Directed Flow of Information in Chimera States

Abstract

We investigated interactions within chimera states in a phase oscillator network with two coupled subpopulations. To quantify interactions within and between these subpopulations, we estimated the corresponding (delayed) mutual information that -in general -quantifies the capacity or the maximum rate at which information can be transferred to recover a sender's information at the receiver with a vanishingly low error probability. After verifying their equivalence with estimates based on the continuous phase data, we determined the mutual information using the time points at which the individual phases passed through their respective Poincaré sections. This stroboscopic view on the dynamics may resemble, e.g., neural spike times, that are common observables in the study of neuronal information transfer. This discretization also increased processing speed significantly, rendering it particularly suitable for a fine-grained analysis of the effects of experimental and model parameters. In our model, the delayed mutual information within each subpopulation peaked at zero delay, whereas between the subpopulations it was always maximal at non-zero delay, irrespective of parameter choices. We observed that the delayed mutual information of the desynchronized subpopulation preceded the synchronized subpopulation. Put differently, the oscillators of the desynchronized subpopulation were 'driving' the ones in the synchronized subpopulation. These findings were also observed when estimating mutual information of the full phase trajectories. We can thus conclude that the delayed mutual information of discrete time points allows for inferring a functional directed flow of information between subpopulations of coupled phase oscillators.

Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review

“…Martens et al [169] outlined the basins of attraction of the coexisting stable synchrony patterns and thereby answering the question as to which (macroscopic or microscopic) initial conditions converge to either state. Through directed perturbations it is possible to switch between different synchrony patterns and thus functional configurations of the network that are of relevance in neuroscience [32,170], thus embodying memory states or controlling the predominant direction of information flow between subpopulations of oscillators [33]. Further work addresses the robustness of chimeras against various inhomogeneities, including heterogeneous frequencies [100,171], network heterogeneity [172], and additive noise [171].…”

“…In the following, we consider a network where each neuron emits a pulse-like signal of the form P n (θ ) = a n (1 -cos θ ) n (33) as it fires (the phase θ increases through π , see Figs. 5 and 2).…”

“…The dynamical repertoire of a population of Theta neurons can be understood using the Ott-Antonsen equations for the limit N → ∞. We follow the work by Luke et al [93] who considered a network with pulsatile coupling (33) with nontrivial width n = 2 and direct synaptic coupling. According to (35) the pulse shape evaluates to P (2)…”

“…In the brain, there are a wide range of rhythms but the presence of dominant rhythms in different frequency bands indicate that some level of synchrony is common at multiple scales [25,26]. Indeed, synchrony has been associated with solving functional tasks including, but not limited to, memory [27], computational functions [28], cognition [29], attention [30,31], routing of information [31][32][33], control of gait and motion [34], or breathing [35,36]. As a specific example, coordination of dynamics at the theta frequency (4)(5)(6)(7)(8)(9)(10)(11)(12) between hippocampus and frontal cortex is enhanced in spatial memory tasks [37].…”

Phase Synchronization in Neural Systems

“…1. To generate the figure, we used a stochastic extension of the Kuramoto model (7) and defined spike events via Poincaré sections of the phase oscillators' trajectories (Deschle et al 2019). At around t % 90 ms, the coupling strengths k was increased beyond the critical value k c , and, after a brief transient period, the population fires in synchrony at a rate given by the mean of the oscillators natural frequencies.…”