Control of Synchronization Patterns in Neural-like Boolean Networks

Rosin, David P.; Rontani, Damien; Gauthier, Daniel J.; Schöll, Eckehard

doi:10.1103/physrevlett.110.104102

Cited by 92 publications

(84 citation statements)

References 35 publications

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“…Many versions of CS have been displayed. [48][49][50][51][52][53][54][55][56] These involve many different scenarios (unidirectional coupling, time delays, special network structures, etc. ), many of which are engineered to yield certain cluster synchronization patterns.…”

Section: B Networkmentioning

confidence: 99%

Synchronization of chaotic systems

Pecora

Carroll

2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

422

326

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We review some of the history and early work in the area of synchronization in chaotic systems. We start with our own discovery of the phenomenon, but go on to establish the historical timeline of this topic back to the earliest known paper. The topic of synchronization of chaotic systems has always been intriguing, since chaotic systems are known to resist synchronization because of their positive Lyapunov exponents. The convergence of the two systems to identical trajectories is a surprise. We show how people originally thought about this process and how the concept of synchronization changed over the years to a more geometric view using synchronization manifolds. We also show that building synchronizing systems leads naturally to engineering more complex systems whose constituents are chaotic, but which can be tuned to output various chaotic signals. We finally end up at a topic that is still in very active exploration today and that is synchronization of dynamical systems in networks of oscillators.

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Section: B Networkmentioning

confidence: 99%

Synchronization of chaotic systems

Pecora

Carroll

2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

422

326

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show abstract

“…Equally important, and perhaps more ordinary, is partial or cluster synchronization (CS), in which patterns or sets of synchronized elements emerge 3 . Recent work on CS has been restricted to networks where the synchronization pattern is induced either by tailoring the network geometry or by the intentional introduction of heterogeneity in the time delays or node dynamics [4][5][6][7][8][9][10][11] . These anecdotal studies illustrate the interesting types of CS that can occur, and suggest a broader relationship between the network structure and synchronization patterns.…”

mentioning

confidence: 99%

“…The non-trivial clusters are the nodes [1,8], [2,3,7,9], [4,6], [5,10] (the numbering of nodes matches the row and column numbers of A). The transformation matrix is …”

mentioning

confidence: 99%

Cluster synchronization and isolated desynchronization in complex networks with symmetries

et al. 2014

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Synchronization is of central importance in power distribution, telecommunication, neuronal and biological networks. Many networks are observed to produce patterns of synchronized clusters, but it has been difficult to predict these clusters or understand the conditions under which they form. Here we present a new framework and develop techniques for the analysis of network dynamics that shows the connection between network symmetries and cluster formation. The connection between symmetries and cluster synchronization is experimentally confirmed in the context of real networks with heterogeneities and noise using an electrooptic network. We experimentally observe and theoretically predict a surprising phenomenon in which some clusters lose synchrony without disturbing the others. Our analysis shows that such behaviour will occur in a wide variety of networks and node dynamics. The results could guide the design of new power grid systems or lead to new understanding of the dynamical behaviour of networks ranging from neural to social.

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“…In recent decades, many works focused on the synchronization between neurons [1][2][3][4][5] as this mechanism was believed to be vital for several cognitive functions. The concept of small-world networks by Watts and Strogatz was also included [1,6].…”

Section: Introductionmentioning

confidence: 99%

Spatial evolution of Hindmarsh–Rose neural network with time delays

Łepek¹,

Fronczak²

2018

Nonlinear Dyn

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Spatial relations between neurons in the network with time delays play a crucial role in determining dynamics of the system. During the development of the nervous system, different types of neurons group together to enable specific functions of the network. Right spatial distances, thus right time delays between cells are crucial for an appropriate functioning of the system. To model the process of neural migration, we proposed simple but effective model of network spatial evolution based on Hindmarsh-Rose neurons and Metropolis-Hastings Monte Carlo algorithm. Under the specific assumptions and using appropriate parameters of the neural evolution, the network can converge to the desirable state giving the opportunity of achieving large variety of spectra. We show that there is a specific range of network size in space which allows it to generate assumed output. A network or generally speaking a system with time delays (corresponding to the arrangement in the physical space) of specific output properties has a specific spatial dimension that allows it to function properly.

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Control of Synchronization Patterns in Neural-like Boolean Networks

Cited by 92 publications

References 35 publications

Synchronization of chaotic systems

Synchronization of chaotic systems

Cluster synchronization and isolated desynchronization in complex networks with symmetries

Spatial evolution of Hindmarsh–Rose neural network with time delays

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