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- W2342843033 abstract "Synchronization is an important phenomenon which plays a central role in the function or dysfunction of a wide spectrum of biological and technological networks. Despite the vast literature on network synchronization, the majority of research activities have been focused on oscillators connected through one network. However, in many realistic biological and engineering systems the units can be coupled via multiple, independent networks. This thesis contributes toward the rigorous understanding of the emergence of stable synchronization in dynamical networks with mixed coupling. A mixed network is composed of subgraphs connecting a subnetwork of oscillators via one of the individual oscillator’s variables. An illustrative example is a network of Lorenz systems with mixed couplings where some of the oscillators are coupled through the x-variable, some through the y-variable and some through both. This thesis presents a new general synchronization method called the Mixed Connection Graph method, which removes a long-standing obstacle in studying synchronization in mixed dynamical networks of different nature. This method links the stability theory, including the Lyapunov function approach with graph theoretical quantities. The application of the method to specific networks reveals surprising, counterintuitive effects, not seen in networks with one connection graph. INDEX WORDS: Dynamical System, Synchronization, Stability, Graph Theory SYNCHRONIZATION IN DYNAMICAL NETWORKS WITH MIXED COUPLING" @default.
- W2342843033 created "2016-06-24" @default.
- W2342843033 creator A5039966946 @default.
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- W2342843033 date "2016-01-01" @default.
- W2342843033 modified "2023-09-23" @default.
- W2342843033 title "Synchronization in Dynamical Networks with Mixed Coupling" @default.
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