Effect of node-degree correlation on synchronization of identical pulse-coupled oscillators

LaMar, M. Drew; Smith, Gregory D.

doi:10.1103/physreve.81.046206

Cited by 24 publications

(26 citation statements)

References 35 publications

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“…This result is consistent with the recent work by LaMar and Smith (2010), who investigated how correlation between in-degree and out-degree decreases the time until complete synchrony in noiseless pulse-coupled PRC models.…”

Section: Discussionsupporting

confidence: 92%

Synchronization from Second Order Network Connectivity Statistics

Zhao¹,

Beverlin²,

Netoff³

et al. 2011

Front. Comput. Neurosci.

136

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We investigate how network structure can influence the tendency for a neuronal network to synchronize, or its synchronizability, independent of the dynamical model for each neuron. The synchrony analysis takes advantage of the framework of second order networks, which defines four second order connectivity statistics based on the relative frequency of two-connection network motifs. The analysis identifies two of these statistics, convergent connections, and chain connections, as highly influencing the synchrony. Simulations verify that synchrony decreases with the frequency of convergent connections and increases with the frequency of chain connections. These trends persist with simulations of multiple models for the neuron dynamics and for different types of networks. Surprisingly, divergent connections, which determine the fraction of shared inputs, do not strongly influence the synchrony. The critical role of chains, rather than divergent connections, in influencing synchrony can be explained by their increasing the effective coupling strength. The decrease of synchrony with convergent connections is primarily due to the resulting heterogeneity in firing rates.

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Section: Discussionsupporting

confidence: 92%

Synchronization from Second Order Network Connectivity Statistics

Zhao¹,

Beverlin²,

Netoff³

et al. 2011

Front. Comput. Neurosci.

136

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show abstract

“…We further hypothesize that such an anti-correlation leads to a distribution of synaptic connectivity motifs that is different than for a random network (Milo et al, 2002). Experiments show that barrel cortical circuits have a motif distribution that is different from random (Song et al, 2005; Perin et al, 2011), whereas theoretical studies show that networks with non-random motif distribution have different synchronization properties (Roxin, 2011; Zhao et al, 2011; Litwin-Kumar and Doiron, 2012) (LaMar and Smith, 2010) and can emerge through synaptic plasticity during reward-based learning (Bourjaily and Miller, 2011a,b). Our work is the first that focuses on the effect on network dynamics of correlations between the in- and out-degree of the same neuron, rather than between in- and/or out-degrees of different neurons, which is referred to as assortativity (Newman, 2010).…”

Section: Introductionmentioning

confidence: 99%

Simultaneous stability and sensitivity in model cortical networks is achieved through anti-correlations between the in- and out-degree of connectivity

Vasquez

Houweling

Tiesinga

2013

Front. Comput. Neurosci.

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Neuronal networks in rodent barrel cortex are characterized by stable low baseline firing rates. However, they are sensitive to the action potentials of single neurons as suggested by recent single-cell stimulation experiments that reported quantifiable behavioral responses in response to short spike trains elicited in single neurons. Hence, these networks are stable against internally generated fluctuations in firing rate but at the same time remain sensitive to similarly-sized externally induced perturbations. We investigated stability and sensitivity in a simple recurrent network of stochastic binary neurons and determined numerically the effects of correlation between the number of afferent ("in-degree") and efferent ("out-degree") connections in neurons. The key advance reported in this work is that anti-correlation between in-/out-degree distributions increased the stability of the network in comparison to networks with no correlation or positive correlations, while being able to achieve the same level of sensitivity. The experimental characterization of degree distributions is difficult because all pre-synaptic and post-synaptic neurons have to be identified and counted. We explored whether the statistics of network motifs, which requires the characterization of connections between small subsets of neurons, could be used to detect evidence for degree anti-correlations. We find that the sample frequency of the 3-neuron "ring" motif (1→2→3→1), can be used to detect degree anti-correlation for sub-networks of size 30 using about 50 samples, which is of significance because the necessary measurements are achievable experimentally in the near future. Taken together, we hypothesize that barrel cortex networks exhibit degree anti-correlations and specific network motif statistics.

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“…However, to our knowledge, so far there is no known pulse coupled oscillator system that satisfies all these requirements simultaneously. In particular, theoretical results suffer from constraints regarding at least one of the requirements: synchronization may be guaranteed only in the absence of delays [18][19][20], only for specific network topologies [21][22][23][24][25] or only for a certain subset of initial conditions [26][27][28][29]. Synchronization on different network topologies.…”

Section: Introductionmentioning

confidence: 99%

Guaranteeing global synchronization in networks with stochastic interactions

et al. 2012

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We design the interactions between oscillators communicating via variably delayed pulse coupling to guarantee their synchronization on arbitrary network topologies. We identify a class of response functions and prove convergence to network-wide synchrony from arbitrary initial conditions. Synchrony is achieved if the pulse emission is unreliable or intentionally probabilistic. These results support the design of scalable, reliable and energyefficient communication protocols for fully distributed synchronization as needed, e.g., in mobile phone networks, embedded systems, sensor networks and autonomously interacting swarm robots.

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Effect of node-degree correlation on synchronization of identical pulse-coupled oscillators

Cited by 24 publications

References 35 publications

Synchronization from Second Order Network Connectivity Statistics

Synchronization from Second Order Network Connectivity Statistics

Simultaneous stability and sensitivity in model cortical networks is achieved through anti-correlations between the in- and out-degree of connectivity

Guaranteeing global synchronization in networks with stochastic interactions

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