Scaling Laws in the Transient Dynamics of Firefly-like Oscillators

Rubido, Nicolás; Cabeza, Cécilia; Ramírez-Ávila, Gonzalo Marcelo; Martı́, Arturo C.

doi:10.1088/1742-6596/285/1/012026

Cited by 3 publications

(4 citation statements)

References 22 publications

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“…The reason for such universal behavior to exist is that the system, Eq. ( 1), is scalable into a non-dimensional form which only depends on the ratio between λ and γ and the coupling strength β [6]. The atypical case, V 1 (0) = V 2 (0), corresponds to the synchronization manifold [17] of the coupled system when the LCOs have identical parameters (λ and γ), hence, its synchronization time vanishes for any coupling strength.…”

Section: Two-lco Dynamicsmentioning

confidence: 99%

See 1 more Smart Citation

The role of intermediaries in the synchronization of pulse-coupled oscillators

García

Rubido

Martı́

et al. 2014

Eur. Phys. J. Spec. Top.

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The role of intermediaries in the synchronization of small groups of light controlled oscillators (LCO) is addressed. A single LCO is a two-time-scale phase oscillator. When pulse-coupling two LCOs, the synchronization time decreases monotonously as the coupling strength increases, independent of the initial conditions and frequency detuning. In this work we study numerically the effects that a third LCO induces to the collective behavior of the system. We analyze the new system by dealing with directed heterogeneous couplings among the units. We report a novel and robust phenomenon, absent when coupling two LCOs, which consists of a discontinuous relationship between the synchronization time and coupling strength or initial conditions. The mechanism responsible for the appearance of such discontinuities is discussed.

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Section: Two-lco Dynamicsmentioning

confidence: 99%

“…In particular, a paradigmatic example of synchronous behavior is observed in gregarious fireflies communities [2]. Initially inspired in the emissions of gregarious fireflies, light controlled oscillators (LCOs) are aimed to study the mechanisms which drive their collective behavior into synchronization [3,4,5,6,7].…”

Section: Introductionmentioning

confidence: 99%

The role of intermediaries in the synchronization of pulse-coupled oscillators

García

Rubido

Martı́

et al. 2014

Eur. Phys. J. Spec. Top.

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“…Regarding relaxation oscillators, their synchronization has been widely studied when they are pulse-coupled-i.e. when the interaction occurs only during the rapid cycle phases [2, 3,[7][8][9][10][11][12][13][14][15][16][17]. This includes:…”

Section: Introductionmentioning

confidence: 99%

Synchronization dynamics of two mutually coupled 555-IC based electronic oscillators

Santillán

2018

Rev. Mex. Fís.

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We designed and implemented an electronic oscillatory system consisting of two mutually coupled oscillators (each one based on the 555-timer IC working in astable mode), and investigated its synchronization dynamics. For that purpose, we characterized the phase-locking rhythms achieved in a large set of values of the uncoupled frequency ratio and of the coupling strength between both oscillators. We further developed an ODE mathematical model that qualitative reproduces the obtained experimental results and provides further insight into the system behavior.

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“…Our circuit design is inspired on closely related experimental and theoretical work that has been carried out on forced astable multivibrators, some of which has even used the same 555 timer chip employed here [Allen, 1983a,b;Tang et al, 1983]. In particular, we followed the works of [Guisset et al, 2007;Ramírez-Ávila et al, 2003Ramírez-Ávila et al, , 2007Ramírez-Ávila et al, , 2011Ramírez-Ávila et al, , 2010Rubido et al, 2011aRubido et al, , 2009Rubido et al, , 2011b, in which oscillators based upon the 555 IC are coupled through light. In these articles, the system behavior has been extensively studied from the point of view of phase-response curves, phase dynamics, noise influence, and Arnol'd tongues; and not only for the master-slave situation, but also for mutual-interaction.…”

Section: Introductionmentioning

confidence: 99%

Periodic Forcing of a 555-IC Based Electronic Oscillator in the Strong Coupling Limit

Santillán

2016

Int. J. Bifurcation Chaos

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We designed and developed a master-slave electronic oscillatory system (based on the 555-timer IC working in the astable mode), and investigated its dynamic behavior regarding synchronization. For that purpose we measured the rotation numbers corresponding to the phase-locking rhythms achieved in a large set of values of the normalized forcing frequency (NFF) and of the coupling strength between the master and the slave oscillators. In particular we were interested in the system behavior in the strong-coupling limit, because such problem has not been extensively studied from an experimental perspective. Our results indicate that, in such a limit, a degenerate codimension-2 bifurcation point at NFF=2 exists, in which all the phase-locking regions converge. These findings were corroborated by means of a mathematical model developed to that end, as well as by ad hoc further experiments.

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Scaling Laws in the Transient Dynamics of Firefly-like Oscillators

Cited by 3 publications

References 22 publications

The role of intermediaries in the synchronization of pulse-coupled oscillators

The role of intermediaries in the synchronization of pulse-coupled oscillators

Synchronization dynamics of two mutually coupled 555-IC based electronic oscillators

Periodic Forcing of a 555-IC Based Electronic Oscillator in the Strong Coupling Limit

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