Search results for "attractors"
showing 10 items of 24 documents
Remarks on GRN-type systems
2020
Systems of ordinary differential equations that appear in gene regulatory networks theory are considered. We are focused on asymptotical behavior of solutions. There are stable critical points as well as attractive periodic solutions in two-dimensional and three-dimensional systems. Instead of considering multiple parameters (10 in a two-dimensional system) we focus on typical behaviors of nullclines. Conclusions about possible attractors are made.
Attractors/Basin of Attraction
2020
It is a controversial issue to decide who first coined the term “attractor”. According to Peter Tsatsanis, the editor of the English version of Prédire n’est pas expliquer, it was René Thom who first introduced such a term. It is necessary, however, to remember that Thom thought that it was first introduced by the American mathe- matician Steven Smale, “although Smale says it was Thom that coined the neolo- gism “attractor”“(Tsatsanis 2010: 63–64 n. 20). From this point of view, Bob Williams expressed a more cautious opinion by saying that “the word “attractor” was invented by these guys, Thom and Smale” (Cucker and Wong 2000: 183). But other mathematicians are of the opinion that the term …
From Topology to Quasi-Topology. The Complexity of the Notional Domain
2016
This article examines a fundamental metalinguistic construction of the theory of enunciative operations: the notional domain. In particular, we try to explain some elementary topological concepts on which this construction is based and we try to show the key role they play in the description of some basic linguistic operations.
Attracteurs et bifurcations en dynamique holomorphe
2019
Noise-induced behavioral change driven by transient chaos
2022
We study behavioral change in the context of a stochastic, non-linear consumption model with preference adjusting, interdependent agents. Changes in long-run consumption behavior are modelled as noise induced transitions between coexisting attractors. A particular case of multistability is considered: two fixed points, whose immediate basins have smooth boundaries, coexist with a periodic attractor, with a fractal immediate basin boundary. If a trajectory leaves an immediate basin, it enters a set of complexly intertwined basins for which final state uncertainty prevails. The standard approach to predicting transition events rooted in the stochastic sensitivity function technique due to Mil…
Hidden and self-excited attractors in radiophysical and biophysical models
2017
One of the central tasks of investigation of dynamical systems is the problem of analysis of the steady (limiting) behavior of the system after the completion of transient processes, i.e., the problem of localization and analysis of attractors (bounded sets of states of the system to which the system tends after transient processes from close initial states). Transition of the system with initial conditions from the vicinity of stationary state to an attractor corresponds to the case of a self-excited attractor. However, there exist attractors of another type: hidden attractors are attractors with the basin of attraction which does not have intersection with a small neighborhoods of any equ…
A gallery of Chua's Attractors - Part VI
2007
Analytical-numerical methods for finding hidden oscillations in dynamical systems
2012
Language in Complexity. The Emerging Meaning
2017
This contributed volume explores the achievements gained and the remaining puzzling questions by applying dynamical systems theory to the linguistic inquiry. In particular the book is divided into three parts, each one addressing of the following topics: a) Facing complexity in the right way: mathematics and complexity; b) Complexity and theory of language; c) From empirical observation to formal models: investigations of specifici linguistic phenomena, like enunciation, deixis, or the meaning of the metaphorical phrases.
Attractors of stochastic lattice dynamical systems with a multiplicative noise and non-Lipschitz nonlinearities
2012
AbstractIn this paper we study the asymptotic behavior of solutions of a first-order stochastic lattice dynamical system with a multiplicative noise.We do not assume any Lipschitz condition on the nonlinear term, just a continuity assumption together with growth and dissipative conditions, so that uniqueness of the Cauchy problem fails to be true.Using the theory of multi-valued random dynamical systems we prove the existence of a random compact global attractor.