Chimeras in Leaky Integrate-and-Fire Neural Networks: Effects of Reflecting Connectivities

The effects of nonlocal and reflecting connectivity are investigated in coupled Leaky Integrate-and-Fire (LIF) elements, which assimilate the exchange of electrical signals between neurons. Earlier investigations have demonstrated that non-local and hierarchical network connectivity often induces complex synchronization patterns and chimera states in systems of coupled oscillators. In the LIF system we show that if the elements are non-locally linked with positive diffusive coupling in a ring architecture the system splits into a number of alternating domains. Half of these domains contain elements, whose potential stays near the threshold, while they are interrupted by active domains, where the elements perform regular LIF oscillations. The active domains move around the ring with constant velocity, depending on the system parameters. The idea of introducing reflecting non-local coupling in LIF networks originates from signal exchange between neurons residing in the two hemispheres in the brain. We show evidence that this connectivity induces novel complex spatial and temporal structures: for relatively extensive ranges of parameter values the system splits in two coexisting domains, one domain where all elements stay near-threshold and one where incoherent states develop with multileveled mean phase velocity distribution.Comment: 12 pages, 12 figure

Finite Size Effects in Networks of Coupled Neurons

We use extensive computer simulations to study synchronization phenomena in networks of biological neurons. Each individual neuron is modeled using the leaky integrate-and-fire (LIF) scheme, while many neurons are coupled nonlocally in a network. In this system chimera states develop, which are complex states consisting of coexisting synchronous and asynchronous network areas. We study the influence of the network size on the properties and the form of chimera states. We show that for constant coupling strength, the number of the synchronous/asynchronous domains depends quantitatively on the coupling ratio. This dependence allows to extract synchronization properties in large ensembles of neurons after extrapolating from simulations of small networks. Since computer simulations of even small neuron networks are highly demanding in memory and CPU time, this property is particularly important in view of the large number of neurons involved in any cognitive function. In total, the number of neurons in the human brain is of the order of 1010, and each of them is connected with an average of 103 other neurons. © Springer Nature Switzerland AG 2020

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

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. © 2018, EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature