Related papers: Sensitive dependence and transitivity of fuzzified…
Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…
Time-Dependent Density Functional Theory is mathematically formulated through non-linear coupled time-dependent 3-dimensional partial differential equations and it is natural to expect a strong sensitivity of its solutions to variations of…
In this paper, we study properties of sensitivity, transitivity and chaos for non-autonomous discrete systems(NDS). Firstly, we present some different sufficient conditions for NDS to be chaotic. Then, we relate the transitivity with the…
In this contribution, the transitivity property of commutative first-order linear time-varying systems is investigated with and without initial conditions. It is proven that transitivity property of first-order systems holds with and…
Consider a periodically forced nonlinear system which can be presented as a collection of smaller subsystems with pairwise interactions between them. Each subsystem is assumed to be a massive point moving with friction on a compact surface,…
We present a numerical analysis for SiO_2 of the fraction of diffusive direction f_diff for temperatures T on both sides of the fragile-to-strong crossover. The T-dependence of f_diff clearly reveals this change in dynamical behavior. We…
The main objective of this article are two-fold. First, we introduce some general principles on phase transition dynamics, including a new dynamic transition classification scheme, and a Ginzburg-Landau theory for modeling equilibrium phase…
Motivated by networked systems in random environment and controlled hybrid stochastic dynamic systems, this work focuses on modeling and analysis of a class of switching diffusions consisting of continuous and discrete components. Novel…
We consider testing whether a set of Gaussian variables, selected from the data, is independent of the remaining variables. We assume that this set is selected via a very simple approach that is commonly used across scientific disciplines:…
We study the stability of switched systems where the dynamic modes are described by systems of higher-order linear differential equations not necessarily sharing the same state space. Concatenability of trajectories at the switching…
In this paper, we study the dynamics of a non-autonomous dynamical system $(X,\mathbb{F})$ generated by a sequence $(f_n)$ of continuous self maps converging uniformly to $f$. We relate the dynamics of the non-autonomous system…
We develop a rigorous theory of external influences on finite discrete dynamical systems, going beyond the perturbation paradigm, in that the external influence need not be a small contribution. Indeed, the covariance condition can be…
Perfect adaptation in a dynamical system is the phenomenon that one or more variables have an initial transient response to a persistent change in an external stimulus but revert to their original value as the system converges to…
We give sufficient conditions for stability of a continuous-time linear switched system consisting of finitely many subsystems. The switching between subsystems is governed by an underlying graph. The results are applicable to switched…
The critical dynamics of superconductors in the charged regime is reconsidered within field-theory. For the dynamics the Ginzburg-Landau model with complex order parameter coupled to the gauge field suggested earlier [Lannert et al. Phys.…
Although the explicit commutativitiy conditions for second-order linear time-varying systems have been appeared in some literature, these are all for initially relaxed systems. This paper presents explicit necessary and sufficient…
Considering deterministic classical lattice systems with continuous variables, we show that, if the initial conditions are sampled according to a probability distribution in which the dynamical variables are statistically independent, the…
This papers shows that nonlinear filter in the case of deterministic dynamics is stable with respect to the initial conditions under the conditions that observations are sufficiently rich, both in the context of continuous and discrete time…
This paper proposes a multi-class online fuzzy classifier for dynamic environments. A fuzzy classifier comprises a set of fuzzy if-then rules where human users determine the antecedent fuzzy sets beforehand. In contrast, the consequent real…
This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic…