Locating omega-limit sets using height functions

Journal of Differential Equations

Volumn 248, Issue 10, 2010, Pages 2458-2469

  Arsie, Alessandro ^a   Ebenbauer, Christian ^b  

^a UNIVERSITY OF TOLEDO   (United States)

^b UNIVERSITY OF STUTTGART   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77249157228     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2009.11.012     Document Type: Article

References (18)

1. A. Arsie, C. Ebenbauer, Refining LaSalle 's invariance principle, in: Proceedings of the ACC 2009, St. Louis, MO, USA, 2009, pp. 108-112
2. Brockett R.W. Dynamical systems that sort lists, diagonalize matrices and solve linear programming problems. Linear Algebra Appl. 146 (1991) 76-91
3. Butler G., and Waltman P. Persistence in dynamical systems. J. Differential Equations 63 2 (1986) 255-263
4. C. Ebenbauer, A dynamical system that computes eigenvalues and diagonalizes matrices with a real spectrum, in: Proc. of the 46th IEEE Conference on Decision and Control (CDC), New Orleans, USA, 2007, pp. 1704-1709
5. Ebenbauer C., and Arsie A. On an eigenflow equation and its Lie algebraic generalization. Commun. Inf. Syst. 8 (2008) 147-170
6. Fernandes M., and Zanolin F. Repelling conditions for boundary sets using Lyapunov-like functions (ii). Persistence and periodic solutions. J. Differential Equations 86 (1990) 33-58
7. Freedman H.I., and Waltman P. Persistence in models of three interacting predator-prey populations. Math. Biosci. 68 (1984) 213-231
8. Freedman H.I., Ruan S., and Tang M. Uniform persistence and flows near a closed positively invariant set. J. Differential Equations 6 4 (1994)
9. Helmke U. Global convergence of nonlinear cascade flows with Morse-Bott zero dynamics. Systems Control Lett. 58 6 (2009) 389-394
10. LaSalle J.P. The Stability of Dynamical Systems. with an appendix by Zvi Artstein (1976), SIAM Press
11. Lee J.M. Introduction to Smooth Manifolds (2002), Springer-Verlag
12. Munkres J. Topology (2000), Prentice Hall
13. Patrao M. Morse decomposition of semiflows on topological spaces. J. Dynam. Differential Equations 19 1 (2007)
14. Sanfelice R.G., Goebel R., and Teel A.R. Invariance principles for hybrid systems with connections to detectability and asymptotic stability. IEEE Trans. Automat. Control 52 (2007) 2282-2297
15. Slemrod M. The LaSalle invariance principle in infinite-dimensional Hilbert space. Dynamical Systems Approaches to Nonlinear Problems in Systems and Circuits (1988), SIAM, Philadelphia, PA
16. Sternberg S. Lectures on Differential Geometry (1964), Prentice Hall, Englewood Cliffs, NJ
17. Whitney H. A function not constant on a connected set of critical points. Duke Math. J. 1 (1935) 514
18. Whitney H. Elementary structure of real algebraic varieties. Ann. of Math. 66 3 (1957) 545-556