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Related papers: Stability of multivalued attractors

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Takens' Embedding Theorem asserts that when the states of a hidden dynamical system are confined to a low-dimensional attractor, complete information about the states can be preserved in the observed time-series output through the delay…

Dynamical Systems · Mathematics 2014-06-17 Han Lun Yap , Armin Eftekhari , Michael B. Wakin , Christopher J. Rozell

In this article, we discuss a new version of metric fixed point theory especially of Banach Contraction Principle, Ran-Reurings Theorem and others.

Functional Analysis · Mathematics 2018-03-23 Qamrul Haque Khan , Tawseef Rashid

In this paper we introduce a notion of an attractor for local semiflows on topological spaces, which in some cases seems to be more suitable than the existing ones in the literature. Based on this notion we develop a basic attractor theory…

Dynamical Systems · Mathematics 2015-07-06 Desheng Li , Youbin Xiong , Jintao Wang

We introduce and study a new type of mappings in metric spaces termed $n$-point Kannan-type mappings. A fixed-point theorem is proved for these mappings. In general case such mappings are discontinuous in the domain but necessarily…

General Topology · Mathematics 2025-04-22 Ravindra K. Bisht , Evgeniy Petrov

It is well known that fixed point problems of contractive-type mappings defined on cone metric spaces over Banach algebras are not equivalent to those in usual metric spaces (see [3] and [10]). In this framework, the novelty of the present…

Functional Analysis · Mathematics 2019-06-17 Cristian Daniel Alecsa

A Banach space $X$ is said to have property (K) if every $w^*$-convergent sequence in $X^*$ admits a convex block subsequence which converges with respect to the Mackey topology. We study the connection of this property with strongly weakly…

Functional Analysis · Mathematics 2016-01-25 Antonio Avilés , José Rodríguez

Let $T$ be a $C^{1}$ competitive map on a rectangular region $R\subset \mathbb{R}^{2}$. The main results of this paper give conditions which guarantee the existence of an invariant curve $C$, which is the graph of a continuous increasing…

Dynamical Systems · Mathematics 2012-03-06 Gabriel Lugo , Frank J. Palladino

We prove that the diametral strong diameter 2 property of a Banach space (meaning that, in convex combinations of relatively weakly open subsets of its unit ball, every point has an "almost diametral" point) is stable under 1-sums, i.e.,…

Functional Analysis · Mathematics 2016-03-29 Rainis Haller , Katriin Pirk , Märt Põldvere

In this paper, we present the generalized iterated function system for constructing of common fractals of generalized contractive mappings in the setup of dislocated metric spaces. The well-posedness of attractors based problems of rational…

Dynamical Systems · Mathematics 2023-06-02 Talat Nazir , Sergei Silvestrov

The Banach contraction principle is the most celebrated fixed point theorem, it has been generalized in various directions. In this paper, inspired by the concept of $(\phi, F)-$contraction in metric spaces, introduced by Wardowski. We…

General Topology · Mathematics 2022-01-19 Mohamed Rossafi , Abdelkarim Kari

A Smarandache multi-space is a union of $n$ spaces $A_1,A_2,..., A_n$ with some additional conditions holding. Combining Smarandache multi-spaces with classical metric spaces, the conception of multi-metric space is introduced. Some…

General Mathematics · Mathematics 2007-05-23 Linfan Mao

Let $M$ be a locally compact metric space endowed with a continuous flow $\phi : M \times \mathbb{R} \longrightarrow M$. Frequently an attractor $K$ for $\phi$ exists which is of interest, not only in itself but also the dynamics in its…

Dynamical Systems · Mathematics 2014-06-23 J. J. Sánchez-Gabites

In this paper, we will show that a periodic nonlinear, time-varying dissipative system that is defined on a genus-p surface contains one or more invariant sets which act as attractors. Moreover, we shall generalize a result in [Martins,…

Dynamical Systems · Mathematics 2015-05-13 Yi Song , Stephen P. Banks

In the Normed space theory, the existence of fixed points is one of the main tools in improving efficiency of iterative algorithms in optimization, numerical analysis and various mathematical applications. This study introduces and…

Optimization and Control · Mathematics 2024-05-15 Akansha Tyagi , Sachin Vashistha

In this paper we investigate how many periodic attractors maps in a small neighbourhood of a given map can have. For this purpose we develop new tools which help to make uniform cross-ratio distortion estimates in a neighbourhood of a map…

Dynamical Systems · Mathematics 2013-03-19 O Kozlovski

We develop a novel and unifying setting for phase retrieval problems that works in Banach spaces and for continuous frames and consider the questions of uniqueness and stability of the reconstruction from phaseless measurements. Our main…

Functional Analysis · Mathematics 2016-12-23 Rima Alaifari , Philipp Grohs

We examine the effects of symmetry--preserving and breaking interactions in a drive--response system where the response has an invariant symmetry in the absence of the drive. Subsequent to the onset of generalized synchronization, we find…

Chaotic Dynamics · Physics 2015-06-15 Manish Agrawal , Awadhesh Prasad , Ram Ramaswamy

In this paper, considering a wider class of simulation functions some fixed point results for multivalued mappings in $\alpha$-complete metric spaces have been presented. Results obtained in this paper extend and generalize some well-known…

General Mathematics · Mathematics 2018-01-17 Deepesh Kumar Patel

In this paper, we deal with a notion of Banach space-valued mappings defined on a set consisting of finite graphs with uniformly bounded vertex degree. These functions will be endowed with certain boundedness and additivity criteria. We…

Combinatorics · Mathematics 2015-01-14 Felix Pogorzelski

Boolean networks at the critical point have been a matter of debate for many years as, e.g., scaling of number of attractor with system size. Recently it was found that this number scales superpolynomially with system size, contrary to a…

Disordered Systems and Neural Networks · Physics 2009-11-10 Konstantin Klemm , Stefan Bornholdt