Adaptation Noise And Self Organizing Systems

We discuss a model of an economic community consisting of N interacting agents. The state of each agent at any time is characterized, in general, by a mixed strategy profile drawn from a space of s pure strategies. The community evolves as agents update their strategy profiles in response to payoffs received from other agents. The evolution equation is a generalization of the replicator equation. We argue that when N is sufficiently large and the payoff matrix elements satisfy suitable inequalities, the community evolves to retain the full diversity of available strategies even as individual agents specialize to pure strategies.

A new approach for the study of social games and communications is proposed. Games are simulated between cognitive players who build the opponent's internal model and decide their next strategy from predictions based on the model. In this paper, internal models are constructed by the recurrent neural network (RNN), and the iterated prisoner's dilemma game is performed. The RNN allows us to express the internal model in a geometrical shape. The complicated transients of actions are observed before the stable mutually defecting equilibrium is reached. During the transients, the model shape also becomes complicated and often experiences chaotic changes. These new chaotic dynamics of internal models reflect the dynamical and high-dimensional rugged landscape of the internal model space.

We analyze in detail a one-dimensional stochastically driven running sandpile. The dynamics shows three different phases, depending on the on-site relaxation rate and stochastic driving rate. Two phases are characterized by the presence of travelling waves. The third shows algebraic relaxation.

Understanding the relationship between taxonomic and morphological changes is important in identifying the reasons for accelerated morphological diversification early in the history of animal phyla. Here, a simple general model describing the joint dynamics of taxonomic diversity and morphological disparity is presented and applied to the data on the diversification of blastozoans. I show that the observed patterns of deceleration in clade diversification can be explicable in terms of the geometric structure of the morphospace and the effects of extinction and speciation on morphological disparity without invoking major declines in the size of morphological transitions or taxonomic turnover rates. The model allows testing of hypotheses about patterns of diversification and estimation of rates of morphological evolution. In the case of blastozoans, I find no evidence that major changes in evolutionary rates and mechanisms are responsible for the deceleration of morphological diversification seen during the period of this clade's expansion. At the same time, there is evidence for a moderate decline in overall rates of morphological diversification concordant with a major change (from positive to negative values) in the clade's growth rate.

In this paper we review previous work and present new work concerning the relationship between dynamical systems theory and computation. In particular, we review work by Langton \cite{Langton90} and Packard \cite{Packard88} on the relationship between dynamical behavior and computational capability in cellular automata (CA). We present results from an experiment similar to the one described in \cite{Packard88}, that was cited there as evidence for the hypothesis that rules capable of performing complex computations are most likely to be found at a phase transition between ordered and chaotic behavioral regimes for CA (the ``edge of chaos''). Our experiment produced very different results from the original experiment, and we suggest that the interpretation of the original results is not correct. We conclude by discussing general issues related to dynamics, computation, and the ``edge of chaos'' in cellular automata.

The early-time critical dynamics of continuous, Ising-like phase transitions is studied numerically for two-dimensional lattices of coupled chaotic maps. Emphasis is laid on obtaining accurate estimates of the dynamic critical exponents \theta' and z. The critical points of five different models are investigated, varying the mode of update, the coupling, and the local map. Our results suggest that the nature of update is a relevant parameter for dynamic universality classes of extended dynamical systems, generalizing results obtained previously for the static properties. They also indicate that the universality observed for the static properties of Ising-like transitions of synchronously-updated systems does not hold for their dynamic critical properties.

We present numerical results based on a simplified ecological system in evolution, showing features of extinction similar to that claimed for the biosystem on Earth. In the model each species consists of a population in interaction with the others, that reproduces and evolves in time. Each species is simultaneously a predator and a prey in a food chain. Mutations that change the interactions are supposed to occur randomly at a low rate. Extinctions of populations result naturally from the predator-prey dynamics. The model is not pinned in a fitness variable, and natural selection arises from the dynamics.

We studied the effects of time correlation of subsequent patterns on the convergence of on-line learning by a feedforward neural network with backpropagation algorithm. By using chaotic time series as sequences of correlated patterns, we found that the unexpected scaling of converging time with learning parameter emerges when time-correlated patterns accelerate learning process.

We introduce a new model of evolution on a fitness landscape possessing a tunable degree of neutrality. The model allows us to study the general properties of molecular species undergoing neutral evolution. We find that a number of phenomena seen in RNA sequence-structure maps are present also in our general model. Examples are the occurrence of "common" structures which occupy a fraction of the genotype space which tends to unity as the length of the genotype increases, and the formation of percolating neutral networks which cover the genotype space in such a way that a member of such a network can be found within a small radius of any point in the space. We also describe a number of new phenomena which appear to be general properties of neutrally evolving systems. In particular, we show that the maximum fitness attained during the adaptive walk of a population evolving on such a fitness landscape increases with increasing degree of neutrality, and is directly related to the fitness of the most fit percolating network.

Unlike computation or the numerical analysis of differential equations, simulation does not have a well established conceptual and mathematical foundation. Simulation is an arguable unique union of modeling and computation. However, simulation also qualifies as a separate species of system representation with its own motivations, characteristics, and implications. This work outlines how simulation can be rooted in mathematics and shows which properties some of the elements of such a mathematical framework has. The properties of simulation are described and analyzed in terms of properties of dynamical systems. It is shown how and why a simulation produces emergent behavior and why the analysis of the dynamics of the system being simulated always is an analysis of emergent phenomena. A notion of a universal simulator and the definition of simulatability is proposed. This allows a description of conditions under which simulations can distribute update functions over system components, thereby determining simulatability. The connection between the notion of simulatability and the notion of computability is defined and the concepts are distinguished. The basis of practical detection methods for determining effectively non-simulatable systems in practice is presented. The conceptual framework is illustrated through examples from molecular self-assembly end engineering.