Complexity and synchronization

Turalska, Malgorzata; Luković, Mirko; West, Bruce J.; Grigolini, Paolo

doi:10.1103/physreve.80.021110

Cited by 67 publications

(111 citation statements)

References 34 publications

Supporting

Mentioning

108

Contrasting

Unclassified

Order By: Relevance

“…(1) with μ = 1.5. We note that when K > 1, the DM model has two equilibrium states corresponding to the bottoms of a double-well potential [26]. At criticality the barrier disappears, resulting in the potential of Eq.…”

Section: Renewal Non-poisson Fluctuationsmentioning

confidence: 99%

Linear response at criticality

Bologna

Grigolini

2012

Phys. Rev. E

Self Cite

View full text Add to dashboard Cite

We study a set of cooperatively interacting units at criticality, and we prove with analytical and numerical arguments that they generate the same renewal non-Poisson intermittency as that produced by blinking quantum dots, thereby giving a stronger support to the results of earlier investigation. By analyzing how this out-ofequilibrium system responds to harmonic perturbations, we find that the response can be described only using a new form of linear response theory that accounts for aging and the nonergodic behavior of the underlying process. We connect the undamped response of the system at criticality to the decaying response predicted by the recently established nonergodic fluctuation-dissipation theorem for dichotomous processes using information about the second moment of the fluctuations. We demonstrate that over a wide range of perturbation frequencies the response of the cooperative system is greatest when at criticality.

show abstract

Section: Renewal Non-poisson Fluctuationsmentioning

confidence: 99%

Linear response at criticality

Bologna

Grigolini

2012

Phys. Rev. E

Self Cite

View full text Add to dashboard Cite

show abstract

“…The foundation of these papers is sociological and similar to that of the economical model illustrated in the work of Sornette [15]. Thus, the authors [18,19] did not discuss the connection of the DMM with the Ising model and adopted the nonrealistic but often made assumption of all-to-all coupling among the network's units, thereby confining the emergence of an inverse power law, namely, of temporal complexity, to the same time scale as that of the units in isolation.…”

Section: Introductionmentioning

confidence: 99%

“…The thermodynamical condition M = L = ∞ was discussed extensively by authors of [18,19], who showed that under those conditions the ratios…”

Section: Detailed Description Of the Modelmentioning

confidence: 99%

“…The parameter Q denotes the height of the potential barrier separating the wells, and D stands for the diffusion coefficient. Following [19] we expect the barrier to be a function of the coupling constant K and the diffusion to depend on the number of nodes L. By fitting the shoulder, once for a case where L is kept constant and K varies, and secondly for an opposite condition, we assess the above hypothesis. The fitting procedure revealed that the barrier height Q is a linear function of K (Q ∼ K) and that the diffusion coefficient D is inversely proportional to the system size L (D ∼ 1/L).…”

Section: Order Parameter Reversal Timesmentioning

confidence: 99%

“…One is [17], which converts the 3D Ising model into a critical map generating type I intermittent dynamics and consequently the same temporal complexity as the one under discussion herein. The emergence of nonPoisson renewal properties was also discussed in [18,19], which is devoted to illustrating the cooperative properties of a DMM. The foundation of these papers is sociological and similar to that of the economical model illustrated in the work of Sornette [15].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Temporal complexity of the order parameter at the phase transition

2011

Self Cite

View full text Add to dashboard Cite

We study a decision making model in a condition where it is equivalent to the two-dimensional Ising model, and we show that at the onset of phase transition it generates temporal complexity, namely, nonstationary and nonergodic fluctuations. We argue that this is a general property of criticality, thereby opening the door to the application of the recently discovered phenomenon of complexity matching: For an efficient transfer of information to occur, a perturbing complex network must share the same temporal complexity as the perturbed complex network.

show abstract

Neural Dynamics: Criticality, Cooperation, Avalanches, and Entrainment between Complex Networks

Grigolini

Zare²,

West

2014

Criticality in Neural Systems

Self Cite

View full text Add to dashboard Cite

The discovery of avalanches in neural systems [1] has aroused substantial interest among neurophysiologists and, more generally, among researchers in complex networks [2] as well. The main purpose of this chapter is to provide evidence in support of the hypothesis that the phenomenon of neural avalanches [1] is generated by the same cooperative properties as those responsible for a surprising effect that we call cooperation-induced synchronization, illustrated in [3]. The phenomenon of neural entrainment [4] is another manifestation of the same cooperative property. We also address the important issue of the connection between neural avalanches and criticality. Avalanches are thought to be a manifestation of criticality, and especially self-organized criticality [5,6]. At the same time, criticality is accompanied by long-range correlation [5] and a plausible model for neural dynamics is expected to account for the astounding interaction between agents separated by relatively large distances. General agreement exists in the literature that brain function rests on these crucial properties, and the phase transition theory for physical phenomena [7] is thought to afford the most important theoretical direction for further research work on this subject. In this theory criticality emerges at a specific single value of a control parameter, designated by the symbol K c . In this chapter we illustrate a theoretical model generating avalanches, long-range correlation and entrainment, as a form of cooperation-induced synchronization, over a wide range of values of the control parameter K, thereby suggesting that the form of criticality within the brain is not the ordinary criticality of physical phase transitions but is instead the extended criticality recently introduced by Longo and co-workers [8] to explain biological processes.Cooperation is the common effort of the elements of a network for their mutual benefit. We use the term cooperation in the same loose sense as that adopted, for instance, by Montroll [9] to shed light on the equilibrium condition realized by the interacting spins of the Ising model. Although the term cooperation, frequently used in this chapter, does not imply a network's cognition, we follow the conceptual

show abstract

Complexity and synchronization

Cited by 67 publications

References 34 publications

Linear response at criticality

Linear response at criticality

Temporal complexity of the order parameter at the phase transition

Neural Dynamics: Criticality, Cooperation, Avalanches, and Entrainment between Complex Networks

Contact Info

Product

Resources

About