284,617 research outputs found

    Synchronization of fractional order chaotic systems

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    The chaotic dynamics of fractional order systems begin to attract much attentions in recent years. In this brief report, we study the master-slave synchronization of fractional order chaotic systems. It is shown that fractional order chaotic systems can also be synchronized.Comment: 3 pages, 5 figure

    Amplitude death in coupled chaotic oscillators

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    Amplitude death can occur in chaotic dynamical systems with time-delay coupling, similar to the case of coupled limit cycles. The coupling leads to stabilization of fixed points of the subsystems. This phenomenon is quite general, and occurs for identical as well as nonidentical coupled chaotic systems. Using the Lorenz and R\"ossler chaotic oscillators to construct representative systems, various possible transitions from chaotic dynamics to fixed points are discussed.Comment: To be published in PR

    Mode fluctuations as fingerprint of chaotic and non-chaotic systems

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    The mode-fluctuation distribution P(W)P(W) is studied for chaotic as well as for non-chaotic quantum billiards. This statistic is discussed in the broader framework of the E(k,L)E(k,L) functions being the probability of finding kk energy levels in a randomly chosen interval of length LL, and the distribution of n(L)n(L), where n(L)n(L) is the number of levels in such an interval, and their cumulants ck(L)c_k(L). It is demonstrated that the cumulants provide a possible measure for the distinction between chaotic and non-chaotic systems. The vanishing of the normalized cumulants CkC_k, k≥3k\geq 3, implies a Gaussian behaviour of P(W)P(W), which is realized in the case of chaotic systems, whereas non-chaotic systems display non-vanishing values for these cumulants leading to a non-Gaussian behaviour of P(W)P(W). For some integrable systems there exist rigorous proofs of the non-Gaussian behaviour which are also discussed. Our numerical results and the rigorous results for integrable systems suggest that a clear fingerprint of chaotic systems is provided by a Gaussian distribution of the mode-fluctuation distribution P(W)P(W).Comment: 44 pages, Postscript. The figures are included in low resolution only. A full version is available at http://www.physik.uni-ulm.de/theo/qc/baecker.htm

    Projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random networks

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    We study projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random networks. We relax some limitations of previous work, where projective-anticipating and projective-lag synchronization can be achieved only on two coupled chaotic systems. In this paper, we can realize projective-anticipating and projective-lag synchronization on complex dynamical networks composed by a large number of interconnected components. At the same time, although previous work studied projective synchronization on complex dynamical networks, the dynamics of the nodes are coupled partially linear chaotic systems. In this paper, the dynamics of the nodes of the complex networks are time-delayed chaotic systems without the limitation of the partial-linearity. Based on the Lyapunov stability theory, we suggest a generic method to achieve the projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random dynamical networks and find both the existence and sufficient stability conditions. The validity of the proposed method is demonstrated and verified by examining specific examples using Ikeda and Mackey-Glass systems on Erdos-Renyi networks.Comment: 14 pages, 6 figure

    Spectral Statistics: From Disordered to Chaotic Systems

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    The relation between disordered and chaotic systems is investigated. It is obtained by identifying the diffusion operator of the disordered systems with the Perron-Frobenius operator in the general case. This association enables us to extend results obtained in the diffusive regime to general chaotic systems. In particular, the two--point level density correlator and the structure factor for general chaotic systems are calculated and characterized. The behavior of the structure factor around the Heisenberg time is quantitatively described in terms of short periodic orbits.Comment: uuencoded file with 1 eps figure, 4 page
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