Emergent Dynamics of Electrically Excitable and Passive Cells in Biological and Small-World Networks

Ganguly, Arkoprava (2025) Emergent Dynamics of Electrically Excitable and Passive Cells in Biological and Small-World Networks. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS Dissertation of Arkoprava Ganguly (20MS118)) 20MS118_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (8MB)

Abstract

Living tissues often mix excitable cells that fire sharp action potentials with passive cells that respond in a graded way. This thesis asks a simple question: what collective behaviour occurs when such different elements are wired together on real and synthetic networks? How do these combine to generate the rich activity observed in real nervous tissue? To do so we build a unified, dimensionless model that places an excitable FitzHugh–Nagumo unit and a passive RC element on equal footing, then wire a collection of such elements on networks formed by chemical and electrical synapses. The same framework runs on the anatomical C. elegans connectome and on purpose-made Watts–Strogatz small-world graphs, letting us vary cell ratios, coupling strengths, topology and network size over wide parameter ranges. Our immediate goal is to chart how changing the mix of spiking and passive cells leads to correlated oscillations, multicluster states and inherent chaos. Global measures such as correlation-based functional graphs, Louvain community detection, state-space manifolds from principal-component analysis and preliminary Lyapunov exponents reveal how local interaction rules scale up to network-level order. The broader aim is more ambitious. By showing that simple, well-understood components can display unexpected behaviour when posing as a collective, we try to illustrate that more is indeed different. The result is a flexible framework that trades a little biological detail for a lot of analytical control, opening the door to systematic explorations of emergent phenomena in neural systems and other complex networks. 3

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