Beta-rhythm oscillations and synchronization transition in network models of Izhikevich neurons: effect of topology and synaptic type

Despite their significant functional roles, beta-band oscillations are least understood. Synchronization in neuronal networks have attracted much attention in recent years with the main focus on transition type. Whether one obtains explosive transition or a continuous transition is an important feature of the neuronal network which can depend on network structure as well as synaptic types. In this study we consider the effect of synaptic interaction (electrical and chemical) as well as structural connectivity on synchronization transition in network models of Izhikevich neurons which spike regularly with beta rhythms. We find a wide range of behavior including continuous transition, explosive transition, as well as lack of global order. The stronger electrical synapses are more conducive to synchronization and can even lead to explosive synchronization. The key network element which determines the order of transition is found to be the clustering coefficient and not the small world effect, or the existence of hubs in a network. These results are in contrast to previous results which use phase oscillator models such as the Kuramoto model. Furthermore, we show that the patterns of synchronization changes when one goes to the gamma band. We attribute such a change to the change in the refractory period of Izhikevich neurons which changes significantly with frequency.Comment: 7 figures, 1 tabl

Phase synchronization in a network of Izhikevich neurons with electrical synapses

<p>This code simulates a complex network of Izhikevich neurons with electrical synapses. The dependence of phase synchronization order parameter on coupling strength and also the network activity is calculated. The differential equations of Izhikevich neuron’s dynamics are integrated using Rung-Kutta method. Many features such as network topology can be changed easily.</p

Izhikevich neurons with diffusive coupling.f90

<p>This code simulates a complex network of Izhikevich neurons with electrical synapses. The dependence of phase synchronization order parameter on coupling strength and also the network activity is calculated. The differential equations of Izhikevich neuron’s dynamics are integrated using Rung-Kutta method.</p

Optimal reinforcement learning near the edge of synchronization transition

Recent experimental and theoretical studies have indicated that the putative criticality of cortical dynamics may corresponds to a synchronization phase transition. The critical dynamics near such a critical point needs further investigation specifically when compared to the critical behavior near the standard absorbing state phase transition. Since the phenomena of learning and self-organized criticality (SOC) at the edge of synchronization transition can emerge jointly in spiking neural networks due to the presence of spike-timing dependent plasticity (STDP), it is tempting to ask: What is the relationship between synchronization and learning in neural networks? Further, does learning benefit from SOC at the edge of synchronization transition? In this paper, we intend to address these important issues. Accordingly, we construct a biologically inspired model of an autonomous cognitive system which learns to perform stimulus-response tasks. We train this system using a reinforcement learning rule implemented through dopamine-modulated STDP. We find that the system exhibits a continuous transition from synchronous to asynchronous neural oscillations upon increasing the average axonal time delay. We characterize the learning performance of the system and observe that it is optimized near the synchronization transition. We also study neuronal avalanches in the system and provide evidence that optimized learning is achieved in a slightly supercritical state.Comment: 9 pages, 5 figures. To appear in Physical Review