Autonomous and forced dynamics of oscillator ensembles with global nonlinear coupling: An experimental study

Abstract

We perform experiments with 72 electronic limit-cycle oscillators, globally coupled via a linear or nonlinear feedback loop. While in the linear case we observe a standard Kuramoto-like synchronization transition, in the nonlinear case, with increase of the coupling strength, we first observe a transition to full synchrony and then a desynchronization transition to a quasiperiodic state. However, in this state the ensemble remains coherent so that the amplitude of the mean field is nonzero, but the frequency of the mean field is larger than frequencies of all oscillators. Next, we analyze effects of common periodic forcing of the linearly or nonlinearly coupled ensemble and demonstrate regimes when the mean field is entrained by the force whereas the oscillators are not.

Interplay of coupling and common noise at the transition to synchrony in oscillator populations

“…We consider phase oscillators, what corresponds to the situation of small noise, so that noise always tends to synchronize the ensemble. This setup corresponds to experiments with metronomes on a common support18, if the latter is subject to a random force, and to experiments with coupled electronic oscillators1920 with an additional driving noisy current. Our theory generalizes previous studies of noise-driven ensembles with2122 and without coupling23 (dynamics of two oscillators with coupling and common and intrinsic noises has been studied in ref.…”

From chaos to quasi-periodicity

“…Then, a soft birth of a two-frequency torus occurs, which is caused by the NeimarkSacker bifurcation NS and characterized by two zero exponents Λ 1 = Λ 2 = 0. A further decrease in μ leads to the birth of a three-frequency torus with three zero Lyapunov exponents 3) . This is caused by the quasi-periodic Hopf bifurcation QH [25] and easily detected in Fig.…”

“…The problem of interaction between oscillators is a topic of interest in various fields of physics, chemistry and biology [1][2][3][4][5][6][7][8]. The simplest case is when individual oscillators exhibit periodic oscillations.…”

Dynamics of coupled chaotic oscillators: from chaos to quasiperiodicity

“…При дальнейшем уменьшении связи наблюдается возникновение трехчастотного тора с тремя нулевыми показателями. 3 Это происходит в результате квази-периодической бифуркации Хопфа (QH) [25]. Этот факт хорошо идентифицируется с помо-щью графика на рисунке 4: до точки бифуркации третий и четвертый показатели равны, Λ 3 = Λ 4 .…”

“…Задача о взаимодействии осцилляторов различной природы привлекает внимание ис-следователей в разных областях физики, химии, биологии [1][2][3][4][5][6][7][8]. В простейшем случае ин-дивидуальные осцилляторы демонстрируют периодические колебания.…”