Dynamics of adaptive recurrent neural networks

In this thesis a simple, phenomenological model of a neural network with plasticity is presented in the form of a slow-fast adaptive dynamical recurrent neural network. The plasticity rule is chosen from the class of Hebbian learning rules, in which the synaptic connection between two neurons evolves continuously as a function of their correlation in the recent past. Initially an analysis of networks of two neurons is presented, which exhibit relaxation oscillations in which one neuron switches between an ’off’ state, where it takes a negative value, and an ’on’ state, where it takes a positive value, while the other neuron stays in one on/off state. Then, by means of an example with a nine neuron network, the system is shown to exhibit both stable frequency cluster synchronization and transient frequency cluster synchronization.

Grantor dc:publisher

University College Cork

Year dc:date.issued

2023

Author dc:creator

• Fox, David

Advisors dc:contributor.advisor

• Amann, Andreas
• Keane, Andrew

• Nonlinear dynamics
• Bifurcation theory
• Dynamical systems
• Computaional neuroscience
• Neural networks
• Recurrent neural networks
• Synchronization
• Slow-fast systems
• Multiple timescales
• Adaptive dynamical networks

Statement dc:rights

• © 2023, David Fox.

Licence dc:rights.uri

• https://creativecommons.org/licenses/by-nc-nd/4.0/

Language dc:language.iso

en

Handle dc:identifier.uri

https://hdl.handle.net/10468/16503

OAI identifier oai:identifier

oai:cora.ucc.ie:10468/16503