Adaptive coupling induced multi-stable states in complex networks
نویسندگان
چکیده
Adaptive coupling, where the coupling is dynamical and depends on the behaviour of the oscillators in a complex system, is one of the most crucial factors to control the dynamics and streamline various processes in complex networks. In this paper, we have demonstrated the occurrence of multi-stable states in a system of identical phase oscillators that are dynamically coupled. We find that the multi-stable state is comprised of a two cluster synchronization state where the clusters are in anti-phase relationship with each other and a desynchronization state. We also find that the phase relationship between the oscillators is asymptotically stable irrespective of whether there is synchronization or desynchronization in the system. The time scale of the coupling affects the size of the clusters in the two cluster state. We also investigate the effect of both the coupling asymmetry and plasticity asymmetry on the multi-stable states. In the absence of coupling asymmetry, increasing the plasticity asymmetry causes the system to go from a two clustered state to a desynchronization state and then to a two clustered state. Further, the coupling asymmetry, if present, also affects this transition. We also analytically find the occurrence of the above mentionedmulti-stable–desynchronization–multi-stable state transition. A brief discussion on the phase evolution of nonidentical oscillators is also provided. Our analytical results are in good agreement with our numerical observations. © 2013 Elsevier B.V. All rights reserved.
منابع مشابه
Synchronization 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 کاملبررسی پایداری حالت همگام در شبکهای از نگاشتهای آشوبناک با روش سنجه ماتریسی
Stability of synchronous state is a fundamental problem in synchronization. We study Matrix Measure as an approach for investigating of stability of synchronous states of chaotic maps on complex networks. Matrix Measure is a measure which depends on network structure. Using this measure and comparing with synchronization threshold which depends on the function of the map, show us how the synchr...
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 کاملA Robust Distributed Estimation Algorithm under Alpha-Stable Noise Condition
Robust adaptive estimation of unknown parameter has been an important issue in recent years for reliable operation in the distributed networks. The conventional adaptive estimation algorithms that rely on mean square error (MSE) criterion exhibit good performance in the presence of Gaussian noise, but their performance drastically decreases under impulsive noise. In this paper, we propose a rob...
متن کاملAdaptive Leader-Following and Leaderless Consensus of a Class of Nonlinear Systems Using Neural Networks
This paper deals with leader-following and leaderless consensus problems of high-order multi-input/multi-output (MIMO) multi-agent systems with unknown nonlinear dynamics in the presence of uncertain external disturbances. The agents may have different dynamics and communicate together under a directed graph. A distributed adaptive method is designed for both cases. The structures of the contro...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013