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 ◽  
...  
1979 ◽  
Vol 27 (1) ◽  
pp. 108-124 ◽  
Author(s):  
P. E. Kloeden

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.


2012 ◽  
Vol 26 (25) ◽  
pp. 1246016
Author(s):  
ZDENĚK BERAN ◽  
SERGEJ ČELIKOVSÝ

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.


2017 ◽  
Vol 22 (5) ◽  
pp. ⅰ-ⅳ
Author(s):  
María J. Garrido-Atienza ◽  
◽  
Oleksiy V. Kapustyan ◽  
José Valero ◽  
◽  
...  

2002 ◽  
Vol 7 (9) ◽  
pp. 453-473 ◽  
Author(s):  
Noriaki Yamazaki

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.


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

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