Forwards and pullback behaviour of a non-autonomous Lotka-Volterra system

Nonlinearity

Volumn 16, Issue 4, 2003, Pages 1277-1293

  Langa, José A ^a   Robinson, James C ^b   Suárez, Antonio ^a  

^a UNIVERSITY OF SEVILLE   (Spain)

^b UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0242371887     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/16/4/305     Document Type: Article

References (37)

1. Ahmad S 1988 On almost periodic solutions of the competing species problem Proc. Am. Math. Soc. 102 855-61
2. Ahmad S 1993 On the nonautonomous Volterra-Lotka competition equation Proc. Am. Math. Soc. 117 199-205
3. Ahmad S 1999 Extinction of species in nonautonomous Lotka-Volterra systems Proc. Am. Math. Soc. 127 2905-10
4. Ahmad S and Lazer A C 1995 On the nonautonomous N-competing species problems Appl. Anal. 57 309-23
5. Aulbach B and Wanner T 1996 Integral manifolds for Carathéodory type differential equations in Banach spaces Six Lectures on Dynamical Systems ed B Aulbach and F Colonius (Singapore: World Scientific) pp 45-119
6. Cheban D N, Kloeden P E and Schmalfuss B 2002 The relationship between pullback, forwards and global attractors of non-autonomous dynamical systems Nonlinear Dyn. Syst. Theory 2 9-28
7. Chepyzhov V V and Vishik M I 1994 Attractors of non-autonomous dynamical systems and their dimension. J. Math. Pure Appl. 73 279-333
8. Chueshov I 2001 Order-preserving skew-product flows and non-autonomous parabolic systems Acta Appl. Math. 65 185-205
9. Coppel W A 1978 Dichotomies in Stability Theory (Lecture Notes in Mathematics No 629) (Berlin: Springer)
10. Crauel H 2001 Random point attractors versus random set attractors J. London Math. Soc. 63 413-27
11. _, Debussche A and Flandoli F 1997 Random attractors J. Dyn. Diff. Eqns 9 307-41
12. Glendinning P A 1994 Stability, Instability and Chaos: An Introduction to the Theory of Nonlinear Differential Equations (Cambridge Texts in Applied Mathematics) (Cambridge: Cambridge University Press)
13. Hale J K 1969 Ordinary Differential Equations (Baltimore, MD: Wiley)
14. Hess P and Lazer A C 1991 On an abstract competition model and applications Nonlinear Anal. TMA 16 917-40
15. Kloeden P E 1997 In memoriam Mark A Krasnosel'skii, Moscow: 27 April 1920-13 February 1997. With assistance from N A Bobylev, V S Kozyakin, A M Krasnosel'skii, A V Pokrovskii and B N Sadovskiǐ Mitt. Ges. Angew. Math. Mech. 20 13-14
16. Kloeden P E and Schmalfuss B 1998 Asymptotic behaviour of non-autonomous difference inclusions Systems Control Lett. 33 275-80
17. Langa J A and Suárez A 2002 Pullback permanence for non-autonomous partial differential equations Electron. J. Diff. Eqns 2002 no 72 1-20
18. Langa J A, Robinson J C and Suárez A 2002 Stability, instability, and bifurcation phenomena in non-autonomous differential equations Nonlinearity 15 887-903
19. Langa J A, Robinson J C and Suárez A 2003 Pullback permanence in a non-autonomous competitive Lotka-Volterra model J. Diff. Eqns 190 214-38
20. Malhotra N and Wiggins S 1998 Geometric structures, lobe dynamics, and Lagrangian transport in flows with aperiodic time-dependence, with applications to Rossby wave flow J. Nonlinear Sci. 8 401-56
21. Markus L 1956 Asymptotically autonomous differential systems Contributions to the Theory of Nonlinear Oscillations III (Annals of Mathematics Studies 36) ed S Lefschetz (Princeton: Princeton University Press) pp 17-29
22. Mischaikow K, Smith H and Thieme H R 1995 Asymptotically autonomous semiflows: chain recurrence and Lyapunov functions Trans. Am. Math. Soc. 347 1669-85
23. Montes de Oca F and Zeeman L 1996 Extinction in nonautonomous competitive Lotka-Volterra systems Proc. Am. Math. Soc. 124 3677-87
24. Murray J D 1993 Mathematical Biology (New York: Springer)
25. Redheffer R 1996 Nonautonomous Lotka-Volterra systems, I J. Diff. Eqns 127 519-41
26. Redheffer R 1996 Nonautonomous Lotka-Volterra systems, II J. Diff. Eqns 132 1-20
27. Robinson J C 2001 Infinite-Dimensional Dynamical Systems (Cambridge: Cambridge University Press)
28. Sacker R J and Sell G R 1974 Existence of dichotomies and invariant splitting for linear differential systems I J. Diff. Eqns 15 429-58
29. Sacker R J and Sell G R 1976 Existence of dichotomies and invariant splitting for linear differential systems II J. Diff. Eqns 22 478-96
30. Sacker R J and Sell G R 1976 Existence of dichotomies and invariant splitting for linear differential systems in J. Diff. Eqns 22 497-522
31. Schmalfuss B 2000 Attractors for the non-autonomous dynamical systems Proc. Equadiff 99 (Berlin) ed B Fiedler et al (Singapore: World Scientific) pp 684-9
32. Sell G 1967 Non-autonomous differential equations and dynamical systems Trans. Am. Math. Soc. 127 241-83
33. Siegmund S 2002 Dichotomy spectrum for nonautonomous differential equations J. Dyn. Diff. Eqns 14 243-58
34. Smith H L 1995 Monotone Dynamical Systems (Mathematical Surveys and Monographs) (Providence, RI: AMS) vol 41
35. Temam R 1988 Infinite-Dimensional Dynamical Systems in Mechanics and Physics (New York: Springer)
36. Thieme H 1994 Asymptotically autonomous differential equations in the plane Rocky Mountain J. Math. 24 351-380
37. Yi Y 1993 A generalized integral manifold theorem J. Diff. Eqns 102 153-87