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We present an exact solution of headway distribution of the asymmetric simple exclusion model with open boundary conditions and compare it to the headway distributions of the highway traffic.
Coarse timesteppers provide a bridge between microscopic / stochastic system descriptions and macroscopic tasks such as coarse stability/bifurcation computations. Exploiting this computational enabling technology, we present a framework for designing observers and controllers based on microscopic simulations, that can be used for their coarse control. The proposed methodology provides a bridge between traditional numerical analysis and control theory on the one hand and microscopic simulation on the other.
We present a parallel implementation of cellular automata to simulate chemical reactions on surfaces. The scaling of the computer time with the number of processors for this parallel implementation is quite close to the ideal T/P, where T is the computer time used for one single processor and P the number of processors. Two examples are presented to test the algorithm, the simple A+B->0 model and a realistic model for CO oxidation on Pt(110). By using large parallel simulations, it is possible to derive scaling laws which allow us to extrapolate to even larger system sizes and faster diffusion coefficients allowing us to make direct comparisons with experiments.
It has been pointed out that if an autocatalytic cycle produces primitive membrane chemicals, it can compose a self-maintaining proto cell. Moreover, it is known that a proto cell can divide itself spontaneously as it grows. An unsolved problem is how such a catalytic system can evolve in the pre-cellular environment. Here we examine, as the first step, the evolution of catalysts that have different activity in generating membrane chemicals using a Lattice-Gas-like model. We demonstrated that a self-replicating proto-cell emerges from random initial configuration. We also showed that cells with higher activity of membrane production evolve through cellular selection.
It is shown that for the N-neighbor and K-state cellular automata, the class II, class III and class IV patterns coexist at least in the range $\frac{1}{K} \le λ\le 1-\frac{1}{K} $. The mechanism which determines the difference between the pattern classes at a fixed $λ$ is found, and it is studied quantitatively by introducing a new parameter $F$. Using the parameter F and $λ$, the phase diagram of cellular automata is obtained for 5-neighbor and 4-state cellular automata. PACS: 89.75.-k Complex Systems
The aim of this article is to address the question of the endogenization of mimetic processes in formal models of social systems. Starting from some studies about cognitive differences between humans and animals, we propose a formal framework which has the advantage to endogenise mimetic rules and give a comprehensive description of a heterogeneous population structure at the behavioural level as well as at the level of the choices of mimetic laws. In order to illustrate this point, we apply this formalism to a spatial evolutionary game.
For any finite lattice of size 2N, it is shown that the GKL automaton will evolve into attractors if the initial configurations contains an homogeneous block of size larger than N. The best time estimation for reaching these attracting states is obtained. Our results also confirm to the case of infinite lattice which has been obtained previously.
We propose the use of Deterministic Generalized Asynchronous Random Boolean Networks [Gershenson, 2002] as models of contextual deterministic discrete dynamical systems. We show that changes in the context have drastic effects on the global properties of the same networks, namely the average number of attractors and the average percentage of states in attractors. We introduce the situation where we lack knowledge on the context as a more realistic model for contextual dynamical systems. We notice that this makes the network non-deterministic in a specific way, namely introducing a non-Kolmogorovian quantum-like structure for the modelling of the network [Aerts, 1986]. In this case, for example, a state of the network has the potentiality (probability) of collapsing into different attractors, depending on the specific form of lack of knowledge on the context.
The virtual ant introduced by C. Langton has an interesting behavior, which has been studied in several contexts. Here we give a construction to calculate any boolean circuit with the trajectory of a single ant. This proves the P-hardness of the system and implies, through the simulation of one dimensional cellular automata and Turing machines, the universality of the ant and the undecidability of some problems associated to it.
Number-conserving cellular automata (NCCA) are particularly interesting, both because of their natural appearance as models of real systems, and because of the strong restrictions that number-conservation implies. Here we extend the definition of the property to include cellular automata with any set of states in $\Zset$, and show that they can be always extended to ``usual'' NCCA with contiguous states. We show a way to simulate any one dimensional CA through a one dimensional NCCA, proving the existence of intrinsically universal NCCA. Finally, we give an algorithm to decide, given a CA, if its states can be labeled with integers to produce a NCCA, and to find this relabeling if the answer is positive.
We consider transformations between attractor basins of binary cylindrical cellular automata resulting from mutations. A t-point mutation of a state consists in toggling t sites in that state. Results of such mutations are described by a rule-dependent probability matrix. The structure of this matrix is studied in relation to the structure of the state transition diagram and several theorems relating these are proved for the case of additive rules. It is shown that the steady state of the Markov process defined by the probability matrix is always the uniform distribution over the state transition diagram. Some results on eigenvalues are also obtained.
Number-conserving (or {\em conservative}) cellular automata have been used in several contexts, in particular traffic models, where it is natural to think about them as systems of interacting particles. In this article we consider several issues concerning one-dimensional cellular automata which are conservative, monotone (specially ``non-increasing''), or that allow a weaker kind of conservative dynamics. We introduce a formalism of ``particle automata'', and discuss several properties that they may exhibit, some of which, like anticipation and momentum preservation, happen to be intrinsic to the conservative CA they represent. For monotone CA we give a characterization, and then show that they too are equivalent to the corresponding class of particle automata. Finally, we show how to determine, for a given CA and a given integer $b$, whether its states admit a $b$-neighborhood-dependent relabelling whose sum is conserved by the CA iteration; this can be used to uncover conservative principles and particle-like behavior underlying the dynamics of some CA. Complements at {\tt http://www.dim.uchile.cl/\verb' 'anmoreir/ncca}
In this chapter, I review the main methods and techniques of complex systems science. As a first step, I distinguish among the broad patterns which recur across complex systems, the topics complex systems science commonly studies, the tools employed, and the foundational science of complex systems. The focus of this chapter is overwhelmingly on the third heading, that of tools. These in turn divide, roughly, into tools for analyzing data, tools for constructing and evaluating models, and tools for measuring complexity. I discuss the principles of statistical learning and model selection; time series analysis; cellular automata; agent-based models; the evaluation of complex-systems models; information theory; and ways of measuring complexity. Throughout, I give only rough outlines of techniques, so that readers, confronted with new problems, will have a sense of which ones might be suitable, and which ones definitely are not.
We propose two new evolutionary rules that is not mimic evolution of strategies based on the spatial Prisoner's Dilemma (PD). The former follows the selfish evolutionary rule and then the coexistence phase appears with weak phase transition with mutations. The second rule is that of globally coupled spatial PD where the strategy of an agent is taken so that the total payoff of the whole system increases. Then it is natulally suspected that all agents will become cooperators in general. We, however, find that situations is rather complerx. We find two critical points within the usual conditions in the parameters included the payoff matrix in the PD. Further as we break the condition without losing PD condition, we meet two more essential curitical points. We discuss the areas between these critical points in the parameter space and uncover the various properties by simulating on computer. We show that in some parameter regions, strange properties, that is, like chaotic behaveor appear and the coexistence between defectors and cooperators appears in the large parameter region. Thus we point out that usual non-essential condition among the parameters in the payoff matrix imposed on the PD privent from recovering rich structures in the evolutionally spatial PS.
In this article, we study the evolution of the strategies in a sort of weighted three cornered game, Glico Game. This game has three strategies in each agent and three parameters in the payoff matrix. We divide the parameter region into 8 areas and explore its qualitative and quantitative properties of the evolution of strategies which include Haming distance, correlation functions and the population sequence of each strategy. When the three payoff parameters take nearly values each other, the complex patterns mainly appear and as the difference of parameter values are enlarged, some peculiar strategy trends to be dominant gradually. An interesting fact is that the strongest strategy in the payoff do not necessarily dominate the latice world. There are even the cases where the weakest strategy in the payof dominate. Generally many cases have some period much shoter than the dimension of the configuration space.
We present a computer-assisted approach to approximating coarse optimal switching policies for systems described by microscopic/stochastic evolution rules. The coarse timestepper constitutes a bridge between the underlying kinetic Monte Carlo simulation and traditional, continuum numerical optimization techniques formulated in discrete time. The approach is illustrated through a simplified kinetic Monte Carlo simulation of NO reduction on a Pt catalyst: a switch between two coexisting stable steady states is implemented by minimal manipulation of a system parameter.
We derive the Euler equations as the hydrodynamic limit of a stochastic model of a hard-sphere gas on a lattice. We show that the system does not produce entropy.
In this paper we study the phase transitions of different types of Random Boolean networks. These differ in their updating scheme: synchronous, semi-synchronous, or asynchronous, and deterministic or non-deterministic. It has been shown that the statistical properties of Random Boolean networks change considerable according to the updating scheme. We study with computer simulations sensitivity to initial conditions as a measure of order/chaos. We find that independently of their updating scheme, all network types have very similar phase transitions, namely when the average number of connections of nodes is between one and three. This critical value depends more on the size of the network than on the updating scheme.