Dynamical systems over the space of upper semicontinuous fuzzy sets

2012 ◽  
Vol 209 ◽  
pp. 89-103 ◽  
Author(s):  
Yangeng Wang ◽  
Guo Wei
Keyword(s):  
Dynamical Systems ◽  
Fuzzy Sets ◽  
Upper Semicontinuous

scholarly journals Bounded Motions of the Dynamical Systems Described by Differential Inclusions

2009 ◽  
Vol 2009 ◽  
pp. 1-9
Author(s):  
Nihal Ege ◽  
Khalik G. Guseinov
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Sufficient Conditions ◽  
Invariant Sets ◽  
Control Vector ◽  
Upper Semicontinuous ◽  
Right Hand ◽  
The Right

The boundedness of the motions of the dynamical system described by a differential inclusion with control vector is studied. It is assumed that the right-hand side of the differential inclusion is upper semicontinuous. Using positionally weakly invariant sets, sufficient conditions for boundedness of the motions of a dynamical system are given. These conditions have infinitesimal form and are expressed by the Hamiltonian of the dynamical system.

scholarly journals Chaos on Fuzzy Dynamical Systems

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2629
Author(s):  
Félix Martínez-Giménez ◽  
Alfred Peris ◽  
Francisco Rodenas
Keyword(s):  
Dynamical Systems ◽  
Linear Operators ◽  
Vector Spaces ◽  
Topological Vector Spaces ◽  
Distributional Chaos ◽  
Upper Semicontinuous ◽  
Continuous Map ◽  
Upper Semicontinuous Functions ◽  
Nonempty Compact ◽  
Semicontinuous Functions

Given a continuous map f:X→X on a metric space, it induces the maps f¯:K(X)→K(X), on the hyperspace of nonempty compact subspaces of X, and f^:F(X)→F(X), on the space of normal fuzzy sets, consisting of the upper semicontinuous functions u:X→[0,1] with compact support. Each of these spaces can be endowed with a respective metric. In this work, we studied the relationships among the dynamical systems (X,f), (K(X),f¯), and (F(X),f^). In particular, we considered several dynamical properties related to chaos: Devaney chaos, A-transitivity, Li–Yorke chaos, and distributional chaos, extending some results in work by Jardón, Sánchez and Sanchis (Mathematics 2020, 8, 1862) and work by Bernardes, Peris and Rodenas (Integr. Equ. Oper. Theory 2017, 88, 451–463). Especial attention is given to the dynamics of (continuous and linear) operators on metrizable topological vector spaces (linear dynamics).

Dendritations of surfaces

2017 ◽  
Vol 38 (8) ◽  
pp. 2860-2912 ◽  
Author(s):  
ALFONSO ARTIGUE
Keyword(s):  
Dynamical Systems ◽  
Metric Spaces ◽  
Upper Semicontinuous ◽  
Topological Dynamical Systems ◽  
Stable And Unstable Sets ◽  
Foliated Manifolds

In this paper we develop a generalization of foliated manifolds in the context of metric spaces. In particular we study dendritations of surfaces that are defined as maximal atlases of compatible upper semicontinuous local decompositions into dendrites. Applications are given in modeling stable and unstable sets of topological dynamical systems. For this purpose new forms of expansivity are defined.

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