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1.
We prove that a modified version of the Bak-Sneppen model obeys power law behaviour for avalanche duration and size. We do this through a coupling with a suitable branching process which is known to have power law behaviour at criticality. 相似文献
2.
The Bak-Sneppen model of co-evolution is used to derive synthetic time series with a priori specified fractal dimension (or Hurst exponent) through a mixing of processes in various lattice dimensions. Both theoretical and numerical analyses concern the avalanches at the critical threshold and provide a model for time series reconstruction that can be tested as an alternative to the classical fractional Brownian motion (fBm) because of differences in properties. New results on critical threshold and avalanche structure are obtained up to Euclidean dimension d=6. The method involves a lattice-based structure and therefore is suitable for the application of parallel computing. 相似文献
3.
We introduce a modified small-world network adding new links with nonlinearly preferential connection instead of adding randomly, then we apply Bak-Sneppen (BS) evolution model on this network. We study several important structural properties of our network such as the distribution of link-degree, the maximum link-degree, and the length of the shortest path. We further argue several dynamical characteristics of the model such as the important critical value fc, the f0 avalanche, and the mutating condition, and find that those characteristics show particular behaviors. 相似文献
4.
In this paper, we introduce a modified small-world network added with
new links with preferential connection instead of adding randomly,
then we apply Bak-Sneppen (BS) evolution model on this network.
Several dynamical character of the model such as the evolution
graph, f0 avalanche, the critical exponent D and τ, and
the distribution of mutation times of all the nodes, show
particular behaviors different from those of the model based on
the regular network and the small-world network. 相似文献
5.
We introduce a modified small-world network adding new links with
nonlinearly preferential connection instead of adding randomly,
then we apply Bak-Sneppen (BS) evolution model on this network. We
study several important structural properties of our network such
as the distribution of link-degree, the maximum link-degree, and the length of the shortest path. We further argue several dynamical characteristics of the model such as the important
critical value fc, the
f0 avalanche, and the mutating condition, and find that those characteristics show particular behaviors. 相似文献
6.
B. Bakar U. Tirnakli 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,62(1):95-99
We implement the damage spreading technique on 2-dimensional isotropic and anisotropic Bak-Sneppen models. Our extensive numerical
simulations show that there exists a power-law sensitivity to the initial conditions at the statistically stationary state
(self-organized critical state). Corresponding growth exponent α for the Hamming distance and the dynamical exponent z are
calculated. These values allow us to observe a clear data collapse of the finite size scaling for both versions of the Bak-Sneppen
model. Moreover, it is shown that the growth exponent of the distance in the isotropic and anisotropic Bak-Sneppen models
is strongly affected by the choice of the transient time. 相似文献
7.
Perturbative approach to the Bak-Sneppen model 总被引:1,自引:0,他引:1
We study the Bak-Sneppen model in the probabilistic framework of the run time statistics (RTS). This model has attracted a large interest for its simplicity being a prototype for the whole class of models showing self-organized criticality. The dynamics is characterized by a self-organization of almost all the species fitnesses above a nontrivial threshold value, and by a lack of spatial and temporal characteristic scales. This results in avalanches of activity power law distributed. In this Letter we use the RTS approach to compute the value of x(c), the value of the avalanche exponent tau, and the asymptotic distribution of minimal fitnesses. 相似文献
8.
We show that the emergence of criticality in the locally-defined Bak-Sneppen model corresponds to separation over a hierarchy
of timescales. Near to the critical point the model obeys scaling relations, with exponents which we derive numerically for
a one-dimensional system. We further describe how the model can be related to the glass model of Bouchaud (J. Phys. I France
2, 1705 (1992)), and we use this insight to comment on the usual assumption of stationarity in the Bak-Sneppen model. Finally,
we propose a general definition of self-organised criticality which is in partial agreement with other recent definitions.
Received 14 January 2000 and Received in final form 18 April 2000 相似文献
9.
R. Cafiero A. Valleriani J.L. Vega 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,4(4):405-408
We study the behavior under perturbations in the, recently introduced, Bak-Sneppen model with deterministic updating. We focus
our attention on the damage-spreading features and show that the value of the growth exponent for the distance, , coincides with that of the random updating Bak-Sneppen model. Moreover, we generalize this analysis by considering a broader
set of initial perturbations for which the value of is preserved.
Received: 24 June 1998 / Accepted: 9 July 1998 相似文献
10.
Some deviant breakdown-quenching characteristics of silicon photomultipliers are demonstrated and their physical mechanisms are explored. “Twice breakdown” phenomenon, “flat-topped” avalanche pulses and the determination method of the real breakdown voltage of the detector are analyzed. These characteristics are explained by the integration model in terms of avalanche threshold current based on the Haitz's equivalent circuit model. The reasoning results show that the maximum over-voltage for a normal operating silicon photomultiplier equals the product of the avalanche threshold current and the quenching resistor of the avalanche photo-diode (APD) pixel, approximately. Moreover, the model and results can be extended to other small avalanche junctions with quenching resistor. 相似文献
11.
K. E. Lee J. W. Lee 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,50(1-2):271-275
We study a simple model for a neuron function in a collective brain
system. The neural network is composed of an uncorrelated
configuration model (UCM) for eliminating the degree correlation
of dynamical processes. The interaction of neurons is assumed to
be isotropic and idealized. These neuron dynamics are similar to
biological evolution in extremal dynamics with locally isotropic
interaction but has a different time scale. The functioning of
neurons takes place as punctuated patterns based on avalanche
dynamics. In our model, the avalanche dynamics of neurons exhibit
self-organized criticality which shows power-law behavior of the
avalanche sizes. For a given network, the avalanche dynamic
behavior is not changed with different degree exponents of
networks, γ≥2.4 and various refractory periods
referred to the memory effect, Tr. Furthermore, the avalanche
size distributions exhibit power-law behavior in a single scaling
region in contrast to other networks. However, return time
distributions displaying spatiotemporal complexity have three
characteristic time scaling regimes Thus, we find that UCM may be
inefficient for holding a memory. 相似文献
12.
One of the key problems related to the Bak-Sneppen evolution model is to compute the limit distribution of the fitnesses in the stationary regime, as the size of the system tends to infinity. Simulations in [3, 1, 4] suggest that the one-dimensional limit marginal distribution is uniform on (pc, 1), for some pc 0.667. In this paper we define three critical thresholds related to avalanche characteristics. We prove that if these critical thresholds are the same and equal to some pc (we can only prove that two of them are the same) then the limit distribution is the product of uniform distributions on (pc, 1), and moreover pc<0.75. Our proofs are based on a self-similar graphical representation of the avalanches. 相似文献
13.
We considered a Bak-Sneppen model on a Sierpinski gasket fractal. We calculated the avalanche size distribution and the distribution of distances between subsequent minimal sites. To observe the temporal correlations of the avalanche, we estimated the return time distribution, the first-return time, and the all-return time distribution. The avalanche size distribution follows the power law, P(s)∼s−τ, with the exponent τ=1.004(7). The distribution of jumping sites also follows the power law, P(r)∼r−π, with the critical exponent π=4.12(4). We observe the periodic oscillation of the distribution of the jumping distances which originated from the jumps of the level when the minimal site crosses the stage of the fractal. The first-return time distribution shows the power law, Pf(t)∼t−τf, with the critical exponent τf=1.418(7). The all-return time distribution is also characterized by the power law, Pa(t)∼t−τa, with the exponent τa=0.522(4). The exponents of the return time satisfy the scaling relation τf+τa=2 for τf?2. 相似文献
14.
A. F. Rozenfeld K. Laneri E. V. Albano 《The European physical journal. Special topics》2007,143(1):3-8
A dynamic scaling Ansatz for the approach to stationary states in complex systems
is proposed and tested by means of extensive simulations applied to both
the Bak-Sneppen (BS) model, which exhibits robust Self-Organised
Critical (SOC) behaviour, and the Game of Life (GOL) of J. Conway,
whose critical behaviour is under debate. Considering the dynamic scaling behaviour of the density of
sites (ρ(t)), it is shown that i) by starting the dynamic measurements with configurations
such that ρ(t=0) →0, one observes an initial increase of the
density with exponents θ= 0.12(2) and θ= 0.11(2) for the BS and GOL models, respectively;
ii) by using initial configurations with ρ(t=0) →1, the density decays with exponents δ= 0.47(2) and δ= 0.28(2) for the BS
and GOL models, respectively.
It is also shown that the temporal autocorrelation decays with exponents
Ca = 0.35(2) (Ca = 0.35(5)) for the BS (GOL) model.
By using these dynamically determined critical exponents
and suitable scaling relationships, we also obtain the dynamic
exponents z = 2.10(5) (z = 2.10(5)) for the
BS (GOL) model.
Based on this evidence we conclude that the dynamic
approach to stationary states of the investigated models
can be described by suitable power-law functions
of time with well-defined exponents. 相似文献
15.
C.B. Yang X. Cai 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,22(3):375-379
A new type of spatio-temporal correlation function for the process approaching the self-organized criticality is investigated
within the Bak-Sneppen model for biological evolution. In terms of the “directional shorter distance” between the two sites
with minimum fitness at two successive updates, the correlation function is defined and studied numerically for the nearest-
and random-neighbor versions of the model. Qualitatively different behaviors of the jump of the minimal site in the two models
are presented, and the behaviors of the correlation functions are shown also different.
Received 14 April 2001 and Received in final form 28 June 2001 相似文献
16.
R. Cafiero A. Valleriani J.L. Vega 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,7(4):505-508
We study the behavior under perturbations of the Parallel Bak-Sneppen model (PBS) in 1+1 dimension, which has been shown to
belong to the universality class of Directed Percolation (DP) in 1+1 dimensions [#!SD96!#]. We focus our attention on the
damage-spreading features of the PBS model with both random and deterministic updating, which are studied and compared to
the known results for the extremal Bak-Sneppen model (BS) and for DP. For both random and deterministic updating, we observe
a power law growth of the Hamming distance. In addition, we compute analytically the asymptotic plateau reached by the distance
after the growing phase.
Received: 24 September 1998 / Revised: 17 November 1998 / Accepted: 19 November
1998 相似文献
17.
We introduce a sandpile model driven by degree on scale-free networks, where the perturbation is triggered at nodes with the same degree. We numerically investigate the avalanche behaviour of sandpile driven by different degrees on scale-free networks. It is observed that the avalanche area has the same behaviour with avalanche size. When the sandpile is driven at nodes with the minimal degree, the avalanches of our model behave similarly to those of the original Bak-Tang-Wiesenfeld (BTW) model on scale-free networks. As the degree of driven nodes increases from the minimal value to the maximal value, the avalanche distribution gradually changes from a clean power law, then a mixture of Poissonian and power laws, finally to a Poisson-like distribution. The average avalanche area is found to increase with the degree of driven nodes so that perturbation triggered on higher-degree nodes will result in broader spreading of avalanche propagation. 相似文献
18.
Minghua Zhao Jingkun Zhan Yong Fan Zongrui He Yonghong Zhang 《International Journal of Infrared and Millimeter Waves》2008,29(8):741-747
A W band microstrip integrated high order frequency multiplier based on avalanche diode is proposed. The property of avalanche
high order multiplication mode is analyzed based on physical operation mechanism of avalanche diode. According to the harmonics
impedance model of avalanche diode, the microstrip integrated multiplier is designed, fabricated and measured. Output power
of 5.78 mW has been obtained at output frequency of 94.5 GHz with 15th multiplication order and the phase noise is -90 dBc/Hz
and -95 dBc/Hz at 10 KHz and 100 KHz offset. Good results at 13th and 17th multiplication order are also obtained. 相似文献
19.
A. A. Tren’kin 《Technical Physics》2010,55(8):1145-1149
The results of simulation of the current channel microstructure formation in atmospheric nano- second discharges in a uniform
electric field due to the development of instability of the ionization process in the avalanche stage followed by cycling
breakdowns of the avalanche are considered. It is shown that the enhancement of the electric field at the ionization front
due to the intrinsic field of the avalanche leads to the contraction of the path length between consecutive avalanche breakups;
after several breakups, the ionized gas passes to the plasma state. The effect of small electric field perturbations on the
dynamics of microstructure formation is investigated; as a result, the possibility of “induced” avalanche breakup at the instant
of action of perturbations is established. 相似文献
20.
We numerically investigate the avalanche dynamics of the Bak-Tang-Wiesenfeld sandpile model on directed small-world networks. We find that the avalanche size and duration distribution follow a power law for all rewiring probabilities p. Specially, we find that, approaching the thermodynamic limit (L→∞), the values of critical exponents do not depend on p and are consistent with the mean-field solution in Euclidean space for any p>0. In addition, we measure the dynamic exponent in the relation between avalanche size and avalanche duration and find that the values of the dynamic exponents are also consistent with the mean-field values for any p>0. 相似文献