共查询到20条相似文献,搜索用时 289 毫秒
1.
《中国物理快报》2016,(4)
To describe the empirical data of collaboration networks,several evolving mechanisms have been proposed,which usually introduce different dynamics factors controlling the network growth.These models can reasonably reproduce the empirical degree distributions for a number of well-studied real-world collaboration networks.On the basis of the previous studies,in this work we propose a collaboration network model in which the network growth is simultaneously controlled by three factors,including partial preferential attachment,partial random attachment and network growth speed.By using a rate equation method,we obtain an analytical formula for the act degree distribution.We discuss the dependence of the act degree distribution on these different dynamics factors.By fitting to the empirical data of two typical collaboration networks,we can extract the respective contributions of these dynamics factors to the evolution of each networks. 相似文献
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In this study, we consider analytical solutions of space–time fractional derivative foam drainage equation, the nonlinear Korteweg–de Vries equation with time and space-fractional derivatives and time-fractional reaction–diffusion equation by using the extended tanh method. The fractional derivatives are defined in the modified Riemann–Liouville context. As a result, various exact analytical solutions consisting of trigonometric function solutions, kink-shaped soliton solutions and new exact solitary wave solutions are obtained. 相似文献
5.
Y. Kobayashi T. Shibata Y. Kuramoto A. S. Mikhailov 《The European Physical Journal B - Condensed Matter and Complex Systems》2010,76(1):167-178
The present study is devoted to the design and statistical investigations of
dynamical gene expression networks. In our model problem, we aim to design
genetic networks which would exhibit stable periodic oscillations with a
prescribed temporal period. While no rational solution of this problem is
available, we show that it can be effectively solved by running a computer
evolution of the network models. In this process, structural rewiring
mutations are applied to the networks with inhibitory interactions between
genes and the evolving networks are selected depending on whether, after a
mutation, they closer approach the targeted dynamics. We show that, by using
this method, networks with required oscillation periods, varying by up
to three orders of magnitude, can be constructed by changing the
architecture of regulatory connections between the genes. Statistical
properties of designed networks, including motif distributions and
Laplacian spectra, are considered. 相似文献
6.
Hong Qian 《Journal of statistical physics》2010,141(6):990-1013
Based on a stochastic, nonlinear, open biochemical reaction system perspective, we present an analytical theory for cellular
biochemical processes. The chemical master equation (CME) approach provides a unifying mathematical framework for cellular
modeling. We apply this theory to both self-regulating gene networks and phosphorylation-dephosphorylation signaling modules
with feedbacks. Two types of bistability are illustrated in mesoscopic biochemical systems: one that has a macroscopic, deterministic
counterpart and another that does not. In certain cases, the latter stochastic bistability is shown to be a “ghost” of the
extinction phenomenon. We argue the thermal fluctuations inherent in molecular processes do not disappear in mesoscopic cell-sized
nonlinear systems; rather they manifest themselves as isogenetic variations on a different time scale. Isogenetic biochemical
variations in terms of the stochastic attractors can have extremely long lifetime. Transitions among discrete stochastic attractors
spend most of the time in “waiting”, exhibit punctuated equilibria. It can be naturally passed to “daughter cells” via a simple
growth and division process. The CME system follows a set of nonequilibrium thermodynamic laws that include non-increasing
free energy F(t) with external energy drive Q
hk
≥0, and total entropy production rate e
p
=−dF/dt+Q
hk
≥0. In the thermodynamic limit, with a system’s size being infinitely large, the nonlinear bistability in the CME exhibits
many of the characteristics of macroscopic equilibrium phase transition. 相似文献
7.
We observe the phenomenon of stochastic resonant signaling in signal amplification enzyme cascades, where certain optimal reaction rates minimize the average threshold-crossing time. We develop a new analytical technique to obtain the mean first passage time, based on a novel decomposition of the master equation. Our analytical results are in good agreement with the exact numerical simulations. We demonstrate that resonant behavior may be a ubiquitous phenomenon in stochastic threshold crossing in cell signaling. The physical principles behind this phenomenon are elucidated. 相似文献
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The method of separation of variables is applied in order to investigate the analytical solutions of a certain two-dimensional
rectangular heat equation. In the analysis presented here, the partial differential equation is directly transformed into
ordinary differential equations. The closed-form transient temperature distributions and heat transfer rates are generalized
for a linear combination of the products of Fourier-Bessel series of the exponential type. Relevant connections with some
other closely-related recent works are also indicated. 相似文献
9.
Wangli He 《Physics letters. A》2008,372(4):408-416
In this Letter, synchronization of a class of chaotic neural networks with known or unknown parameters is investigated. By combing the adaptive control and linear feedback with update law, a simple, analytical, and rigorous adaptive feedback scheme is derived to achieve synchronization of two coupled neural networks with time-varying delay based on the invariant principle of functional differential equations and parameter identification. With this method, parameter identification and synchronization can be achieved simultaneously. Simulation results are given to justify the theoretical analysis. 相似文献
10.
In this paper, based on the invariant principle of functional differential equations, a simple, analytical, and rigorous adaptive feedback scheme is proposed for the synchronization of almost all kinds of coupled identical neural networks with time-varying delay, which can be chaotic, periodic, etc. We do not assume that the concrete values of the connection weight matrix and the delayed connection weight matrix are known. We show that two coupled identical neural networks with or without time-varying delay can achieve synchronization by enhancing the coupling strength dynamically. The update gain of coupling strength can be properly chosen to adjust the speed of achieving synchronization. Also, it is quite robust against the effect of noise and simple to implement in practice. In addition, numerical simulations are given to show the effectiveness of the proposed synchronization method. 相似文献
11.
Harry Crane 《Journal of statistical physics》2013,153(4):698-726
We study both time-invariant and time-varying Gibbs distributions for configurations of particles into disjoint clusters. Specifically, we introduce and give some fundamental properties for a class of partition models, called permanental partition models, whose distributions are expressed in terms of the α-permanent of a similarity matrix parameter. We show that, in the time-invariant case, the permanental partition model is a refinement of the celebrated Pitman–Ewens distribution; whereas, in the time-varying case, the permanental model refines the Ewens cut-and-paste Markov chains (J. Appl. Probab. 43(3):778–791, 2011). By a special property of the α-permanent, the partition function can be computed exactly, allowing us to make several precise statements about this general model, including a characterization of exchangeable and consistent permanental models. 相似文献
12.
Sungsu Lim Joongbo Shin Namju Kwak Kyomin Jung 《The European Physical Journal B - Condensed Matter and Complex Systems》2016,89(9):188
We study the conditions for the phase transitions of information diffusion in complexnetworks. Using the random clustered network model, a generalisation of the Chung-Lurandom network model incorporating clustering, we examine the effect of clustering underthe Susceptible-Infected-Recovered (SIR) epidemic diffusion model with heterogeneouscontact rates. For this purpose, we exploit the branching process to analyse informationdiffusion in random unclustered networks with arbitrary contact rates, and provide noveliterative algorithms for estimating the conditions and sizes of global cascades,respectively. Showing that a random clustered network can be mapped into a factor graph,which is a locally tree-like structure, we successfully extend our analysis to randomclustered networks with heterogeneous contact rates. We then identify the conditions forphase transitions of information diffusion using our method. Interestingly, for variouscontact rates, we prove that random clustered networks with higher clustering coefficientshave strictly lower phase transition points for any given degree sequence. Finally, weconfirm our analytical results with numerical simulations of both synthetically-generatedand real-world networks. 相似文献
13.
《Physica D: Nonlinear Phenomena》2005,200(1-2):139-155
In this paper, some criteria are derived for global asymptotic stability of a class of neural networks with multiple constant or time-varying delays. Based on the Lyapunov–Krasovskii stability theory for functional differential equations and the linear matrix inequality (LMI) approach, some delay-independent criteria for neural networks with multiple constant delays and delay-dependent criteria for neural networks with multiple time-varying delays are provided to guarantee global asymptotic stability of these networks. The main results are generalizations of some recent results reported in the literature. 相似文献
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S-curve networks and an approximate method for estimating degree distributions of complex networks 下载免费PDF全文
In the study of complex networks almost all theoretical models have the property of infinite growth,but the size of actual networks is finite.According to statistics from the China Internet IPv4(Internet Protocol version 4) addresses,this paper proposes a forecasting model by using S curve(logistic curve).The growing trend of IPv4 addresses in China is forecasted.There are some reference values for optimizing the distribution of IPv4 address resource and the development of IPv6.Based on the laws of IPv4 growth,that is,the bulk growth and the finitely growing limit,it proposes a finite network model with a bulk growth.The model is said to be an S-curve network.Analysis demonstrates that the analytic method based on uniform distributions(i.e.,Barab’asi-Albert method) is not suitable for the network.It develops an approximate method to predict the growth dynamics of the individual nodes,and uses this to calculate analytically the degree distribution and the scaling exponents.The analytical result agrees with the simulation well,obeying an approximately power-law form.This method can overcome a shortcoming of Baraba’si-Albert method commonly used in current network research. 相似文献
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In this paper we have analytically solved the Fokker-Planck equation (FPE) associated with a fairly large class of multiplicative
stochastic processes with time-varying nonliner drift and diffusion coefficients, which has wide applicability in various
areas of physics, e.g. nonlinear optics and chemical reaction dynamics. By exploiting the dynamical symmetry of the FPE, we
apply the Lie-algebraic approach to derive the time-dependent analytical closed-form solutions. The derived solutions fall
into two different categories, namely (i) one with a moving absorbing boundary, and (ii) one with a fixed absorbing boundary
at the origin, depending upon the model parameters. The corresponding escape (or survival) probabilities are also evaluated
analytically. We believe that not only our analytically exact results can serve as standard models upon which the discussion
of more complicated problems can be based, but they can also be useful as a benchmark to test approximate numerical or analytical
procedures. 相似文献
17.
Dynamics of Bright/Dark Solitons in Bose--Einstein Condensates with Time-Dependent Scattering Length and External Potential 下载免费PDF全文
We present an analytical study on the dynamics of bright and dark solitons in Bose-Einstein condensates with time-varying atomic scattering length in a time-varying external parabolic potential. A set of exact soliton solutions of the one-dimensional Gross-Pitaevskii equation are obtained, including fundamental bright solitons, higher-order bright solitons, and dark solitons. The results show that the soliton's parameters (amplitude, width, and period) can be changed in a controllable manner by changing the scattering length and external potential. This may be helpful to design experiments. 相似文献
18.
《Waves in Random and Complex Media》2013,23(4):678-693
ABSTRACTIn this paper, we present the exact solutions obtained for the space–time conformable generalized Hirota–Satsuma-coupled KdV equation and coupled mKdV equation using the Atangana’s conformable derivative. The conformable sub-equation method is applied to obtain the solutions; the solutions obtained are compared with the extended tanh-function method for the special case when the fractional order takes the integer order. The analytical solutions show that the conformable sub-equation method is very effective for the conformable-coupled KdV and mKdV equations. 相似文献
19.
This paper introduces an adaptive procedure for the problem
of synchronization and parameter identification for chaotic
networks with time-varying delay by combining adaptive control
and linear feedback. In particular, we consider that the equations $\dot {x}_i (t)$ (for $i =r+1, r+2,\ldots , n$) can be expressed
by the former $\dot {x}_i (t)$ (for $i = 1, 2,\ldots , r$), which is
not the same as the previous equation. This approach is also able to
track changes in the operating parameters of chaotic
networks rapidly and the speed of synchronization and parameter
estimation can be adjusted. In addition, this method is quite robust
against the effect of slight noise and the estimated value of a
parameter fluctuates around the correct value. 相似文献
20.
Bingwen Liu 《Physics letters. A》2008,372(4):424-428
In this Letter, we consider a class of delayed cellular neural networks with time-varying coefficients. By applying Lyapunov functional method and differential inequality techniques, we establish new results to ensure that all solutions of the networks converge exponentially to zero point. 相似文献