Dynamics of a perturbed random neuronal network with burst-timing-dependent plasticity
Graduate Program in Science, State University of Ponta Grossa, Ponta Grossa, PR, Brazil
2 Mathematics and Statistics Department, State University of Ponta Grossa, Ponta Grossa, PR, Brazil
3 University Center UNIFATEB, Telêmaco Borba, PR, Brazil
4 Graduate Program in Chemical Engineering Federal Technological University of Paraná, Ponta Grossa, PR, Brazil
5 Institute of Science and Technology, Federal University of São Paulo-UNIFESP, São José dos Campos, SP, Brazil
6 Department of Physiology and Pharmacology, State University of New York Downstate Health Sciences University, Brooklyn, NY, USA
7 Center for Mathematics, Computation, and Cognition, Federal University of ABC, São Bernardo do Campo, SP, Brazil
Accepted: 27 September 2022
Published online: 17 October 2022
Neuroplasticity, also known as brain plasticity or neuronal plasticity, allows the brain to improve its connections or rewire itself. The synaptic modifications can help the brain to enhance fitness, to promote existing cognitive capabilities, and to recover from some brain injuries. Furthermore, brain plasticity has impacts on neuronal synchronisation. In this work, we build a neuronal network composed of coupled Rulkov neurons with excitatory connections randomly distributed. We consider burst-timing-dependent plasticity to investigate the effects of external perturbations, such as periodic and random pulses, on the neuronal synchronous behaviour. The plasticity changes the synaptic weights between the presynaptic and postsynaptic neurons, and as a consequence the burst synchronisation. We verify that the external periodic and random pulsed perturbations can induce synchronisation and desynchronisation states. One of our main results is to demonstrate that bursting synchronisation and desynchronisation in a network with burst-timing-dependent plasticity can emerge according to alterations of the initial synaptic weights. Furthermore, we show that external periodic and random pulsed currents can be an effective method to suppress neuronal activities related to pathological synchronous behaviour.
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