Adiabatic small noise fluctuations around anticipated synchronization: A perspective from scalar master–slave dynamics

Budini, Adrián A.; Cáceres, Manuel O.

doi:10.1016/j.physa.2008.04.011

Cited by 8 publications

(3 citation statements)

References 23 publications

(50 reference statements)

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“…All computations were performed with MATLAB R2015a (The MathWorks, Inc., Natick, MA), including its cpsd function to estimate power and phase spectra.) A discussion concluders this paper: An important difference of ARD to anticipatory synchronization [9,10] is that in the latter, τ C ≈ τ is to be expected [18], and has been observed even for stochastic forcing of the master system [19]. The inequality τ C < τ reflects that ARD cannot completely settle on the anticipation manifold, and that the group delay is frequency dependent.…”

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confidence: 78%

Signal prediction by anticipatory relaxation dynamics

Voss

2016

Phys. Rev. E

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Real-time prediction of signals is a task often encountered in control problems as well as by living systems. Here a model-free prediction approach based on the coupling of a linear relaxation-delay system to a smooth, stationary signal is described. The resulting anticipatory relaxation dynamics (ARD) is a frequencydependent predictor of future signal values. ARD not only approximately predicts signals on average but can anticipate the occurrence of signal peaks, too. This can be explained by recognizing ARD as an input/output system with negative group delay. It is completely characterized, including its prediction horizon, by its analytically given frequency response function.

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confidence: 78%

Signal prediction by anticipatory relaxation dynamics

Voss

2016

Phys. Rev. E

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“…This method of coupling is encapsulated by the term k(x 1 2 y 1,t ), where K is a coupling strength parameter and y 1,t (t) is defined as y 1 (t 2 t). Delay coupling is known to produce a robust effect of anticipating synchronization, wherein the slave maintains a negative relative phase with the master (Budini & Caćeres, 2008;Voss, 2000). A simulation of this system is shown in Figure 6.…”

Section: Strong Anticipation In a Simulated Systemmentioning

confidence: 99%

The Muddle of Anticipation

Stepp

Turvey

2015

Ecological Psychology

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In J. J. Gibson's classic paper "The Problem of Temporal Order in Stimulation and Perception" (1966a), he referred to the difficulties encountered when attempting a sharp distinction between memory and perception as "the muddle of memory." Resolution of the muddle by J. J. Gibson proceeded by blurring the distinction itself. We develop the conjugate "muddle of anticipation" similarly by blurring the sharp distinction traditionally drawn between anticipation and perception. The subsequent redefinition of the problem is grounded in strong anticipation equated with anticipating synchronization-that which arises from a system itself via lawful regularities embedded in the system's ordinary mode of function. We identify the fit of strong anticipation's properties to J. J. Gibson's ecological approach and in so doing introduce the possibility of a potentially deep connection between them, namely, that the coordination of perception with surroundings (direct perception) is a special case of strong anticipation. TWO MUDDLESJ. J. Gibson (1966a) wrote about the "muddle of memory," referring to the difficulty of defining memory in any way other than through introspection, which

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“…The proposed CS comes from the concept of synchronization for coupled drive-response chaotic systems proposed in [14]. Since 1990, researchers have paid significant attention to synchronization control of two chaotic systems [15,16] and its applications in the fields of information science, secure communication, biological systems, etc [17][18][19]. In [14], a driver system generates a signal sent over a channel to a response system, which uses this signal to synchronize itself with the driver system.…”

Section: Introductionmentioning

confidence: 99%

Counterpart synchronization of duplex networks with delayed nodes and noise perturbation

Xiang

et al. 2015

J. Stat. Mech.

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Abstract. In the real world, many complex systems are represented not by single networks but rather by sets of interdependent ones. In these specific networks, nodes in one network mutually interact with nodes in other networks. This paper focuses on a simple representative case of two-layer networks (the so-called duplex networks) with unidirectional inter-layer couplings. That is, each node in one network depends on a counterpart in the other network. Accordingly, the former network is called the response layer and the latter network is the drive layer. Specifically, synchronization between each node in the drive layer and its counterpart in the response layer (counterpart synchronization, or CS) of this sort of duplex networks with delayed nodes and noise perturbation is investigated. Based on the LaSalle-type invariance principle, a control technique is proposed and a sufficient condition is developed for realizing counterpart synchronization of duplex networks.Furthermore, two corollaries are derived as special cases. In addition, node dynamics within each layer can be various and topologies of the two layers are not necessarily identical. Therefore, the proposed synchronization method can be applied to a wide range of multiplex networks. Numerical examples are provided to illustrate the feasibility and effectiveness of the results.

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Adiabatic small noise fluctuations around anticipated synchronization: A perspective from scalar master–slave dynamics

Cited by 8 publications

References 23 publications

Signal prediction by anticipatory relaxation dynamics

Signal prediction by anticipatory relaxation dynamics

The Muddle of Anticipation

Counterpart synchronization of duplex networks with delayed nodes and noise perturbation

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