Studies on Non linear dynamics in Complex Networks

Sundaresan, Santosh (2013) Studies on Non linear dynamics in Complex Networks. Masters thesis, Indian Institute of Science Education and Research Kolkata.

PDF (MS Dissertation of Santosh Sundaresan) Santosh_Sundaresan_(08MS51)-MSThesis.pdf - Submitted Version Restricted to Repository staff only Download (1MB)

Abstract

After reviewing the classic theorem in order to get a feel of the mathematical knowledge of chaos theory, the present work discusses the aspect of synchronization theory and deals mainly with the aspect of phase synchronization. After that it introduces the SIR model in the complex network framework. Once these models are fit in the respective framework, this work tried to see what kind of behaviors are possible. Among these different dynamical behaviors, synchronization and epidemic spreading on networks are closely related. For example, with the spread of an infective disease, people may reduce the frequency of interpersonal contact and take collective protective measures with increased regularity (for example, by washing hands frequently with clear water and soap, avoiding going to crowded place, and so on). This means that the spread of information between people during transmission of an epidemic disease can induce spontaneously collective risk-minimisation behaviour in spite of (or at least independently of) the actual disease pathology. Similar phenomena can also be found in many animal-borne infections. Hence, synchronization of individual’s behavior and their epidemic behavior on networks can occur simultaneously and interplay adaptively and we will try to model such a network where this feature is present. We will investigate mathematically the correlation between the dynamical synchronization and the epidemic behavior on such complex network models. Lastly, it takes a look at the way this model is simulated numerically and gives the results of the simulations in various cases and concludes whether the model was successful in accomplishing what is was initially set out to do.

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