ترغب بنشر مسار تعليمي؟ اضغط هنا

Analysis of parameter mismatches in the master stability function for network synchronization

82   0   0.0 ( 0 )
 نشر من قبل Francesco Sorrentino Dr.
 تاريخ النشر 2011
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

In this letter, we perform a sensitivity analysis on the master stability function approach for the synchronization of networks of coupled dynamical systems. More specifically, we analyze the linear stability of a nearly synchronized solution for a network of coupled dynamical systems, for which the individual dynamics and output functions of each unit are approximately identical and the sums of the entries in the rows of the coupling matrix slightly deviate from zero. The motivation for this parametric study comes from experimental instances of synchronization in human-made or natural settings, where ideal conditions are difficult to observe.



قيم البحث

اقرأ أيضاً

All interesting and fascinating collective properties of a complex system arise from the intricate way in which its components interact. Various systems in physics, biology, social sciences and engineering have been successfully modelled as networks of coupled dynamical systems, where the graph links describe pairwise interactions. This is, however, too strong a limitation, as recent studies have revealed that higher-order many-body interactions are present in social groups, ecosystems and in the human brain, and they actually affect the emergent dynamics of all these systems. Here, we introduce a general framework that allows to study coupled dynamical systems accounting for the precise microscopic structure of their interactions at any possible order. We consider the most general ensemble of identical dynamical systems, organized on the nodes of a simplicial complex, and interacting through synchronization-non-invasive coupling function. The simplicial complex can be of any dimension, meaning that it can account, at the same time, for pairwise interactions, three-body interactions and so on. In such a broad context, we show that complete synchronization exists as an invariant solution, and we give the necessary condition for it to be observed as a stable state in terms of a Master Stability Function. This generalizes the existing results valid for pairwise interactions (i.e. graphs) to the case of complex systems with the most general possible architecture. Moreover, we show how the approach can be simplified for specific, yet frequently occurring, instances, and we verify all our theoretical predictions in synthetic and real-world systems. Given the completely general character of the method proposed, our results contribute to the theory of dynamical systems with many-body interactions and can find applications in an extremely wide range of practical cases.
We consider synchronization of weighted networks, possibly with asymmetrical connections. We show that the synchronizability of the networks cannot be directly inferred from their statistical properties. Small local changes in the network structure c an sensitively affect the eigenvalues relevant for synchronization, while the gross statistical network properties remain essentially unchanged. Consequently, commonly used statistical properties, including the degree distribution, degree homogeneity, average degree, average distance, degree correlation, and clustering coefficient, can fail to characterize the synchronizability of networks.
Synchronization, in which individual dynamical units keep in pace with each other in a decentralized fashion, depends both on the dynamical units and on the properties of the interaction network. Yet, the role played by the network has resisted compr ehensive characterization within the prevailing paradigm that interactions facilitating pair-wise synchronization also facilitate collective synchronization. Here we challenge this paradigm and show that networks with best complete synchronization, least coupling cost, and maximum dynamical robustness, have arbitrary complexity but quantized total interaction strength that constrains the allowed number of connections. It stems from this characterization that negative interactions as well as link removals can be used to systematically improve and optimize synchronization properties in both directed and undirected networks. These results extend the recently discovered compensatory perturbations in metabolic networks to the realm of oscillator networks and demonstrate why less can be more in network synchronization.
Although most networks in nature exhibit complex topology the origins of such complexity remains unclear. We introduce a model of a growing network of interacting agents in which each new agents membership to the network is determined by the agents e ffect on the networks global stability. It is shown that out of this stability constraint, scale free networks emerges in a self organized manner, offering an explanation for the ubiquity of complex topological properties observed in biological networks.
In the study of dynamical systems on networks/graphs, a key theme is how the network topology influences stability for steady states or synchronized states. Ideally, one would like to derive conditions for stability or instability that instead of mic roscopic details of the individual nodes/vertices rather make the influence of the network coupling topology visible. The master stability function is an important such tool to achieve this goal. Here we generalize the master stability approach to hypergraphs. A hypergraph coupling structure is important as it allows us to take into account arbitrary higher-order interactions between nodes. As for instance in the theory of coupled map lattices, we study Laplace type interaction structures in detail. Since the spectral theory of Laplacians on hypergraphs is richer than on graphs, we see the possibility of new dynamical phenomena. More generally, our arguments provide a blueprint for how to generalize dynamical structures and results from graphs to hypergraphs.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا