Abstract
We analyze the collective behavior of a mean-field model of phase-oscillators of Kuramoto–Daido type coupled through pairwise interactions which depend on phase differences: the coupling function is composed of three harmonics. We provide convincing evidence of a transient but long-lasting chaotic collective chaos, which persists in the thermodynamic limit. The regime is analyzed with the help of clever direct numerical simulations, by determining the maximum Lyapunov exponent and assessing the transversal stability to the self-consistent mean field. The structure of the invariant measure is finally described in terms of a resolution-dependent entropy.
Highlights
The collective dynamics of systems of coupled oscillators has been extensively studied in the last decades
We analyze the collective behavior of a mean-field model of phase-oscillators of Kuramoto–Daido type coupled through pairwise interactions which depend on phase differences: the coupling function is composed of three harmonics
When the collective dynamics is irregular, ΛT(τ ) fluctuates as confirmed by the data plotted in figure 9; this typically implies the existence of an entire range of Lyapunov exponents as captured by multifractal formalism, L(q) = lim 1 ln eΛT(τ)q, τ→∞ qτ where · denotes an ensemble average over different trajectories
Summary
The collective dynamics of systems of coupled oscillators has been extensively studied in the last decades. This is true and it has even been understood that chaos can be observed in as few as four oscillators coupled through phase differences [20] Starting from this setup and increasing the number of oscillators, two scenarios can arise: (i) either the chaos dilutes itself becoming increasingly weak and eventually disappearing; (ii) clusters form around the chaotic oscillators giving rise to a pseudo-macroscopic dynamics, i.e., a dynamics where the macroscopic chaos is just the consequence of a trivial arrangement around a few centers. Is it possible to obtain collective chaos in ensembles of identical phase oscillators?
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