Related papers: Chaos for Cowen-Douglas operators
Deterministic chaos is phenomenon from nonlinear dynamics and it belongs to greatest advances of twentieth-century science. Chaotic behavior appears apart of mathematical equations also in wide range in observable nature, so as in there…
The Devaney, Li-Yorke and distributional chaos in plane $\mathbb{R}^2$ can occur in the continuous dynamical system generated by Euler equation branching. Euler equation branching is a type of differential inclusion $\dot x \in \{f(x),g(x)…
In the large-$N$, classical limit, the Bose-Hubbard dimer undergoes a transition to chaos when its tunnelling rate is modulated in time. We use exact and approximate numerical simulations to determine the features of the dynamically…
This is a survey on the recent theory of chaos in partial differential equations.
Let $A,$ $T$ and $B$ be bounded linear operators on a Banach space. This paper is concerned mainly with finding some necessary and sufficient conditions for convergence in operator norm of the sequences $\left\{ A^{n}TB^{n}\right\} $ and…
Chaos criterion for quantum field theory is proposed. Its correspondence with classical chaos criterion in semi-classical regime is shown. It is demonstrated for real scalar field that proposed chaos criterion can be used to investigate…
Motivated by C*-algebra theory, ultragraph edge shift spaces generalize shifts of finite type to the infinite alphabet case. In this paper we study several notions of chaos for ultragraph shift spaces. More specifically, we show that…
Koopman operator describes evolution of observables in the phase space, which could be used to extract characteristic dynamical features of a nonlinear system. Here, we show that it is possible to carry out interesting symbolic partitions…
Chaos as typical property of non-linear systems has revealed its crucial role in various problems of astrophysics and cosmology. The problems discussed at these lectures include planetary dynamics, galactic dynamics, reconstruction of the…
This paper is concerned with strong Li-Yorke chaos induced by A-coupled-expansion for time-varying (i.e., nonautonomous) discrete systems in metric spaces. Some criteria of chaos in the strong sense of Li-Yorke are established via strict…
In this paper, for finite discrete field $F$, nonempty set $\Gamma$, weight vector $\mathfrak{w}=({\mathfrak w}_\alpha)_{\alpha\in\Gamma}\in F^\Gamma$ and weighted generalized shift $\sigma_{\varphi,{\mathfrak w}}:F^\Gamma\to F^\Gamma$, we…
In this paper, the linear differential expression of order $n \ge 2$ with distribution coefficients of various singularity orders is considered. We obtain the associated matrix for the regularization of this expression. Furthermore, we…
It is an increasingly important problem to study conditions on the structure of a network that guarantee a given behavior for its underlying dynamical system. In this paper we report that a Boolean network may fall within the chaotic…
Li-Yorke chaos is a popular and well-studied notion of chaos. Several simple and useful characterizations of this notion of chaos in the setting of linear dynamics were obtained recently. In this note we show that even simpler and more…
A new technique for obtaining rigorous results concerning the global dynamics of nonlinear systems is described. The technique combines abstract existence results based on the Conley index theory with computer- assisted computations. As an…
We prove a number of decoupling inequalities for nonhomogeneous random polynomials with coefficients in Banach space. Degrees of homogeneous components enter into comparison as exponents of multipliers of terms of certain Poincar\'e-type…
A procedure is described for defining a generalized solution for stochastic differential equations using the Cameron-Martin version of the Wiener Chaos expansion. Existence and uniqueness of this Wiener Chaos solution is established for…
This work addresses the propagation of chaos properties in a class of moderately interacting particle systems for the approximation of singular kinetic McKean-Vlasov SDEs driven by alpha-stable processes.
This paper continues the study of [11, 13] for stationary solutions of stochastic linear retarded functional differential equations with the emphasis on delays which appear in those terms including spatial partial derivatives. As a…
The Mackey--Glass equation, which was proposed to illustrate nonlinear phenomena in physiological control systems, is a classical example of a simple looking time delay system with very complicated behavior. Here we use a novel approach for…