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Exploring Collective Dynamics of Networks: Limits of the Ott-Antonsen Approach
Başlık:
Exploring Collective Dynamics of Networks: Limits of the Ott-Antonsen Approach
Yazar:
Watson, Scott T., author.
ISBN:
9780438116559
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 electronic resource (117 pages)
Genel Not:
Source: Dissertation Abstracts International, Volume: 79-11(E), Section: B.
Advisors: Paul So; Ernest Barreto Committee members: Evelyn Sander.
Özet:
In this work, we explore the collective dynamics of coupled phase oscillator networks. We go over the history of such systems, and the attempts at understanding their potentially complex behaviors. We examine how the dynamics of the mean field of such a system evolves over time, and the important reduction of Ott and Antonsen in understanding the asymptotic behavior of large, heterogenous networks. We then examine the predictions this theory generates, and compare them to finite-size network simulations. We see how fluctuations around the predicted states scale as 1/√N, and explore how correlations between the oscillators and parameters can induce anomalous transients. We then add complexity to such systems by introducing a network of networks formulation, and find that an interesting reduction can be achieved if the populations are exact copies of each other. We introduce the Watanabe-Strogatz theory to help describe these systems, and find that the approach to the asymptotic state for the mean field can be described by an exponential decay in terms of the degree of diversity of the network Delta as e--Delta t. In the asymptotic limit, we can recover the Ott-Antonsen equations, showing how diversity is an important factor to the theory. Finally, we examine in detail a small two-population system in the network of networks formulation, and explore its asymptotic states as we break its inter-{} and intra-coupling symmetries. Looking at a wide range of parameter sets for this system, we find that while the incoherent state is fully characterizable, the partially-coherent state is still very complex, with catastrophe theory providing a helpful organizing principle.
Notlar:
School code: 0883
Tüzel Kişi Ek Girişi:
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Yer Numarası | Demirbaş Numarası | Shelf Location | Lokasyon / Statüsü / İade Tarihi |
---|---|---|---|
XX(692910.1) | 692910-1001 | Proquest E-Tez Koleksiyonu | Arıyor... |
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