Pullback incremental attraction

Peter E. Kloeden; Thomas Lorenz

Nonautonomous Dynamical Systems (2014)

  • Volume: 1, page 53-60, electronic only
  • ISSN: 2353-0626

Abstract

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A pullback incremental attraction, a nonautonomous version of incremental stability, is introduced for nonautonomous systems that may have unbounded limiting solutions. Its characterisation by a Lyapunov function is indicated.

How to cite

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Peter E. Kloeden, and Thomas Lorenz. "Pullback incremental attraction." Nonautonomous Dynamical Systems 1 (2014): 53-60, electronic only. <http://eudml.org/doc/266979>.

@article{PeterE2014,
abstract = {A pullback incremental attraction, a nonautonomous version of incremental stability, is introduced for nonautonomous systems that may have unbounded limiting solutions. Its characterisation by a Lyapunov function is indicated.},
author = {Peter E. Kloeden, Thomas Lorenz},
journal = {Nonautonomous Dynamical Systems},
keywords = {Nonautonomous dynamical system; nonautonomous differential equation; pullback incremental stability; Lyapunov function; pullback attractors; nonautonomous dynamical system},
language = {eng},
pages = {53-60, electronic only},
title = {Pullback incremental attraction},
url = {http://eudml.org/doc/266979},
volume = {1},
year = {2014},
}

TY - JOUR
AU - Peter E. Kloeden
AU - Thomas Lorenz
TI - Pullback incremental attraction
JO - Nonautonomous Dynamical Systems
PY - 2014
VL - 1
SP - 53
EP - 60, electronic only
AB - A pullback incremental attraction, a nonautonomous version of incremental stability, is introduced for nonautonomous systems that may have unbounded limiting solutions. Its characterisation by a Lyapunov function is indicated.
LA - eng
KW - Nonautonomous dynamical system; nonautonomous differential equation; pullback incremental stability; Lyapunov function; pullback attractors; nonautonomous dynamical system
UR - http://eudml.org/doc/266979
ER -

References

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  1. [1] D. Angeli, A Lyapunov approach to the incremental stability properties, IEEE Trans. Automat. Control 47 (2002), 410-421. 
  2. [2] T. Caraballo, M.J. Garrido Atienza and B. Schmalfuß, Existence of exponentially attracting stationary solutions for delay evolution equations. Discrete Contin. Dyn. Syst. Ser. A 18 (2007), 271-293. Zbl1125.60058
  3. [3] T. Caraballo, P.E. Kloeden and B. Schmalfuß, Exponentially stable stationary solutions for stochastic evolution equations and their perturbation. Appl. Math. Optim. 50 (2004), 183-207. Zbl1066.60058
  4. [4] C.M. Dafermos, An invariance principle for compact processes, J. Differential Equations 9 (1971), 239-252. 
  5. [5] L. Grüne, P.E. Kloeden, S. Siegmund and F.R. Wirth, Lyapunov’s second method for nonautonomous differential equations, Discrete Contin. Dyn. Syst. Ser. A 18 (2007), 375-403. Zbl1128.37010
  6. [6] P.E. Kloeden, Lyapunov functions for cocycle attractors in nonautonomous difference equations, Izvetsiya Akad Nauk Rep Moldovia Mathematika 26 (1998), 32-42. 
  7. [7] P.E. Kloeden, A Lyapunov function for pullback attractors of nonautonomous differential equations, Electron. J. Differ. Equ. Conf. 05 (2000), 91-102. Zbl0964.34041
  8. [8] P.E. Kloeden and T. Lorenz, Stochastic differential equations with nonlocal sample dependence, Stoch. Anal. Appl. 28 (2010), 937-945. Zbl1205.60131
  9. [9] P.E. Kloeden and T. Lorenz, Mean-square random dynamical systems, J. Differential Equations 253 (2012), 1422- 1438. Zbl1267.37018
  10. [10] P.E. Kloeden and M. Rasmussen, Nonautonomous Dynamical Systems, Amer. Math. Soc., Providence, 2011. 
  11. [11] B.S. Rüffer, N. van de Wouw and M. Mueller, Convergent systems vs. incremental stability, Systems Control Lett. 62 (2013), 277-285. Zbl1261.93072
  12. [12] E.D. Sontag, Comments on integral variants of ISS, Systems Control Lett. 34 (1998), 93-100. Zbl0902.93062
  13. [13] A.M. Stuart and A.R. Humphries, Dynamical Systems and Numerical Analysis, Cambridge University Press, Cambridge, 1996. Zbl0869.65043
  14. [14] Fuke Wu and P.E. Kloeden, Mean-square random attractors of stochastic delay differential equations with random delay, Discrete Contin. Dyn. Syst. Ser. B 18, No.6, (2013), 1715-1734. Zbl1316.34083
  15. [15] T. Yoshizawa, Stability Theory by Lyapunov’s Second Method. Math. Soc Japan, Tokyo, 1966. 

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