Detecting directed interactions of networks by random variable resetting

Shi, Rundong; Deng, Changbao; Wang, Shihong

doi:10.1209/0295-5075/124/18002

Cited by 10 publications

(3 citation statements)

References 39 publications

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“…The recent development of powerful methods for reconstruction of coupling functions from measured data has allowed a linkage between the theory and the methods concerned, offering opportunities to investigate many real experimental systems and their interactions [34][35][36][37][38][39][40][41][42][43][44][45]. These methods have mediated applications, not only in different subfields of physics and mathematics, but also in quite different scientific fields.…”

Section: Recent Work On Coupling Functionsmentioning

confidence: 99%

Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences

Stankovski

Pereira

McClintock

et al. 2019

Phil. Trans. R. Soc. A.

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Dynamical systems are widespread, with examples in physics, chemistry, biology, population dynamics, communications, climatology and social science. They are rarely isolated but generally interact with each other. These interactions can be characterized by coupling functions—which contain detailed information about the functional mechanisms underlying the interactions and prescribe the physical rule specifying how each interaction occurs. Coupling functions can be used, not only to understand, but also to control and predict the outcome of the interactions. This theme issue assembles ground-breaking work on coupling functions by leading scientists. After overviewing the field and describing recent advances in the theory, it discusses novel methods for the detection and reconstruction of coupling functions from measured data. It then presents applications in chemistry, neuroscience, cardio-respiratory physiology, climate, electrical engineering and social science. Taken together, the collection summarizes earlier work on coupling functions, reviews recent developments, presents the state of the art, and looks forward to guide the future evolution of the field.This article is part of the theme issue ‘Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences’.

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Section: Recent Work On Coupling Functionsmentioning

confidence: 99%

Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences

Stankovski

Pereira

McClintock

et al. 2019

Phil. Trans. R. Soc. A.

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show abstract

“…In [25], the Koopman operator theory and sparse identification techniques are combined to achieve accurate identification of nonlinear coupling functions. Moreover, adaptive master-slave synchronization-based methods [26,27], statistic-based methods [28] and variable (or phase) resetting-based methods [15,29] also achieve success.…”

Section: Introductionmentioning

confidence: 99%

Network Structure Identification Based on Measured Output Data Using Koopman Operators

Mei

Oguchi

2022

Mathematics

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This paper considers the identification problem of network structures of interconnected dynamical systems using measured output data. In particular, we propose an identification method based on the measured output data of each node in the network whose dynamic is unknown. The proposed identification method consists of three steps: we first consider the outputs of the nodes to be all the states of the dynamics of the nodes, and the unmeasurable hidden states to be dynamical inputs with unknown dynamics. In the second step, we define the dynamical inputs as new variables and identify the dynamics of the network system with measured output data using Koopman operators. Finally, we extract the network structure from the identified dynamics as the information transmitted via the network. We show that the identified coupling functions, which represent the network structures, are actually projections of the dynamical inputs onto the space spanned by some observable functions. Numerical examples illustrate the validity of the obtained results.

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“…Recently, Zhang et al proposed a new method to detect time delays and the average coupling strengths through the correlations induced by fast-varying noises (here called FVN). [36] The random state variable resetting (RSVR) [37,38] method proposed by Shi et al, as an active control method, can be used to detect the interactions in dynamical networks. By randomly resetting the state variable of a driving node, the influence of other nodes and variables on a response node can be simplified as background average and fluctuations, and then the equivalent coupling function of a driving node to a response node can be reconstructed using only the data of two related nodes.…”

Section: Introductionmentioning

confidence: 99%

Inferring interactions of time-delayed dynamic networks by random state variable resetting

2022

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Time delays exist widely in real systems, and time-delayed interactions can result in abundant dynamic behaviors and functions in dynamic networks. Inferring the time delays and interactions is challenging due to systematic nonlinearity, noises, a lack of information, and so on. Recently, Shi et al. proposed a random state variable resetting method to detect the interactions in a continuous-time dynamic network. By arbitrarily resetting the state variable of a driving node, the equivalent coupling functions of the driving node to any response node in the network can be reconstructed. In this paper, we introduce this method in time-delayed dynamic networks. To infer actual time delays, the nearest neighbor correlation (NNC) function for a given time delay is defined. The significant increments of NNC originate from the delayed effect. Based on the increments, the time delays can be reconstructed and the reconstruction errors depend on the sampling time interval. After time delays are accurately identified, the equivalent coupling functions can also be reconstructed. The numerical results have fully verified the validity of the theoretical analysis.

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Detecting directed interactions of networks by random variable resetting

Cited by 10 publications

References 39 publications

Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences

Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences

Network Structure Identification Based on Measured Output Data Using Koopman Operators

Inferring interactions of time-delayed dynamic networks by random state variable resetting

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