Neimark-Sacker bifurcation for periodic delay differential equations

Nonlinear Analysis, Theory, Methods and Applications

Volumn 60, Issue 6, 2005, Pages 1025-1044

  Röst, Gergely ^a  

^a UNIVERSITY OF SZEGED   (Hungary)

Author keywords

Floquet multipliers; Neimark Sacker bifurcation; Periodic delay equation; Projection method; Spectral projection

Indexed keywords

FLOQUET MULTIPLIERS; NEIMARK-SACKER BIFURCATION; PERIODIC DELAY EQUATION; PROJECTION METHOD; SPECTRAL PROJECTION;

DIFFERENTIAL EQUATIONS; FUNCTIONS; LINEAR EQUATIONS; NEURAL NETWORKS; PARAMETER ESTIMATION; THEOREM PROVING;

BIFURCATION (MATHEMATICS);

EID: 11344265918     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2004.08.043     Document Type: Article

References (19)

1. F. Balibrea Gallego, and J.C. Valverde Fajardo Bifurcations and nondegenerated conditions of higher degree and a new simple proof of the Hopf-Neimark-Sacker bifurcation theorem J. Math. Anal. Appl. 237 1999 93 105
2. J. Carr Applications of the Centre Manifold Theory Applied Mathematical Sciences vol. 35 1981 Springer New York
3. O. Diekmann, S.A. Van Gils, S.M. Verduyn Lunel, and H.-O. Walther Delay Equations, Functional-, Complex-, and Nonlinear Analysis Applied Mathematical Sciences vol. 110 1995 Springer New York
4. T. Faria Normal forms for periodic retarded functional-differential equations Proc. Roy. Soc. Edinburgh 127A 1997 21 46
5. J.K. Hale, and S.M. Verduyn Lunel Introduction to Functional Differential Equations Applied Mathematical Sciences vol. 99 1993 Springer New York
6. B.D. Hassard, N.D. Kazarinoff, and Y.-H. Wan Theory and Applications of Hopf Bifurcation London Mathematical Society Lecture Note Series vol. 41 1981 Cambridge University Press Cambridge
7. G. Iooss Bifurcation of Maps and Applications Mathematics Studies vol. 36 1979 North-Holland Amsterdam
8. T. Krisztin Periodic orbits and the global attractor for delayed monotone negative feedback Proceedings of Colloques Qualitative Theory Differential Equations (1999, Szeged), Electron. J. Qual. Theory Differ. Equ. 15 2000 1 12
9. T. Krisztin, Unstable sets of periodic orbits and the global attractor for delayed feedback, Topics in Functional Differential and Difference Equation, 1999, Lisbon, Fields Institute of Communications, vol. 29, American Mathematical Society, Providence, RI, 2001, pp. 267-296.
10. T. Krisztin, and H-O. Walther Unique periodic orbits for delayed positive feedback and the global attractor J. Dynamic Differential Equations 13 2001 1 57
11. T. Krisztin, H.-O. Walther, and J. Wu Shape, Smoothness and Invariant Stratification of an Attracting Set for Delayed Monotone Positive Feedback Fields Institute Monographs vol. 11 1999 American Mathematical Society Providence, RI
12. Yu.A. Kuznetsov, Elements of Applied Bifurcation Theory, in: Applied Mathematical Sciences, vol. 112, second ed., Springer, New York, 1998.
13. B. Lani-Wayda Erratic solutions of simple delay equations Trans. Amer. Math. Soc. 351 1999 901 945
14. S.M. Verduyn Lunel, Spectral theory for delay equations, Systems, Approximation, Singular Operators, and Related Topics, IWOTA 2000, Bordeaux, Operational Theory Advances Applied, vol. 129, Birkhäuser, Basel, 2001, pp. 465-507.
15. H.-O. Walther The 2-dimensional attractor of x ′ (t) = - μ x (t) + f (x (t - 1)) Mem. Amer. Math. Soc. 113 1995 Nr. 544
16. H.-O. Walther Contracting return maps for monotone delayed feedback Discrete Contin. Dynamics Systems 7 2001 259 274
17. H.-O. Walther, and A.L. Skubachevskii On Floquet multipliers for slowly oscillating periodic solutions of nonlinear functional-differential equations (Russian) Tr. Mosk. Mat. Obs. 64 2003 3 53
18. S. Wiggins Introduction to Applied Nonlinear Dynamical Systems and Chaos Texts in Applied Mathematics vol. 2 1990 Springer New York
19. J. Wu Symmetric functional differential equations and neural networks with memory Trans. Amer. Math. Soc. 350 1998 4799 4838