Title: The role of mathematical pathways in modeling computational neurosciences

Dr. Argha Mondal

Assist. Prof., Department of Mathematics, Sidho-Kanho-Birsha University, India & University of Essex, UK

Abstract: The topic is the successful applications of applied mathematical tools and dynamical systems to solve biological problems. It can be described as mathematical frameworks for complex analysis of excitatory/oscillatory single neurons and networks for functional mechanisms in neural systems. The single neuron exhibits a highly complex dynamical behavior interconnected via Synaptic coupling: Chemical, electrical coupling, and autaptic coupling. We investigate different firing characteristics or modes (such as various types of spiking, bursting, chattering, fast spiking, mixed mode oscillations etc.) to study firing activities on the deterministic, noise induced excitable systems as a continuous excitable cable. We work on the abnormal firing of self-organized neurons as well as the networks and their functional behavior with synchronization. Bursting is a manifestation of the slow-fast dynamics observed in neuroscience including pathological brain states. To make it more biologically plausible, we implement fractional order dynamics that can be appropriately applied in Computational neuroscience to investigate neuronal responses in single as well as network of neurons.