Complex dynamics of elementary cellular automata emerging from chaotic rules

We show techniques of analyzing complex dynamics of cellular automata (CA) with chaotic behaviour. CA are well known computational substrates for studying emergent collective behaviour, complexity, randomness and interaction between order and chaotic systems. A number of attempts have been made to classify CA functions on their space-time dynamics and to predict behaviour of any given function. Examples include mechanical computation, \lambda{} and Z-parameters, mean field theory, differential equations and number conserving features. We aim to classify CA based on their behaviour when they act in a historical mode, i.e. as CA with memory. We demonstrate that cell-state transition rules enriched with memory quickly transform a chaotic system converging to a complex global behaviour from almost any initial condition. Thus just in few steps we can select chaotic rules without exhaustive computational experiments or recurring to additional parameters. We provide analysis of well-known chaotic functions in one-dimensional CA, and decompose dynamics of the automata using majority memory exploring glider dynamics and reactions

How groups can foster consensus: The case of local cultures

A local culture denotes a commonly shared behaviour within a cluster of firms. Similar to social norms or conventions, it is an emergent feature resulting from the firms' interaction in an economic network. To model these dynamics, we consider a distributed agent population, representing e.g. firms or individuals. Further, we build on a continuous opinion dynamics model with bounded confidence ($\epsilon$), which assumes that two agents only interact if differences in their behaviour are less than $\epsilon$. Interaction results in more similarity of behaviour, i.e. convergence towards a common mean. This framework is extended by two major concepts: (i) The agent's in-group consisting of acquainted interaction partners is explicitly taken into account. This leads to an effective agent behaviour reflecting that agents try to continue to interact with past partners and thus to keep sufficiently close to them. (ii) The in-group network structure changes over time, as agents can form new links to other agents with sufficiently close effective behaviour or delete links to agents no longer close in behaviour. Thus, our model provides a feedback mechanism between the agents' behaviour and their in-group structure. Studying its consequences by means of agent-based computer simulations, we find that for narrow-minded agents (low $\epsilon$) the additional feedback helps to find consensus more often, whereas for open-minded agents (high $\epsilon$) this does not hold. This counterintuitive result is explained by simulations of the network evolution

An Essay on Welfare State Dynamics

The expansion of welfare-state arrangements is seen as the result of dynamic interaction between market behaviour and political behaviour, often with considerable time lags, sometimes generating either virtuous or vicious circles. Such interaction may also involve induced (endogenous) changes in social norms and political preferences. Moreover, the internationalisation process not only limits the ability of national governments to redistribute income; they also increase the political demands for international mobility of welfare-state benefits and social services. I also discuss the dynamics of reforms and retreats of welfare-state arrangements.welfare state, welfare-state dynamics, political equilibrium, social norms

An Essay on Welfare State Dynamics

The expansion of welfare-state arrangements is seen as the result of dynamic interaction between market behaviour and political behaviour, often with considerable time lags, sometimes generating either virtuous or vicious circles. Such interaction may also involve induced (endogenous) changes in social norms and political pre­ferences. Moreover, the internationalisation process not only limits the ability of national governments to redistribute income; they also increase the political demands for international mobility of welfare-state benefits and social services. I also discuss the dynamics of reforms and retreats of welfare-state arrangements.Welfare State; Welfare-State Dynamics; Political Equilibrium; Social Norms

An Essay on Welfare State Dynamics

The expansion of welfare-state arrangements is seen as the result of dynamic interaction between market behaviour and political behaviour, often with considerable time lags, sometimes generating either virtuous or vicious circles. Such interaction may also involve induced (endogenous) changes in social norms and political preferences. Moreover, the internationalisation process not only limits the ability of national governments to redistribute income; they also increase the political demands for international mobility of welfare-state benefits and social services. I also discuss the dynamics of reforms and retreats of welfare-state arrangements.welfare state; welfare-state dynamics; political equilibrium; social norms

Consistent approximations of the zeno behaviour in affine-type switched dynamic systems

This paper proposes a new theoretic approach to a specific interaction of continuous and discrete dynamics in switched control systems known as a Zeno behaviour. We study executions of switched control systems with affine structure that admit infinitely many discrete transitions on a finite time interval. Although the real world processes do not present the corresponding behaviour, mathematical models of many engineering systems may be Zeno due to the used formal abstraction. We propose two useful approximative approaches to the Zeno dynamics, namely, an analytic technique and a variational description of this phenomenon. A generic trajectory associated with the Zeno dynamics can finally be characterized as a result of a specific projection or/and an optimization procedure applied to the original dynamic model. The obtained analytic and variational techniques provide an effective methodology for constructive approximations of the general Zeno-type behaviour. We also discuss shortly some possible applications of the proposed approximation schemes

Sensorimotor coordination and metastability in a situated HKB model

Oscillatory phenomena are ubiquitous in nature and have become particularly relevant for the study of brain and behaviour. One of the simplest, yet explanatorily powerful, models of oscillatory Coordination Dynamics is the Haken–Kelso–Bunz (HKB) model. The metastable regime described by the HKB equation has been hypothesised to be the signature of brain oscillatory dynamics underlying sensorimotor coordination. Despite evidence supporting such a hypothesis, to our knowledge, there are still very few models (if any) where the HKB equation generates spatially situated behaviour and, at the same time, has its dynamics modulated by the behaviour it generates (by means of the sensory feedback resulting from body movement). This work presents a computational model where the HKB equation controls an agent performing a simple gradient climbing task and shows (i) how different metastable dynamical patterns in the HKB equation are generated and sustained by the continuous interaction between the agent and its environment; and (ii) how the emergence of functional metastable patterns in the HKB equation – i.e. patterns that generate gradient climbing behaviour – depends not only on the structure of the agent's sensory input but also on the coordinated coupling of the agent's motor–sensory dynamics. This work contributes to Kelso's theoretical framework and also to the understanding of neural oscillations and sensorimotor coordination

Kondo insulators in the periodic Anderson model: a local moment approach

The symmetric periodic Anderson model is well known to capture the essential physics of Kondo insulator materials. Within the framework of dynamical mean-field theory, we develop a local moment approach to its single-particle dynamics in the paramagnetic phase. The approach is intrinsically non-perturbative, encompasses all energy scales and interaction strengths, and satisfies the low-energy dictates of Fermi liquid theory. It captures in particular the strong coupling behaviour and exponentially small quasiparticle scales characteristic of the Kondo lattice regime, as well as simple perturbative behaviour in weak coupling. Particular emphasis is naturally given to strong coupling dynamics, where the resultant clean separation of energy scales enables the scaling behaviour of single-particle spectra to be obtained.Comment: 15 pages, 10 postscript figures, accepted for publication in EPJ B; HyperTex disable