DYNA 2008, in Honor of Maurício Peixoto and David Rand, University of Minho, Braga, Portugal, September 8-12, 2008
We present a brief survey of focal decomposition stressing how this subject relates naturally to some a priori unrelated mathematical and physical subjects.
We present an infinite dimensional space of C 1 + smooth conjugacy classes of circle diffeomorphisms that are C 1 + fixed points of renormalization. We exhibit a one-to-one correspondence between these C 1 + fixed points of renormalization and C 1 + conjugacy classes of Anosov diffeomorphisms.
We analyze the main dynamical properties of the evolutionarily stable strategy (ℰ𝒮𝒮) for asymmetric two-population games of finite size and its corresponding replicator dynamics. We introduce a definition of ℰ𝒮𝒮 for two-population asymmetric games and a method of symmetrizing such an asymmetric game. We show that every strategy profile of the asymmetric game corresponds to a strategy in the symmetric...
We study an economy with heterogenous workers and firms as a two population game, in normal form, and its evolutionary dynamics implied by strategic complementarities. The population of firms is distributed in two groups, innovative and non innovative, while workers need to choose between two strategies, acquiring skills or remaining unskilled. Without having knowledge of the firms’ distribution,...
The Theory of Planned Behavior studies the decision-making mechanisms of individuals. We propose the Bayesian-Nash Equilibria as one, of many, possible mechanisms of transforming human intentions in behavior. This process corresponds to the best strategic individual decision taking in account the collective response. We built a game theoretical model to understand the role of leaders in decision-making...
We describe some recent results on the dynamics of singular-hyperbolic (Lorenz-like) attractors Λ introduced in [26]: (1) there exists an invariant foliation whose leaves are forward contracted by the flow; (2) there exists a positive Lyapunov exponent at every orbit; (3) attractors in this class are expansive and so sensitive with respect to initial data; (4) they have zero volume if the flow is...
Quantum Information is a new area of research which has been growing rapidly since last decade. This topic is very close to potential applications to the so called Quantum Computer. In our point of view it makes sense to develop a more “dynamical point of view” of this theory. We want to consider the concepts of entropy and pressure for “stationary systems” acting on density matrices which generalize...
We present for a general audience the state of the art on the generic properties of C 2 Hamiltonian dynamical systems.
In recent years various methods from the field of artificial intelligence (AI) have been applied to economic problems. The subarea of multiagent systems (MAS) is particularly useful as it enables to simulate individuals or organizations and various interactions among them. In this paper we investigate a scenario with a set of agents, each belonging to a certain sector of activity (e.g. agriculture,...
We present a tourism model where the choice of a tourism resort by a tourist depends not only on the product offered in the resort, but depends also on the characteristics of the other tourists present in the resort. In order to explore the effect of the types of the tourists in the allocation of tourists across resorts, we introduce a game theoretical model and we describe some relevant Nash equilibria.
In this paper we explore results that establish a link between dynamical systems and computability theory (not numerical analysis). In the last few decades, computers have increasingly been used as simulation tools for gaining insight into dynamical behavior. However, due to the presence of errors inherent in such numerical simulations, with few exceptions, computers have not been used for the nobler...
Our main interest is to study the relevant biological thresholds that appear in epidemic and immunological dynamical models. We compute the thresholds, of the SIRI epidemic models, that determine the appearance of an epidemic disease. We compute the thresholds, of a Tregs immunological model, that determine the appearance of an immune response.
In this chapter we present some global convergence theorems for difference equations and systems. We also present specific examples of difference equations and systems to illustrate how most of these theorems apply.
The synchronization of a network depends on a number of factors, including the strength of the coupling, the connection topology and the dynamical behaviour of the individual units. In the first part of this work, we fix the network topology and obtain the synchronization interval in terms of the Lyapounov exponents for piecewise linear expanding maps in the nodes. If these piecewise linear maps have...
We consider a recently proposed generalisation of the Kimura equation, a Fokker–Planck type equation describing the evolution of p(x, t), the probability of finding a fraction x of mutants at time t in a population evolving according to standard models in evolutionary biology. We present a detailed description of the solution, and we show that it naturally divides in two different time scales: the...
We examine models of yield curves through chaotic dynamical systems whose dynamics can be unfolded using non-linear embeddings in higher dimensions. We refine recent techniques used in the state space reconstruction of spatially extended time series in order to forecast the dynamics of yield curves. We use daily LIBOR GBP data (January 2007–June 2008) in order to perform forecasts over a one-month...
This is a brief survey of recent results on the KAM stability of quasiperiodic dynamics using renormalization of vector fields.
We provide an extension to Merton’s famous continuous time model of optimal consumption and investment, in the spirit of previous works by Pliska and Ye, to allow for a wage earner to have a random lifetime and to use a portion of the income to purchase life insurance in order to provide for his estate, while investing his savings in a financial market consisting of one risk-free security and an arbitrary...
We present a survey of some of the most updated results on the dynamics of periodic and almost periodic difference equations.