Synchronization regions of two pulse-coupled electronic piecewise linear oscillators

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

“…Although Eq. (1) is a piecewise linear coupled set of differential equations, a general and unique analytical solution, which is piecewise smooth, exists for each initial condition [5]. In particular, a solution for two coupled LCOs in a MS (left panel) and MI (right panel) configuration are shown in Fig.…”

“…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].…”

Scaling Laws in the Transient Dynamics of Firefly-like Oscillators

“…2. It has been shown [18] analytically that the system exhibits two fixed points in the return map (one stable and the other unstable) for a wide range of frequency detuning between oscillators and coupling strengths. Thus, coupled dynamics tends to create two limit cycles, one attractive and other repelling.…”

“…Whereas in the (0, 0) (upper right section) is slightly translated. This is explained by analysing the return maps, where the fixed point is not located exactly in a corner [18]. Therefore, calculations of Floquet exponents introduce a systematic error that can be dismissed if the charging part of the time series is taken into account.…”

“…Time-scale parameters for both systems are set in order to have identical individuals oscillating at a ω = 30 rad/s frequency. The Kuramoto model is solved by means of a fourth order Runge-Kutta schemes, whilst LCOs are solved by using piecewise analytic solutions numerically implemented as in previous works [18]. As can be seen from these figures, transients behave in a self-similar way.…”