TY - JOUR

T1 - Scaling laws in the transient dynamics of firefly-like oscillators

AU - Rubido, N.

AU - Cabeza, C.

AU - Ávila, G. M.Ramírez

AU - Martí, A.

PY - 2011

Y1 - 2011

N2 - Fireflies constitute a paradigm of pulse-coupled oscillators. In order to tackle the problems related to synchronisation transients of pulse-coupled oscillators, a Light-Controlled Oscillator (LCO) model is presented. A single LCO constitutes a one-dimensional relaxation oscillator described by two distinct time-scales meant to mimic fireflies in the sense that: it is capable of emitting light in a pulse-like fashion and detect the emitted by others in order to adjust its oscillation. We present dynamical results for two interacting LCOs in the torus for all possible coupling configurations. Transient times to the synchronous limit cycle are obtained experimentally and numerically as a function of initial conditions and coupling strengths. Scaling laws are found based on dimensional analysis and critical exponents calculated, thus, global dynamic is restricted. Furthermore, an analytical orthogonal transformation that allows to calculate Floquet multipliers directly from the time series is presented. As a consequence, local dynamics is also fully characterized. This transformation can be easily extended to a system with an arbitrary number of interacting LCOs.

AB - Fireflies constitute a paradigm of pulse-coupled oscillators. In order to tackle the problems related to synchronisation transients of pulse-coupled oscillators, a Light-Controlled Oscillator (LCO) model is presented. A single LCO constitutes a one-dimensional relaxation oscillator described by two distinct time-scales meant to mimic fireflies in the sense that: it is capable of emitting light in a pulse-like fashion and detect the emitted by others in order to adjust its oscillation. We present dynamical results for two interacting LCOs in the torus for all possible coupling configurations. Transient times to the synchronous limit cycle are obtained experimentally and numerically as a function of initial conditions and coupling strengths. Scaling laws are found based on dimensional analysis and critical exponents calculated, thus, global dynamic is restricted. Furthermore, an analytical orthogonal transformation that allows to calculate Floquet multipliers directly from the time series is presented. As a consequence, local dynamics is also fully characterized. This transformation can be easily extended to a system with an arbitrary number of interacting LCOs.

UR - http://www.scopus.com/inward/record.url?scp=80052042809&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/285/1/012026

DO - 10.1088/1742-6596/285/1/012026

M3 - Artículo

AN - SCOPUS:80052042809

VL - 285

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012026

ER -