Séminaire Randjit Upadhyay

Mercredi 19 décembre 2018 (14h00, Salle G001)

Ranjit Kumar Upadhyay Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad 826004, India.

Titre : Spiking and Bursting Patterns of Fractional-order Neural models.

Résumé : Bursting and spiking oscillations play a major role in processing and transmitting information in the brain through cortical neurons that respond differently to the same signal. These oscillations display complex dynamics that might be produced by using neuronal models and varying many model parameters. Recent studies showed that models with fractional order (exponent) can produce several types of history-dependent and multiple-time-scale neuronal activities without the adjustment of several parameters. The model produces a wide range of neuronal spike responses, including regular spiking, fast spiking, intrinsic bursting, mixed mode oscillations, regular bursting and chattering, by adjusting only the fractional order. Both the active and silent phases of the burst increase when the fractional-order model further deviates from the classical model. Interestingly, for smaller fractional order, the model resumes spiking activity after the pulse signal turned off. This spiking activity and other properties of the fractional-order model are caused by the memory trace that emerges from the fractional-order dynamics and integrates all the past activities of the neuron. On the network level, the response of the neuronal network shows scale-free spiking patterns by varying the fractional orders. Our results suggest that the complex dynamics of spiking and bursting in Izhikevich model can be the result of the long-term dependence and interaction of intracellular and extracellular ionic currents. Pyramidal neurons produce different spiking patterns to process information, communicate with each other and transform information. These spiking patterns have complex and multiple time scale dynamics that have been described with the fractional-order leaky integrate-and-Fire (FLIF). The model produces spikes with high interspike interval variability and displays several spiking properties such as upward spike-frequency adaptation and long spike latency in response to a constant stimulus. We show that the subthreshold voltage and the firing rate of the fractional-order model make transitions from exponential to power law dynamics when the fractional order α decreases from 1 to smaller values. The firing rate displays different types of spike timing adaptation caused by changes on initial values. We also show that the voltage-memory trace and fractional coefficient are the causes of these different types of spiking properties. The voltage-memory trace that represents the long-term memory has a feedback regulatory mechanism and affects spiking activity. The results suggest that fractional-order models might be appropriate for understanding multiple time scale neuronal dynamics. Overall, a neuron with fractional dynamics displays history dependent activities that might be very useful and powerful for effective information processing.

Key Words: memory, power law, fractional model, Spike frequency adaptation Fractional calculus, Power law