Regular Article

Synchronization patterns in LIF neuron networks: merging nonlocal and diagonal connectivity

¹ Institute of Nanoscience and Nanotechnology, National Center for Scientific Research “Demokritos”, 15341 Athens, Greece
² Section of Solid State Physics, Department of Physics, National and Kapodistrian University of Athens, 15784 Athens, Greece
³ School of Electrical and Computer Engineering, National Technical University of Athens, 15780 Athens, Greece

^a e-mail: a.provata@inn.demokritos.gr

Received: 31 July 2018
Received in final form: 6 October 2018
Published online: 5 December 2018

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 favored 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 σ < 1 the synchronous regions have mean phase velocities lower than the asynchronous, while the opposite holds for σ > 1. In the intermediate regime, σ ~ 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 and diagonal coupling generate chimera states with two different levels of synchronous domains mediated by asynchronous regions.