Synchronization in interdependent networks.
نویسندگان
چکیده
We explore the synchronization behavior in interdependent systems, where the one-dimensional (1D) network (the intranetwork coupling strength J(I)) is ferromagnetically intercoupled (the strength J) to the Watts-Strogatz (WS) small-world network (the intranetwork coupling strength J(II)). In the absence of the internetwork coupling (J=0), the former network is well known not to exhibit the synchronized phase at any finite coupling strength, whereas the latter displays the mean-field transition. Through an analytic approach based on the mean-field approximation, it is found that for the weakly coupled 1D network (J(I)≪1) the increase of J suppresses synchrony, because the nonsynchronized 1D network becomes a heavier burden for the synchronization process of the WS network. As the coupling in the 1D network becomes stronger, it is revealed by the renormalization group (RG) argument that the synchronization is enhanced as J(I) is increased, implying that the more enhanced partial synchronization in the 1D network makes the burden lighter. Extensive numerical simulations confirm these expected behaviors, while exhibiting a reentrant behavior in the intermediate range of J(I). The nonmonotonic change of the critical value of J(II) is also compared with the result from the numerical RG calculation.
منابع مشابه
On Synchronization of Interdependent Networks
Abstract It is well-known that the synchronization of diffusively-coupled systems on networks strongly depends on the network topology. In particular, the so-called algebraic connectivity μN−1, or the smallest non-zero eigenvalue of the discrete Laplacian operator plays a crucial role on synchronization, graph partitioning, and network robustness. In our study, synchronization is placed in the ...
متن کاملOn Synchronization of Interdependent Networks
Abstract It is well-known that the synchronization of diffusively-coupled systems on networks strongly depends on the network topology. In particular, the so-called algebraic connectivity μN−1, or the smallest non-zero eigenvalue of the discrete Laplacian operator plays a crucial role on synchronization, graph partitioning, and network robustness. In our study, synchronization is placed in the ...
متن کاملInterdependent Security Game Design over Constrained Linear Influence Networks
In today's highly interconnected networks, security of the entities are often interdependent. This means security decisions of the agents are not only influenced by their own costs and constraints, but also are affected by their neighbors’ decisions. Game theory provides a rich set of tools to analyze such influence networks. In the game model, players try to maximize their utilities through se...
متن کاملSynchronization for Complex Dynamic Networks with State and Coupling Time-Delays
This paper is concerned with the problem of synchronization for complex dynamic networks with state and coupling time-delays. Therefore, larger class and more complicated complex dynamic networks can be considered for the synchronization problem. Based on the Lyapunov-Krasovskii functional, a delay-independent criterion is obtained and formulated in the form of linear matrix inequalities (LMIs)...
متن کاملSynchronization analysis of complex dynamical networks with hybrid coupling with application to Chua’s circuit
Complex dynamic networks have been considered by researchers for their applications in modeling and analyzing many engineering issues. These networks are composed of interconnected nodes and exhibit complex behaviors that are resulted from interactions between these nodes. Synchronization, which is the concept of coordinated behavior between nodes, is the most interested behavior in these netwo...
متن کاملLinear matrix inequality approach for synchronization of chaotic fuzzy cellular neural networks with discrete and unbounded distributed delays based on sampled-data control
In this paper, linear matrix inequality (LMI) approach for synchronization of chaotic fuzzy cellular neural networks (FCNNs) with discrete and unbounded distributed delays based on sampled-data controlis investigated. Lyapunov-Krasovskii functional combining with the input delay approach as well as the free-weighting matrix approach are employed to derive several sufficient criteria in terms of...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Chaos
دوره 21 2 شماره
صفحات -
تاریخ انتشار 2011