Introduction to Focus Issue: Dynamics of oscillator populations

Abstract

Even after about 50 years of intensive research, the dynamics of oscillator populations remain one of the most popular topics in nonlinear science. This Focus Issue brings together studies on such diverse aspects of the problem as low-dimensional description, effects of noise and disorder on synchronization transition, control of synchrony, the emergence of chimera states and chaotic regimes, stability of power grids, etc.

Response theory identifies reaction coordinates and explains critical phenomena in noisy interacting systems

“…As mentioned in section 2, non-critical fluctuations around the invariant solution ρ 0 = 1 2π are typically Gaussian and can be described either by the Central Limit Theorem (9) or the Dean equation (10). Critical fluctuations, instead, exhibit anomalous (w.r.t.…”

“…Interacting agent models are at the basis of the microscopic description of the rich variety of collective, emergent phenomena that high dimensional complex systems often exhibit. Common applications of such models range from synchronisation of nonlinear oscillators [1][2][3][4][5][6][7][8], see also the recent special issue [9], phase transitions in complex energy landscapes [10,11] to opinion dynamics and consensus formation [12,13], socio-economic sciences [14,15], life sciences [16], the dynamics of the brain [17], formation of swarms [18,19], dynamical networks [20], self-gravitating systems [21,22] and algorithms for optimisation and training of neural networks [23][24][25]. In the thermodynamic limit, such systems can exhibit phase transitions resulting from the interplay between the interaction among the agents, their internal dynamics and the noise.…”