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Methods that distinguish dynamical regimes in networks of active elementsmake it possible to design the dynamics of models of realistic networks. Aparticularly salient example is partial synchronization, which may play apivotal role in elucidating the dynamics of biological neural networks. Suchemergent partial synchronization in structurally homogeneous networks iscommonly denoted as chimera states. While several methods for detectingchimeras in networks of spiking neurons have been proposed, these are lesseffective when applied to networks of bursting neurons. Here we introduce thecorrelation dimension as a novel approach to identifying dynamic networkstates. To assess the viability of this new method, we study a network ofintrinsically Hindmarsh-Rose neurons with non-local connections. In comparisonto other measures of chimera states, the correlation dimension effectivelycharacterizes chimeras in burst neurons, whether the incoherence arises inspikes or bursts. The generality of dimensionality measures inherent in thecorrelation dimension renders this approach applicable to any dynamic system,facilitating the comparison of simulated and experimental data. We anticipatethat this methodology will enable the tuning and simulation of when modellingintricate network processes, contributing to a deeper understanding of neuraldynamics.

Dynamical manifold dimensionality as characterization measure of chimera states in bursting neuronal networks