Symbolic local information transfer

Recently, the permutation-information theoretic approach has been used in a broad range of research fields. In particular, in the study of high-dimensional dynamical systems, it has been shown that this approach can be effective in characterizing global properties, including the complexity of their spatiotemporal dynamics. Here, we show that this approach can also be applied to reveal local spatiotemporal profiles of distributed computations existing at each spatiotemporal point in the system. J. T. Lizier et al. have recently introduced the concept of local information dynamics, which consists of information storage, transfer, and modification. This concept has been intensively studied with regard to cellular automata, and has provided quantitative evidence of several characteristic behaviors observed in the system. In this paper, by focusing on the local information transfer, we demonstrate that the application of the permutation-information theoretic approach, which introduces natural symbolization methods, makes the concept easily extendible to systems that have continuous states. We propose measures called symbolic local transfer entropies, and apply these measures to two test models, the coupled map lattice (CML) system and the Bak-Sneppen model (BS-model), to show their relevance to spatiotemporal systems that have continuous states. In the CML, we demonstrate that it can be successfully used as a spatiotemporal filter to stress a coherent structure buried in the system. In particular, we show that the approach can clearly stress out defect turbulences or Brownian motion of defects from the background, which gives quantitative evidence suggesting that these moving patterns are the information transfer substrate in the spatiotemporal system. We then show that these measures reveal qualitatively different properties from the conventional approach using the sliding window method, and are also robust against external noise. In the BS-model, we demonstrate that these measures can provide novel insight to the model, featuring how symbolic local information transfer is related to the dynamical properties of the elements involved in a spatiotemporal dynamics.     

A cellular automata model of epidemics of a heterogeneous susceptibility

In this paper we present a model with spatial heterogeneity based on cellular automata (CA). In the model we consider the relevant heterogeneity of host (susceptible) mixing and the natural birth rate. We divide the susceptible population into three groups according to the immunity of each individual based on the classical susceptible--infected--removed (SIR) epidemic models, and consider the spread of an infectious disease transmitted by direct contact among humans and vectors that have not an incubation period to become infectious. We test the local stability and instability of the disease-free equilibrium by the spectrum radii of Jacobian. The simulation shows that the structure of the nearest neighbour size of the cell (or the degree of the scale-free networks) plays a very important role in the spread properties of infectious disease. The positive equilibrium of the infections versus the neighbour size follows the third power law if an endemic equilibrium point exists. Finally, we analyse the feature of the infection waves for the homogeneity and heterogeneous cases respectively.     

Control of spatiotemporal chaos: dependence of the minimum pinning distance on the spatial measure entropy

We investigate the control of spatiotemporal chaos by external forcing at equidistant points (pinning sites) in one-dimensional systems. A monotonic decrease of the minimum distance between pinning sites versus the spatial measure entropy (in the absence of forcing) can be obtained for an appropriate choice of the forcing procedure. Such a relation between a feature for control and the disorder of the uncontrolled system is shown for four systems: binary cellular automata, coupled logistic equations, a stick-slip model and coupled differential equations.     

自治广义Birkhoff系统的平衡稳定性

研究广义Birkhoff系统的平衡稳定性问题.建立了自治广义Birkhoff系统的平衡方程;给出了自治广义Birkhoff系统的一次近似方程,利用Lyapunov一次近似理论,建立了系统平衡状态稳定性的判据;构建了Lyapunov函数,利用Lyapunov直接法,建立了自治广义Birkhoff系统平衡状态稳定性的判据.给出了若干算例以说明结果的应用.     

Assigning on-ramp flows to maximize highway capacity

In this paper, we study the capacity of a highway with two on-ramps by using a cellular automata traffic flow model. We investigate how to improve the system capacity by assigning traffic flow to the two ramps. The system phase diagram is presented and different regions are classified. It is shown that in region I, in which both ramps are in free flow and the main road upstream of the ramps is in congestion, assigning a higher proportion of the demand to the upstream on-ramp could improve the overall flow, which is consistent with previous studies. This is explained through studying the spatiotemporal patterns and analytical investigations. In contrast, optimal assignment has not been observed in other regions. We point out that our result is robust and model independent under certain conditions.     

Cellular automata and nonlinear dynamical models

A point of view is pursued in which cellular automata (CA) are viewed as a laboratory to investigate nonlinear dynamics. We introduce an irreversible cellular automaton (ICA) with minimal coupling which exhibit class 4 behavior. Periodic structures (phases) are studied along with their stability properties. We observe topological conserved quantities and introduce a classification of structures via a topological number. Time reversal invariant cellular automata (TRCA) are also investigated; we discuss stability of phases and use a concept of local entropy to measure the growth of chaos in slightly perturbed phases. A classification of approach to chaos into 3 classes is proposed for TRCA.     

The Approach Towards Equilibrium in a Reversible Ising Dynamics Model: An Information-Theoretic Analysis Based on an Exact Solution

We study the approach towards equilibrium in a dynamic Ising model, the Q2R cellular automaton, with microscopic reversibility and conserved energy for an infinite one-dimensional system. Starting from a low-entropy state with positive magnetisation, we investigate how the system approaches equilibrium characteristics given by statistical mechanics. We show that the magnetisation converges to zero exponentially. The reversibility of the dynamics implies that the entropy density of the microstates is conserved in the time evolution. Still, it appears as if equilibrium, with a higher entropy density is approached. In order to understand this process, we solve the dynamics by formally proving how the information-theoretic characteristics of the microstates develop over time. With this approach we can show that an estimate of the entropy density based on finite length statistics within microstates converges to the equilibrium entropy density. The process behind this apparent entropy increase is a dissipation of correlation information over increasing distances. It is shown that the average information-theoretic correlation length increases linearly in time, being equivalent to a corresponding increase in excess entropy.     

Self-Organization in Coupled Map Scale-Free Networks

We study the self-organization of phase synchronization in coupled map scale-free networks with chaotic logistic map at each node and find that a variety of ordered spatiotemporal patterns emerge spontaneously in a regime of coupling strength. These ordered behaviours will change with the increase of the average finks and are robust to both the system size and parameter mismatch. A heuristic theory is given to explain the mechanism of self-organization and to figure out the regime of coupling for the ordered spatiotemporal patterns.     

Global exponential convergence analysis of delayed cellular neural networks

Some sufficient criteria have been established to ensure the global exponential stability of delayed cellular neural networks by using an approach based on delay differential inequality. Compared with the method of Lyapunov functionals as in most previous studies, our method is simpler and more effective for a stability analysis of delayed system. Some previously established results in the literature are shown to be special cases of the present result.     

Emergence of self-replicating structures in a cellular automata space

Past cellular automata models of self-replication have always been initialized with an original copy of the structure that will replicate, and have been based on a transition function that only works for a single, specific structure. This article demonstrates for the first time that it is possible to create cellular automata models in which a self-replicating structure emerges from an initial state having a random density and distribution of individual components. These emergent self-replicating structures employ a fairly general rule set that can support the replication of structures of different sizes and their growth from smaller to larger ones. This rule set also allows “random” interactions of self-replicating structures with each other and with other structures within the cellular automata space. Systematic simulations show that emergence and growth of replicants occurs often and is essentially independent of the cellular space size, initial random pattern of components, and initial density of components, over a broad range of these parameters. The number of replicants and the total number of components they incorporate generally approach quasi-stable values with time.     

The dynamics of defect ensembles in one-dimensional cellular automata

We investigate the dynamics of ensembles of diffusive defects in one-dimensional deterministic cellular automata. The work builds on earlier results on individual random walks in cellular automata. Here we give a natural condition guaranteeing diffusive behavior also in the presence of other defects. Simple branching and birth mechanisms are introduced and prototype classes of cellular automata exhibiting weakly interacting walks capable of annihilation and coalescence are studied. Their equilibrium behavior is also characterized. The design principles of cellular automata with desired diffusive interaction properties become transparent from this analysis.     

Zeno''s paradox in quantum cellular automata

The effect of Zeno's paradox in quantum theory is demonstrated with the aid of quantum mechanical cellular automata. It is shown that the degree of non-unitarity of the cellular automaton evolution and the frequency of consecutive measurements of cellular automaton states are operationally indistinguishable.     

三维空间行人疏散的元胞自动机模型

为了有效刻画行人在三维空间中的疏散状况,结合阶梯因素提出了一种新的三维元胞自动机模型,该模型首先基于位置吸引力和碰撞可能性给出了行人移动概率的计算公式,并通过定义元胞演化过程阐述其疏散策略,同时,利用建立的仿真平台进行实验,深入分析了疏散时间、出口流率、出口宽度、初始行人密度以及系统平均速度之间的关系,以此获得更加符合实际情况的行人流特征,结果表明,疏散时间、出口流率与初始行人密度呈现正相关,而与出口宽度呈现负相关,并且系统平均速度和出口宽度对于最优疏散时间存在一个理想阈值。     

An extended master-equation approach applied to aggregation in freeway traffic

We restudy the master-equation approach applied to aggregation in a one-dimensional freeway, where the decay transition probabilities for the jump processes are reconstructed based on a car-following model. According to the reconstructed transition probabilities, the clustering behaviours and the stochastic properties of the master equation in a one-lane freeway traffic model are investigated in detail The numerical results show that the size of the clusters initially below the critical size of the unstable cluster and initially above that of the unstable cluster all enter the same stable state, which also accords with the nucleation theory and is known from the result in earlier work. Moreover, we have obtained more reasonable parameters of the master equation based on some results of cellular automata models.     

Asymptotical stability of multi-delayed cellular neural networks with impulsive effects

In this work, the stability issues of the equilibrium points of multi-delayed cellular neural networks with impulsive effects are investigated. Based on the method of linear matrix inequality (LMI) and parameterized first-order model transformation, several new delay-dependent and delay-independent asymptotical stability conditions are derived by the stability theory of Lyapunov–Krasovskii. A numerical example is given to illustrate the effectiveness of our results.     

广义Birkhoff自治系统平衡状态的流形稳定性

研究广义Birkhoff自治系统平衡状态流形稳定性.建立广义Birkhoff自治系统的受绕运动方程和平衡方程.由Liapunov稳定性理论给出广义Birkhoff自治系统的平衡状态流形稳定性的有关判据.举例说明结果的应用.     

Traveling patterns in cellular automata

A method to identify the invariant subsets of bi-infinite configurations of cellular automata that propagate rigidly with a constant velocity nu is described. Causal traveling configurations, propagating at speeds not greater than the automaton range, mid R:numid R:相似文献   

Cellular automata models of tumour natural shrinkage

In this paper we present three dimensional cellular automata models for tumour growth, with a focus on the tumour’s natural shrinkage caused by the removal of the dead cells’ mortal remains. The significance of this phenomenon for the resulting volume of the in silico tumour is shown. Two algorithms are presented, one using the chain shifting approach for tumour expansion and shrinkage and another improving the performance of the chain shifting approach. Simulations are validated against the experimental results.