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

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.