Multistability and evolution of chimera states in a network of type II Morris–Lecar neurons with asymmetrical nonlocal inhibitory connections
Over the past decades, one of the most exciting and fast developed area of modern synchronization theory is the study of chimera states. Such chimera states states are characterized by the coexistence of multiple synchronous and asynchronous domains, despite that the network topology does not at all predict such structures. Moreover, these states are of interest for describing, for example, partially synchronous activity in the brain neuronal networks and circuits. During cognitively effortful tasks one can observe complex patterns of synchronous and non-synchronous brain activity that wax, wane and reshape themselves either rapidly or slowly, as the task demands. We may posit that dynamics of chimeras and their multistability may be a key to how brain networks form activity patterns that allow to implement such complex cognitive tasks (e.g. contextual memory states, multi-item working memory). In this work we study the evolution of chimera states in a network of Morris-Lecar neurons whose excitability properties echo those of a major class of cortical interneurons and are arranged in a network with asymmetrical nonlocal inhibitory connections mimicking interneuronal networks in the cortex and hippocampus. Using a new measure of network coherence that we have previously introduced (the Adaptive Coherence Measure, ACM) we partition the network state space into regions with a variety of collective behaviors: antiphase synchronous clusters, travelling waves, different types of chimera states as well as spiking death regime; and uncover multistability between these various regimes. We followed how the various chimera states evolve from one to another with key network parameters and found that these switches can be either fast or that the network can demonstrate long transients leading to a quasi-persistence of activity patterns in the border regions hinting at near-criticality behaviors. Hence, our work shows that spiking networks with even a relatively simple connection topologies are capable of complex dynamics, such as may underlie cognitively relevant brain activity.