|1- Ghasemi Esfahani, Z., Valizadeh , A., "Zero-Lag Synchronization Despite Inhomogeneities in a Relay System
", PLoS ONE, 9: (12), 1-22, (2014).|
A novel proposal for the zero-lag synchronization of the delayed coupled neurons, is to connect them indirectly via a third relay neuron. In this study, we develop a Poincaré map to investigate the robustness of the synchrony in such a relay system against inhomogeneity in the neurons and synaptic parameters. We show that when the inhomogeneity does not violate the symmetry of the system, synchrony is maintained and in some cases inhomogeneity enhances synchrony. On the other hand if the inhomogeneity breaks the symmetry of the system, zero lag synchrony can not be preserved. In this case we give analytical results for the phase lag of the spiking of the neurons in the stable state.
|2- Sadeghi , S., Valizadeh, A., "Synchronization of delayed coupled neurons in presence of inhomogeneity", Journal of Computational Neuroscience, 36, 55-66, (2014).|
In principle, two directly coupled limit cycle oscillators can overcome mismatch in intrinsic rates and match their frequencies, but zero phase lag synchronization is just achievable in the limit of zero mismatch, i.e., with identical oscillators. Delay in communication, on the other hand, can exert phase shift in the activity of the coupled oscillators. In this study, we address the question of how phase locked, and in particular zero phase lag synchronization, can be achieved for a heterogeneous system of two delayed coupled neurons. We have analytically studied the possibility of inphase synchronization and near inphase synchronization when the neurons are not identical or the connections are not exactly symmetric. We have shown that while any single source of inhomogeneity can violate isochronous synchrony, multiple sources of inhomogeneity can compensate for each other and maintain synchrony. Numeric studies on biologically plausible models also support the analytic results.
|3- Bolhasani, E., Azizi, Y., Valizadeh, A., "Direct connections assist neurons to detect correlation in small amplitude noises ", Front. Comput. Neurosci, 7, 108-, (2013).|
We address a question on the effect of common stochastic inputs on the correlation of the spike trains of two neurons when they are coupled through direct connections. We show that the change in the correlation of small amplitude stochastic inputs can be better detected when the neurons are connected by direct excitatory couplings. Depending on whether intrinsic firing rate of the neurons is identical or slightly different, symmetric or asymmetric connections can increase the sensitivity of the system to the input correlation by changing the mean slope of the correlation transfer function over a given range of input correlation. In either case, there is also an optimum value for synaptic strength which maximizes the sensitivity of the system to the changes in input correlation.
|4- Bayati, M., Valizadeh, A., "Effect of synaptic plasticity on the structure and dynamics of disordered networks of coupled neurons", Phys. Rev. E, 86, 011925-1-011925-7, (2012).|
In an all-to-all network of integrate-and-fire neurons in which there is a disorder in the intrinsic oscillatory frequencies of the neurons, we show that through spike-timing-dependent plasticity the synapses which have the high-frequency neurons as presynaptic tend to be potentiated while the links originated from the low-frequency neurons are weakened. The emergent effective flowof directed connections introduces the high-frequency neurons as the more influential elements in the network and facilitates synchronization by decreasing the synaptic cost for onset of synchronization.
|5- Valizadeh, A., "Enhanced response of regular networks to local signals in the presence of a fast impurity", Phys. Rev. E, 86, 016101-1-016101-6, (2012).|
We consider an array of inductively coupled Josephson junctions with a fast impurity (a junction with a smaller value of the critical current) and study the consequences of imposing a small amplitude periodic signal at some point in the array. We find that when the external signal is imposed at the impurity, the response of the array is boosted and a small amplitude signal can be detected throughout the array. When the signal is imposed elsewhere, minor effects are seen on the dynamics of the array. The same results have also been seen in the presence of a single fast-spiking neuron in a chain of diffusively coupled FitzHugh-Nagumo neurons.