Some questions concerning attractors for non-autonomous dynamical systems

Johnson, Russell; Villarragut, Víctor M.

doi:10.1016/j.na.2009.02.088

Cited by 6 publications

(6 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The relation between concepts of attractors is studied in [5], [6], [15], [9]. Particularly in relation to the nonautonomous setting with compact topological parameter space, there is a work by [18] which proves that the (nonautonomous) pullback attractor of nonautonomous dynamical systems (in terms of skew product flows) coincides with their so-called Lyapunov attractors.…”

Section: Random Pullback Attractorsmentioning

confidence: 99%

Pullback attractors for stochastic Young differential delay equations

Cong¹,

Duc²,

Hong³

2020

Preprint

View full text Add to dashboard Cite

We study the asymptotic dynamics of stochastic Young differential delay equations under the regular assumptions on Lipschitz continuity of the coefficient functions. Our main results show that, if there is a linear part in the drift term which has no delay factor and has eigenvalues of negative real parts, then the generated random dynamical system possesses a random pullback attractor provided that the Lipschitz coefficients of the remaining parts are small.

show abstract

Section: Random Pullback Attractorsmentioning

confidence: 99%

Pullback attractors for stochastic Young differential delay equations

Cong¹,

Duc²,

Hong³

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…In this context, a local attractor is a pullback attractor when it is a non-empty compact subset on the state space (lemma 3.1). The relationship between different attractors for nonautonomous dynamical systems is considered in [6,19]. It is known that the global attractor for a skew-product dynamical system corresponds to the pullback attractor on the state space [4,6,37].…”

Section: Theorem 11 (Conley Decomposition For Ndss) a Non-autonomoumentioning

confidence: 99%

State space decomposition for non-autonomous dynamical systems

Chen

Duan

2011

Proceedings of the Royal Society of Edinburgh: Section A Mathem

View full text Add to dashboard Cite

Decomposition of state spaces into dynamically different components is helpful for the understanding of dynamical behaviors of complex systems. A Conley type decomposition theorem is proved for nonautonomous dynamical systems defined on a non-compact but separable state space. Namely, the state space can be decomposed into a chain recurrent part and a gradient-like part.This result applies to both nonautonomous ordinary differential equations on Euclidean space (which is only locally compact), and nonautonomous partial differential equations on infinite dimensional function space (which is not even locally compact). This decomposition result is demonstrated by discussing a few concrete examples, such as the Lorenz system and the Navier-Stokes system, under time-dependent forcing.

show abstract

“…Thus, the behaviour depends on both the initial and the actual time. This is why many dynamically relevant objects are contained in the extended state space (one speaks of nonautonomous sets) [ 10 ], rather than being merely subsets of the state space X as in the autonomous case. Furthermore, a complete description of the dynamics in a time-variant setting necessitates a strict distinction between forward and pullback convergence [ 10 , 15 ].…”

Section: Introductionmentioning

confidence: 99%

“…This is why many dynamically relevant objects are contained in the extended state space (one speaks of nonautonomous sets) [ 10 ], rather than being merely subsets of the state space X as in the autonomous case. Furthermore, a complete description of the dynamics in a time-variant setting necessitates a strict distinction between forward and pullback convergence [ 10 , 15 ]. For this reason only a combination of several attractor notions yields the full picture: The pullback attractor [ 4 , 11 , 15 , 20 ] is a compact, invariant nonautonomous set which attracts all bounded sets from the past.…”

Section: Introductionmentioning

confidence: 99%

Forward and Pullback Dynamics of Nonautonomous Integrodifference Equations: Basic Constructions

2020

View full text Add to dashboard Cite

In theoretical ecology, models describing the spatial dispersal and the temporal evolution of species having non-overlapping generations are often based on integrodifference equations. For various such applications the environment has an aperiodic influence on the models leading to nonautonomous integrodifference equations. In order to capture their long-term behaviour comprehensively, both pullback and forward attractors, as well as forward limit sets are constructed for general infinite-dimensional nonautonomous dynamical systems in discrete time. While the theory of pullback attractors, but not their application to integrodifference equations, is meanwhile well-established, the present novel approach is needed in order to understand their future behaviour.

show abstract

Some questions concerning attractors for non-autonomous dynamical systems

Cited by 6 publications

References 20 publications

Pullback attractors for stochastic Young differential delay equations

Pullback attractors for stochastic Young differential delay equations

State space decomposition for non-autonomous dynamical systems

Forward and Pullback Dynamics of Nonautonomous Integrodifference Equations: Basic Constructions

Contact Info

Product

Resources

About