oscillators. We identify a parameter region where OD and a novel nontrivial AD (NT-AD) state coexist. This NT-AD state is unique in comparison with AD owing to the fact that it is created by a subcritical pitchfork bifurcation, and parameter mismatch does not support but destroy this state. We extend our study to a network of mean-field coupled oscillators to show that the transition scenario preserves and the oscillators form a two cluster state.

show abstract

Synchronization of infinitely many coupled limit-cycle type oscillators

Cited by 69 publications

References 11 publications

Total and partial amplitude death in networks of diffusively coupled oscillators

Total and partial amplitude death in networks of diffusively coupled oscillators

Synchronization of integrate and fire oscillators with global coupling

Transition from amplitude to oscillation death under mean-field diffusive coupling

Contact Info

Product

Resources

About