Dynamics of globally delay-coupled neurons displaying subthreshold oscillations

Masoller, Cristina; Torrent, M. C.; García‐Ojalvo, Jordi

doi:10.1098/rsta.2009.0096

Cited by 28 publications

(10 citation statements)

References 30 publications

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“…Astonishingly, even between distant parts of the brain that involve large signal transmission delays, synchronization of neural activity without a time lag has been observed [Roe97,Rod99,Fri97a,Sch06i,Var01]. This striking dynamical phenomenon is known as zero-lag synchronization in time-delay networks [Roe97,Vic08,Fis06,Dah12,Ros05,Hau07a,Mas08,Mas09a,Sen09a,Leh11,Pop11]. Synchronization of neural activity is important because, on one hand, it has been shown to lead to pathological states, such as Parkinson's disease or epilepsy; on the other hand, it has also been shown to 1 2 3…”

Section: Zero-lag Cluster Synchronizationmentioning

confidence: 99%

Dynamics of Complex Autonomous Boolean Networks

Rosin

2015

Springer Theses

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Network science provides a powerful framework for analyzing complex systems found in physics, biology, and social sciences. One way of studying the dynamics of networks is to engineer and measure them in the laboratory, which is particularly difficult with established approaches. In this thesis, I approach this problem using a hardware device with time-delay elements executing Boolean functions that can be connected to autonomous Boolean networks with chaotic, periodic, or excitable dynamics. I am able to make scientific discoveries for networks with each of these three different node dynamics, driven by the large flexibility and the non-ideal effects of the experiment complemented by analytical and numerical investigations.Using network realizations with periodic Boolean oscillators, I study socalled chimera states and find that they can disappear and reappear-the resurgence of chimera states. I measure the transient times of chimera states and find a power-law relationship between the average transient time and the phase space volume with an exponent of κ = −0.28 ± 0.10.I also study cluster synchronization in networks of coupled excitable systems. In these artificial neural networks, I find a breakdown of an established theoretical tool when the heterogeneity of the link time delays is greater than the neural refractory period. This phenomenon is used to derive a control scheme for spiking patterns generated by neural networks.Experimental implementations of these systems take advantage of the fast timescale of electronic logic gates, large scalability, and low price. These properties make the system attractive for technological applications, as I demonstrate by realizing a physical random number generator that has an ultra-high bitrate of 12.8 Gbit/s and a silicon neuron that is a thousand times faster than the fastest preceding silicon neuron. For the study of coupled oscillator networks, I develop a phase-locked loop allowing for multiple drivers that may be advantageous for clock synchronization. Instead of the common topologies with one driver per oscillator, it allows for heavily connected clock networks to increase robustness against failure.iii Z U S A M M E N FA S S U N G • D. P. Rosin, D. Rontani, and D. J. Gauthier. Ultrafast physical generation of random numbers using hybrid Boolean networks. Phys. Rev. E 87, 040902(R) (2013).• D. P. Rosin, D. Rontani, D. J. Gauthier, and E. Schöll. Excitability in autonomous Boolean networks. Europhys. Lett. 100, 30003 (2012).• D. P. Rosin, D. Rontani, D. J. Gauthier, and E. Schöll. Experiments on autonomous Boolean networks. Chaos 23, 025102 (2013).• D. P. Rosin, D. Rontani, and D. J. Gauthier. Synchronization of coupled Boolean phase oscillators. Phys. Rev. E 89, 042907 (2014).• D. P. Rosin, D. Rontani, E. Schöll, and D. J. Gauthier. Transient scaling and resurgence of chimera states in coupled Boolean phase oscillators.

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Section: Zero-lag Cluster Synchronizationmentioning

confidence: 99%

Dynamics of Complex Autonomous Boolean Networks

Rosin

2015

Springer Theses

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“…Time delays commonly exist in biological systems since the finite speed of signal transmission over a distance gives rise to finite time delay, which plays an importance role in the stability of synchronization (He and Cao 2008;Jirsa 2008;Masoller et al 2009;Ramirez et al 2009). For instance, time delay enhancing neuron synchrony, and cortical neurons synchronized by time delay feedback, for details, see (Dhamala et al 2004;Landsman and Schwartz 2007).…”

Section: Introductionmentioning

confidence: 97%

Analyzing inner and outer synchronization between two coupled discrete-time networks with time delays

Sun

Wang

et al. 2010

Cogn Neurodyn

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This paper studies two kinds of synchronization between two discrete-time networks with time delays, including inner synchronization within each network and outer synchronization between two networks. Based on Lyapunov stability theory and linear matrix inequality (LMI), sufficient conditions for two discrete-time networks to be asymptotic stability are derived in terms of LMI. Finally numerical examples are given to illustrate the effectiveness of our derived results. The theoretical understanding provides insights into the dynamics of two or more neural networks with appropriate couplings.

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“…Statistical mechanical techniques are not restricted to the Hopfield model (Coolen and Del Prete, 2003): they have been applied also to biological neural systems both to explain experimental data (Masoller et al, 2009; Montani et al, 2009; Deco et al, 2012) and to provide general models of the brain (Ingber, 1981; Freeman and Vitiello, 2006; Parker and Srivastava, 2013). …”

Section: Introductionmentioning

confidence: 99%

A statistical mechanical problem?

Costa

Ferraro

2014

Front. Psychol.

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The problem of deriving the processes of perception and cognition or the modes of behavior from states of the brain appears to be unsolvable in view of the huge numbers of elements involved. However, neural activities are not random, nor independent, but constrained to form spatio-temporal patterns, and thanks to these restrictions, which in turn are due to connections among neurons, the problem can at least be approached. The situation is similar to what happens in large physical ensembles, where global behaviors are derived by microscopic properties. Despite the obvious differences between neural and physical systems a statistical mechanics approach is almost inescapable, since dynamics of the brain as a whole are clearly determined by the outputs of single neurons. In this paper it will be shown how, starting from very simple systems, connectivity engenders levels of increasing complexity in the functions of the brain depending on specific constraints. Correspondingly levels of explanations must take into account the fundamental role of constraints and assign at each level proper model structures and variables, that, on one hand, emerge from outputs of the lower levels, and yet are specific, in that they ignore irrelevant details.

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Dynamics of globally delay-coupled neurons displaying subthreshold oscillations

Cited by 28 publications

References 30 publications

Dynamics of Complex Autonomous Boolean Networks

Dynamics of Complex Autonomous Boolean Networks

Analyzing inner and outer synchronization between two coupled discrete-time networks with time delays

A statistical mechanical problem?

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