Nous développons dans cette article une version de l’identité balayage, outil la théorie probabiliste du potentiel, adaptée à l’étude systèmes dynamiques préservant mesure. Cette identité balayage généralise propriété selon laquelle les transformations induites préservent restrictions mesure invariante d’origine. En application, nous démontrons, sous certaines hypothèses, que formule Green–Kubo...

Homeostasis is known as a key concept in biology and well-documented on various levels of biological organization. Moreover, homeostasis appears to be strongly related to the stability of biological systems. Stability, on the other hand, is one of the basic concepts in dynamical systems theory. The aim of this paper is to link these two fundamental concepts. A simple model is proposed represent...

We solve a problem by V. I. Arnold dealing with “how random” modular arithmetic progressions can be. After making precise how Arnold proposes to measure the randomness of a modular sequence, we show that this measure of randomness takes a simplified form in the case of arithmetic progressions. This simplified expression is then estimated using the methodology of dynamical analysis, which operat...

A central problem of dynamical systems theory is to identify a reduced description of the dynamical process one can deal easier. In this paper we present a systematic method of identifying those closed sub-systems of a given discrete time dynamical system in the frame of operator theory. It is shown that this problem is closely related to finding invariant sigma algebras of the dynamics. Index ...

In the aftermath of the global financial crisis questions have been raised regarding the value and applicability of modern macroeconomics. Motivated by these developments and recent advances in dynamical systems theory, the papers in this special issue of Macroeconomic Dynamics deal with specific aspects of the economy as a complex evolving dynamic system. JEL classification: A1, B4, E1, G01.

In periodically varying environments, population models generate periodic dynamical systems. To understand the effects of unidirectional dispersal on local patch dynamics in fluctuating environments, dynamical systems theory is used to study the resulting periodic dynamical systems. In particular, a unidirectional dispersal linked two patch nonautonomous metapopulation model is constructed and ...

Cooperative co-evolution is often used to solve difficult optimization problems by means of problem decomposition. In order to do so efficiently, one must have a good understanding of co-evolution’s dynamical behavior. To build such understanding, we have constructed a methodology for analyzing co-evolution based on dynamical systems theory. In this paper we show how it can be applied to invest...