Phase synchronization of coupled bursting neurons and the generalized Kuramoto model

Bursting neurons fire rapid sequences of action potential spikes followed by a quiescent period. The basic dynamical mechanism of bursting is the slow currents that modulate a fast spiking activity caused by rapid ionic currents. Minimal models of bursting neurons must include both effects. We considered one of these models and its relation with a generalized Kuramoto model, thanks to the definition of a geometrical phase for bursting and a corresponding frequency. We considered neuronal networks with different connection topologies and investigated the transition from a non-synchronized to a partially phase-synchronized state as the coupling strength is varied. The numerically determined critical coupling strength value for this transition to occur is compared with theoretical results valid for the generalized Kuramoto model.Comment: 31 pages, 5 figure

Synchronization of coupled neural oscillators with heterogeneous delays

We investigate the effects of heterogeneous delays in the coupling of two excitable neural systems. Depending upon the coupling strengths and the time delays in the mutual and self-coupling, the compound system exhibits different types of synchronized oscillations of variable period. We analyze this synchronization based on the interplay of the different time delays and support the numerical results by analytical findings. In addition, we elaborate on bursting-like dynamics with two competing timescales on the basis of the autocorrelation function.Comment: 18 pages, 14 figure

Synchronised firing patterns in a random network of adaptive exponential integrate-and-fire neuron model

Acknowledgements This study was possible by partial financial support from the following Brazilian government agencies: CNPq, CAPES, and FAPESP (2011/19296-1 and 2015/07311-7). We also wish thank Newton Fund and COFAP.Peer reviewedPostprin

Multiple firing coherence resonances in excitatory and inhibitory coupled neurons

The impact of inhibitory and excitatory synapses in delay-coupled Hodgkin--Huxley neurons that are driven by noise is studied. If both synaptic types are used for coupling, appropriately tuned delays in the inhibition feedback induce multiple firing coherence resonances at sufficiently strong coupling strengths, thus giving rise to tongues of coherency in the corresponding delay-strength parameter plane. If only inhibitory synapses are used, however, appropriately tuned delays also give rise to multiresonant responses, yet the successive delays warranting an optimal coherence of excitations obey different relations with regards to the inherent time scales of neuronal dynamics. This leads to denser coherence resonance patterns in the delay-strength parameter plane. The robustness of these findings to the introduction of delay in the excitatory feedback, to noise, and to the number of coupled neurons is determined. Mechanisms underlying our observations are revealed, and it is suggested that the regularity of spiking across neuronal networks can be optimized in an unexpectedly rich variety of ways, depending on the type of coupling and the duration of delays.Comment: 7 two-column pages, 6 figures; accepted for publication in Communications in Nonlinear Science and Numerical Simulatio

Using a virtual cortical module implementing a neural field model to modulate brain rhythms in Parkinson’s disease

We propose a new method for selective modulation of cortical rhythms based on neural field theory, in which the activity of a cortical area is extensively monitored using a two-dimensional microelectrode array. The example of Parkinson’s disease illustrates the proposed method, in which a neural field model is assumed to accurately describe experimentally recorded activity. In addition, we propose a new closed-loop stimulation signal that is both space- and time- dependent. This method is especially designed to specifically modulate a targeted brain rhythm, without interfering with other rhythms. A new class of neuroprosthetic devices is also proposed, in which the multielectrode array is seen as an artificial neural network interacting with biological tissue. Such a bio-inspired approach may provide a solution to optimize interactions between the stimulation device and the cortex aiming to attenuate or augment specific cortical rhythms. The next step will be to validate this new approach experimentally in patients with Parkinson’s disease