Analysing bursting synchronization in neural network models with external pulsed perturbations

Abstract

The brain has a complex structure and is located at the center of the nervous system. At the cellular level, the nervous system has neurons that send signals rapidly and precisely to other cells. Dynamical features of neurons, bursting synchronization and desynchronization, in a neu- ral network can not only be associated with memory and consciousness, but also be related to unhealthy neural behaviors. To regulate abnormal neural activities, for instance, in patients with neurological disorders, such as epilepsy, Alzheimer’s, and Parkinson’s diseases, external pulsed currents, such as deep brain stimulation, can influence the bursting synchronous behavior in a neural network and cause alterations in neural spiking activities. Throughout this thesis, the

main goals are to demonstrate the emergence of bursting synchronization and desynchroniza- tion in two different neural networks, and also to show the effect of external periodic and random pulsed currents on neural activities related to pathological synchronous behavior in these neu- ral networks. Firstly, a neural network model containing Rulkov’s neurons connected by means of a random structure, Erdös-Rényi model, is built. The formation and destruction of bursting synchronization in a random neural network model with burst-timing-dependent plasticity are investigated. We study the effect of two external pulsed currents, periodic and random pulses, on bursting synchronization in a plastic neural network. Secondly, a neural network composed of coupled subnetworks with small-world properties according to one human cerebral cortex, limbic system, and brain stem is considered. The burst synchronization and desynchronization in the network under external periodic and random pulsed perturbations are studied. Overall,

the results of this thesis show that the burst-timing-dependent plasticity and the synaptic inter- action between presynaptic and postsynaptic neurons can exhibit the formation and destruction of bursting neural synchronization in network models. The external pulsed currents can be an effective method to suppress bursting neural synchronization in neural networks.