Nonequilibrium transitions in complex networks: A model of social interaction

Klemm, Konstantin; Eguı́luz, Vı́ctor M.; Toral, Raúl; Miguel, M. San

doi:10.1103/physreve.67.026120

Cited by 224 publications

(314 citation statements)

References 27 publications

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“…But the main difference with these previous works is the fact that all these phenomena were identified for external noise whereas here the phenomenon evidenced is related to the level of heterogeneities. In the quenched heterogeneity case, outstanding works addressed the problem of chaotic or order-disorder transitions [6,19] or the dynamics of quenched randomly in coupled oscillators [20], both differing from the transition reported here since we do not deal with coupled oscillators, and addressed a transition to synchronized oscillations. A sudden apparition of synchronized large-amplitude arbitrarily slow oscillations is strongly evocative of epileptic seizures.…”

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confidence: 99%

Heterogeneous Connections Induce Oscillations in Large-Scale Networks

Hermann

Touboul

2012

Phys. Rev. Lett.

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Realistic large-scale networks display an heterogeneous distribution of connectivity weights, that might also randomly vary in time. We show that depending on the level of heterogeneity in the connectivity coefficients, different qualitative macroscopic and microscopic regimes emerge. We evidence in particular generic transitions from stationary to perfectly periodic phase-locked regimes as the disorder parameter is increased, both in a simple model treated analytically and in a biologically relevant network made of excitable cells. (i) the precise number of receptors and the extremely slow plasticity mechanisms induce a static disorder termed quenched synaptic heterogeneities.(ii) Thermal noise, channel noise and the intrinsically noisy mechanisms of release and binding of neurotransmitter [4] result in stochastic variations of the synaptic weights termed stochastic synaptic noise. Experimental studies of cortical areas [5] showed that the degree of heterogeneity in the connections significantly impacts the input-output function, rhythmicity and synchrony. Yet, qualitative effects induced by connection heterogeneities are still poorly understood theoretically. One notable exception is the work of Sompolinsky and collaborators [6]. In the thermodynamic limit of a onepopulation firing-rate neuronal network with synaptic weights modeled as centered independent Gaussian random variables, they evidenced a phase transition between a stationary and a chaotic regime as the disorder is increased. Besides stationary and chaotic regimes, synchronized oscillations is a highly relevant macroscopic state. It is related to fundamental cortical functions such as memory, attention, sleep and consciousness, and its impairments relate to serious pathologies such as epilepsy or Parkinson's disease [7,8].In this Letter, we show that both quenched and stochastic heterogeneities induce the emergence of macroscopic, perfectly periodic oscillations in the meanfield limit, corresponding to phase-locked oscillations of all neurons in the network. A generic transition from a stationary to a periodic regime as disorder increases will first be demonstrated in the case of firing-rate neurons. Similar reasoning will lead us to uncover the same transition in a more realistic network featuring excitable cells.Models of cortical areas involve at least two neural populations, one excitatory corresponding e.g. to pyramidal neurons and one inhibitory population modeling interneurons. In the firing-rate model with N neurons and P populations, the dynamics of the membrane potential (V i , i ∈ {1 · · · N }) of all neurons in the network is given by the system equations:where p i is the population index of neuron i, τ pi is a common characteristic time of all neurons of population p i and I pi (t) their deterministic input. The interaction with the other neurons in the network is given by the sum of a synaptic efficacy J ij multiplied by the firing rate of the presynaptic cell, a positive sigmoidal transform (S(·)) of the voltage. Network heterogeneiti...

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confidence: 99%

Heterogeneous Connections Induce Oscillations in Large-Scale Networks

Hermann

Touboul

2012

Phys. Rev. Lett.

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“…behaviour governed by nonlinear dynamical equations and even the links can evolve due to the motion of the nodes [38]. In the last two decades, complex networks theory became an important research topic and its application to numerous complex systems of very different nature including physical [39], chemical [40], biological [41], economic [42], social [43] and climatic [33], among others, gives evidence of its practical importance. Details of complex network theory can be found in the studies of Albert & Barabasi [44] and Boccaletti et al [45].…”

Section: Introductionmentioning

confidence: 99%

Classification of cardiovascular time series based on different coupling structures using recurrence networks analysis

Ramírez-Ávila

Gapelyuk²,

Marwan

et al. 2013

Phil. Trans. R. Soc. A.

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We analyse cardiovascular time series with the aim of performing early prediction of preeclampsia (PE), a pregnancy-specific disorder causing maternal and foetal morbidity and mortality. The analysis is made using a novel approach, namely the ε -recurrence networks applied to a phase space constructed by means of the time series of the variabilities of the heart rate and the blood pressure (systolic and diastolic). All the possible coupling structures among these variables are considered for the analysis. Network measures such as average path length, mean coreness, global clustering coefficient and scale-local transitivity dimension are computed and constitute the parameters for the subsequent quadratic discriminant analysis. This allows us to predict PE with a sensitivity of 91.7 per cent and a specificity of 68.1 per cent, thus validating the use of this method for classifying healthy and preeclamptic patients.

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“…Such spin-flip models are representative of many real situations which offer only two possibilities and therefore are also of great interest [1,17,18], along with the similarities with other physical systems. Axelrod's model for dissemination of culture is particularly different from the rest because the agents interact only if some degree of coincidence exists between them [5][6][7].…”

Section: Introductionmentioning

confidence: 99%

“…A great deal of effort has been devoted to developing models for describing the properties of systems made up of agents with competing opinions [1,[4][5][6][7][14][15][16][17][18][19][20]. This is of great relevance as human conflicts very often arise from the simultaneous existence of incompatible opinions in populations.…”

Section: Introductionmentioning

confidence: 99%

“…Nevertheless, simple statistical models have been developed for describing social systems [1][2][3][4][5][6][7], the economy [8][9][10][11], etc. Despite the great complexity of such real systems, their main properties can be reproduced by simple models which retain their underlying features, and the explanation for this fact is related to the concept of universality [12,13].…”

Section: Introductionmentioning

confidence: 99%

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Dynamical model for competing opinions

Souza

Gonçalves

2012

Phys. Rev. E

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We propose an opinion model based on agents located at the vertices of a regular lattice. Each agent has an independent opinion (among an arbitrary, but fixed, number of choices) and its own degree of conviction. The latter changes every time two agents which have different opinions interact with each other. The dynamics leads to size distributions of clusters (made up of agents which have the same opinion and are located at contiguous spatial positions) which follow a power law, as long as the range of the interaction between the agents is not too short; i.e., the system self-organizes into a critical state. Short range interactions lead to an exponential cutoff in the size distribution and to spatial correlations which cause agents which have the same opinion to be closely grouped. When the diversity of opinions is restricted to two, a nonconsensus dynamic is observed, with unequal population fractions, whereas consensus is reached if the agents are also allowed to interact with those located far from them. The individual agents' convictions, the preestablished interaction range, and the locality of the interaction between a pair of agents (their neighborhood has no effect on the interaction) are the main characteristics which distinguish our model from previous ones.

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Nonequilibrium transitions in complex networks: A model of social interaction

Cited by 224 publications

References 27 publications

Heterogeneous Connections Induce Oscillations in Large-Scale Networks

Heterogeneous Connections Induce Oscillations in Large-Scale Networks

Classification of cardiovascular time series based on different coupling structures using recurrence networks analysis

Dynamical model for competing opinions

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