Evolutionary Kuramoto dynamics unravels origins of chimera states in neural populations.

Abstract

Neural synchronization is central to cognition. However, incomplete synchronization often produces chimera states, where coherent and incoherent dynamics coexist. Recent studies have suggested that these chimera states could be important in human cognitive organization. In particular, chimera states have been suggested as a regulator of cognitive integration and regulation with varying quality as humans age. While previous studies have explored such chimera states using networks of coupled oscillators, it remains unclear why neurons commit to communication or how chimera states persist. Here, we investigate the coevolution of neuronal phases and communication strategies on directed, weighted networks where interaction payoffs depend on phase alignment and may be asymmetric due to unilateral communication. The graph structure enables us to apply a game-theoretic model of Kuramoto-like oscillators to brain connectomes, and the asymmetry captures biochemical differences between communicative and non-communicative neurons. Combined, these two generalizations enable us to apply the computationally-tractable game-theoretic model of Kuramoto models to realistic brain networks and analyze the role of connectome structure on neuron communication. We find that both connection weights and directionality influence the stability of communicative strategies-and, consequently, full synchronization-as well as the strategic nature of neuronal interactions. Applying our framework to the C. elegans connectome, we show that emergent payoff structures, such as the staghunt game, control population dynamics. We demonstrate that weighted, directed connectivity in the Caenorhabditis elegans (C. elegans) connectome is sufficient to generate robust chimera states modulated by payoff asymmetries. Our computational results demonstrate a promising neurogame-theoretic perspective, leveraging evolutionary graph theory to shed light on mechanisms of neuronal coordination beyond classical synchronization models.