Adaptive Phase Coupling And Synchronization Of Complex Networks

In the fields of complex networks and synchronization studies, the dissertation did some deep and detailed studies on adaptive synchronization of complex networks. In the dissertation, a new adaptive coupling dynamics is proposed. The factor of adaptive coupling is first introduced to phase synchronization and improved the performance of synchronization.For the complexity of the node, attractors in dissipative system are studied as the node model, which include limit cycle and chaotic attractors. As for the complexity of network topology, it ranged over many network models, include coupled two chaotic oscillators, global coupled and nearest-neighbor coupled regular networks, as well as complex networks, such as small world networks, scale free networks, and modular networks. The relationship between the coupling dynamics and the energy dissipation in synchronization process is analyzed to study the interaction between several aspects of complexities. The main contributions are as follows:1) The adaptive coupling is applied to impulsive synchronization in coupled two oscillators. Theoretical analysis is given by LaSalle invariance principle and stability theory of impulsive differential equation. The research indicates that the adaptive coupling scheme could reduce the coupling cost and improve the speed of synchronization. This lays the foundation of the further research.2) The adaptive coupling is first introduced to phase synchronization, and the new adaptive phase coupling dynamics is proposed. In the cases of kuramoto oscillators and regular networks, the dynamical characteristic is analyzed. The synchronization speed and the steady-state phase difference can be adjusted by the parameters of the adaptive law.3) Then focuses on the complexity of network topology. The adaptive phase coupling scheme could suppress the negative influences on synchronization introduced by the heterogeneities in degree and intrinsic frequency distributions. The cases of small world, scale free and modular networks are studied. The adaptive phase coupling mechanism could dynamically allocate the coupling cost reasonably between oscillators.4) The energy dissipation during the synchronization process of chaotic oscillators is analyzed and calculated. The adaptive phase coupling mechanism could adjust the coupling strength dynamically according to the energy difference between two oscillators, and the energy compensation is reduced immensely at last. The cases of regular and complex networks are studied.Phase synchronization, adaptation and energy dissipation are international hotspots in complexity science. The dissertation has done innovative researches in these fields. The research approaches involve the development of new scheme, theoretical analysis and numerical simulation. Combined with the new research progresses in the fields of neuroscience and statistical physics, the proposed adaptive phase coupling scheme is more close to the complex adaptive systems in real world.