Synchronization patterns in LIF Neural Networks: Merging Nonlocal and Diagonal Connectivity

TL;DR

This paper explores how diagonal and combined nonlocal-diagonal connectivities influence synchronization and chimera states in Leaky Integrate-and-Fire neural networks, revealing new phenomena and parameter regimes for these complex states.

Contribution

It introduces the effects of diagonal coupling and combined connectivity on chimera states in LIF networks, identifying novel synchronization phenomena and parameter regions for their emergence.

Findings

Chimera states occur for both diagonal and combined connectivities.

Increasing coupling range favors the emergence of chimera states.

Different coupling strengths lead to distinct phase velocity behaviors.

Abstract

The effects of nonlocal and reflecting connectivities have been previously investigated in coupled Leaky Integrate-and-Fire (LIF) elements, which assimilate the exchange of electrical signals between neurons. In this work we investigate the effect of diagonal coupling inspired by findings in brain neuron connectivity. Multi-chimera states are reported both for the simple diagonal and combined nonlocal-diagonal connectivities and we determine the range of optimal parameter regions where chimera states appear. Overall, the measures of coherence indicate that as the coupling range increases (below all-to-all coupling) the emergence of chimera states is favoured and the mean phase velocity deviations between coherent and incoherent regions become more prominent. A number of novel synchronization phenomena are induced as a result of the combined connectivity. We record that for coupling strengths $\sigma < 1$ the synchronous regions have mean phase velocities lower than the asynchronous, while the opposite holds for $\sigma > 1$. In the intermediate regime, $\sigma \sim 1$, the oscillators have common mean phase velocity (i.e., are frequency-locked) but different phases (i.e., they are phase-asynchronous). Solitary states are recorded for small values of the coupling strength, which grow into chimera states as the coupling strength increases.We determine parameter values where the combined effects of nonlocal-diagonal coupling generate chimera states with two different levels of synchronous domains mediated by asynchronous regions.