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Related papers: Deterministic Bak-Sneppen model. Lyapunov spectrum…

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We study the discrete Bak-Sneppen model introduced by Barbay and Kenyon (2001) "On the discrete Bak-Sneppen model of self-organized criticality". We extend their results as well as the non-triviality result of Meester and Znamenskiy (2002)…

Probability · Mathematics 2025-06-19 Serguei Popov , Stanislav Volkov

We discuss the role played by the Lyapunov exponents in the dynamics of Zhang's model of Self-Organized Criticality. We show that a large part of the spectrum (slowest modes) is associated with the energy transpor in the lattice. In…

Statistical Mechanics · Physics 2009-10-31 B. Cessac , Ph. Blanchard , T. Krueger

We study the scaling behavior of the Lyapunov spectra of a chaotic shell model for 3D turbulence. First, we quantify localization of the Lyapunov vectors in the wavenumber space by using the numerical results. Using dimensional arguments of…

chao-dyn · Physics 2008-02-03 M. Yamada , K. Ohkitani

Avalanches of electrochemical activity in brain networks have been empirically reported to obey scale-invariant behavior --characterized by power-law distributions up to some upper cut-off-- both in vitro and in vivo. Elucidating whether…

Neurons and Cognition · Quantitative Biology 2018-01-03 Matteo Martinello , Jorge Hidalgo , Serena di Santo , Amos Maritan , Dietmar Plenz , Miguel A. Muñoz

Elastic systems driven in a disordered medium exhibit a depinning transition at zero temperature and a creep regime at finite temperature and slow drive $f$. We derive functional renormalization group equations which allow to describe in…

Disordered Systems and Neural Networks · Physics 2009-10-31 Pascal Chauve , Thierry Giamarchi , Pierre Le Doussal

Plastic deformation of crystals proceeds through a sequence of intermittent slip avalanches with scale-free (power-law) size distribution. On macroscopic scales, however, plastic flow is known to be smooth and homogeneous. In the present…

Statistical Mechanics · Physics 2009-11-13 Michael Zaiser , Nikos Nikitas

We consider the Bak-Tang-Wiesenfeld (BTW) and the Manna sandpile models of self-organized criticality. In the models, previous studies revealed a signature of long-range temporal correlations in the avalanche activity. We examine the power…

Statistical Mechanics · Physics 2025-07-30 Rahul Chhimpa , Avinash Chand Yadav

We consider the Bak-Tang-Wiesenfeld sandpile model on square lattices in different dimensions (D>=6). A finite size scaling analysis of the avalanche probability distributions yields the values of the distribution exponents, the dynamical…

Condensed Matter · Physics 2009-10-30 S. Lubeck , K. D. Usadel

A dynamic scaling Ansatz for the approach to the Self-Organized Critical (SOC) regime is proposed and tested by means of extensive simulations applied to the Bak-Sneppen model (BS), which exhibits robust SOC behavior. Considering the…

Adaptation and Self-Organizing Systems · Physics 2009-11-11 Karina Laneri , Alejandro F. Rozenfeld , Ezequiel V. Albano

One of the key problems related to the Bak-Sneppen evolution model on the circle is to compute the limit distribution of the fitness at a fixed observation vertex in the stationary regime, as the size of the system tends to infinity.…

Disordered Systems and Neural Networks · Physics 2007-05-23 R. Meester , D. Znamenski

We use a discrete-time formulation to study the asymmetric avalanche process [Phys. Rev. Lett. vol. 87, 084301 (2001)] on a finite ring and obtain an exact expression for the average avalanche size of particles as a function of toppling…

Statistical Mechanics · Physics 2009-11-10 A. M. Povolotsky , V. B. Priezzhev , Chin-Kun Hu

In this work we study the effects of introducing long range interactions in the Bak-Sneppen (BS) model of biological evolution. We analyze a recebtly propopsed version of the BS model where the interactions decay as r^{-alpha}; in this way…

Disordered Systems and Neural Networks · Physics 2009-10-31 Pablo M. Gleiser , Francisco A. Tamarit , Sergio A. Cannas

The structure of Lyapunov spectra for many particle systems with a random interaction between the particles is discussed. The dynamics of the tangent space is expressed as a master equation, which leads to a formula that connects the…

Chaotic Dynamics · Physics 2007-05-23 Tooru Taniguchi , Gary P. Morriss

We study the backwards Markov chain for the Bak-Sneppen model of biological evolution and derive its corresponding reversibility equations. We show that, in contrast to the forwards Markov chain, the dynamics of the backwards chain…

Probability · Mathematics 2020-10-02 Tom Alberts , Ga Yeong Lee , Mackenzie Simper

This paper presents new sufficient conditions for convergence and asymptotic or exponential stability of a stochastic discrete-time system, under which the constructed Lyapunov function always decreases in expectation along the system's…

Systems and Control · Computer Science 2019-06-05 Yuzhen Qin , Ming Cao , Brian D. O. Anderson

We discuss avalanche and finite size fluctuations in a mesoscopic model to describe the shear plasticity of amorphous materials. Plastic deformation is assumed to occur through series of local reorganizations. Yield stress criteria are…

Soft Condensed Matter · Physics 2011-12-06 Mehdi Talamali , Viljo Petäjä , Damien Vandembroucq , Stéphane Roux

This paper applies the theory of continuous phase transitions of statistical mechanics to a slider-block model. The slider-block model is chosen as a representative of systems with avalanches. Similar behavior can be observed in a…

Statistical Mechanics · Physics 2009-09-20 S. G. Abaimov

Avalanche dynamics is an indispensable feature of complex systems. Here we study the self-organized critical dynamics of avalanches on scale-free networks with degree exponent $\gamma$ through the Bak-Tang-Wiesenfeld (BTW) sandpile model.…

Statistical Mechanics · Physics 2007-05-23 D. -S. Lee , K. -I. Goh , B. Kahng , D. Kim

We investigate the behavior of the Lyapunov spectrum of a linear discrete-time system under the action of small perturbations in order to obtain some verifiable conditions for stability and openness of the Lyapunov spectrum. To this end we…

Dynamical Systems · Mathematics 2025-09-03 Adam Czornik , Evgenii Makarov , Michal Niezabitowski , Svetlana Popova , Vasilii Zaitsev

Two cellular automata models with directed mass flow and internal time scales are studied by numerical simulations. Relaxation rules are a combination of probabilistic critical height (probability of toppling $p$) and deterministic critical…

Statistical Mechanics · Physics 2009-10-31 Bosiljka Tadic