scholarly journals Robustness of dynamically gradient multivalued dynamical systems

2019 ◽  
Vol 24 (3) ◽  
pp. 1049-1077
Author(s):  
Rubén Caballero ◽  
◽  
Alexandre N. Carvalho ◽  
Pedro Marín-Rubio ◽  
José Valero ◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Multivalued Dynamical Systems

scholarly journals The funnel boundary of multivalued dynamical systems

1979 ◽  
Vol 27 (1) ◽  
pp. 108-124 ◽  
Author(s):  
P. E. Kloeden
Keyword(s):  
Dynamical Systems ◽  
Regular Boundary ◽  
Locally Compact ◽  
State Spaces ◽  
Multivalued Dynamical Systems ◽  
Set Mappings

AbstractProperties of the funnel boundary are investigated for multivalued dynamical systems defined axiomatically in terms of attainability set mappings on complete, locally compact metric state spaces. The set of regular boundary events is shown to be dense in the funnel boundary and theorems of Fukuhara and Zaremba on peripheral attainability are generalized to the systems considered here.

GENERALIZED SEMIFLOWS AND CHAOS IN MULTIVALUED DYNAMICAL SYSTEMS

2012 ◽  
Vol 26 (25) ◽  
pp. 1246016
Author(s):  
ZDENĚK BERAN ◽  
SERGEJ ČELIKOVSÝ
Keyword(s):  
Dynamical Systems ◽  
Differential Inclusion ◽  
Chaotic Behavior ◽  
Existence Of A Solution ◽  
Right Hand ◽  
Multivalued Dynamical Systems ◽  
The One ◽  
The Right ◽  
Generalized Semiflows

This contribution addresses a possible description of the chaotic behavior in multivalued dynamical systems. For the multivalued system formulated via differential inclusion the practical conditions on the right-hand side are derived to guarantee existence of a solution, which leads to the chaotic behavior. Our approach uses the notion of the generalized semiflow but it does not require construction of a selector on the set of solutions. Several applications are provided by concrete examples of multivalued dynamical systems including the one having a clear physical motivation.

scholarly journals Preface to the special issue "Finite and infinite dimensional multivalued dynamical systems"

2017 ◽  
Vol 22 (5) ◽  
pp. ⅰ-ⅳ
Author(s):  
María J. Garrido-Atienza ◽  
◽  
Oleksiy V. Kapustyan ◽  
José Valero ◽  
◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Special Issue ◽  
Infinite Dimensional ◽  
Multivalued Dynamical Systems

scholarly journals Attractors for Nonautonomous Multivalued Evolution Systems Generated by Time-Dependent Subdifferentials

2002 ◽  
Vol 7 (9) ◽  
pp. 453-473 ◽  
Author(s):  
Noriaki Yamazaki
Keyword(s):  
Dynamical Systems ◽  
Evolution Equations ◽  
Separable Hilbert Space ◽  
Global Attractors ◽  
Time Dependent ◽  
Initial State ◽  
Multivalued Dynamical Systems ◽  
Real Separable Hilbert Space ◽  
The Relationship ◽  
Multivalued Dynamical System

In a real separable Hilbert space, we consider nonautonomous evolution equations including time-dependent subdifferentials and their nonmonotone multivalued perturbations. In this paper, we treat the multivalued dynamical systems associated with time-dependent subdifferentials, in which the solution is not unique for a given initial state. In particular, we discuss the asymptotic behaviour of our multivalued semiflows from the viewpoint of attractors. In fact, assuming that the time-dependent subdifferential converges asymptotically to a time-independent one (in a sense) as time goes to infinity, we construct global attractors for nonautonomous multivalued dynamical systems and its limiting autonomous multivalued dynamical system. Moreover, we discuss the relationship between them.

Monotone trajectories of multivalued dynamical systems

1977 ◽  
Vol 115 (1) ◽  
pp. 99-117 ◽  
Author(s):  
Jean-Pierre Aubin ◽  
Arrigo Cellina ◽  
John Nohel
Keyword(s):  
Dynamical Systems ◽  
Multivalued Dynamical Systems
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