Bifurcation of periodic solutions with large periods for a delay differential equation

Annali di Matematica Pura ed Applicata

Volumn 185, Issue 4, 2007, Pages 577-611

  Walther, Hans Otto ^a  

^a JUSTUS LIEBIG UNIVERSITY   (Germany)

Author keywords

Bifurcation; Delay differential equation; Periodic solution; Takens Bogdanov singularity

Indexed keywords

EID: 34548349305     PISSN: 03733114     EISSN: 16181891     Source Type: Journal    
DOI: 10.1007/s10231-005-0170-8     Document Type: Article

References (14)

1. Brunovský, P., Erdélyi, A., Walther, H.O.: On a model of a currency exchange rate - local stability and periodic solutions. J. Dyn. Diff. Eqs. 16, 393-432 (2004)
2. Brunovský, P., Erdélyi, A., Walther, H.O.: Short-term fluctuations of exchange rates driven by expectations. Preprint (2004).
3. DeGrauwe, P., Grimaldi, M.: The exchange rate and its fundamentals. A chaotic perspective. CESifo Working Paper No. 639 (6), (2002).
4. Diekmann, O., van Gils, S., Verduyn Lunel, S.M., Walther, H.O.: Delay Equations: Functional-, Complex-, and Nonlinear Analysis. Springer, New York (1995)
5. Erdélyi, A.: A delay differential equation model of oscillations of exchange rates. Diploma thesis, Bratislava (2003)
6. Hale, J.K., Verduyn Lunel, S.M.: Introduction to Functional Differential Equations. Springer, New York (1993)
7. Kuznetsov, Yu. A.: Elements of Applied Bifurcation Theory. Springer, New York (1995)
8. Kaplan, J.L., Yorke, J.A.: On the stability of a periodic solution of a differential delay equation. SIAM J. Math. Anal 6, 268-282 (1975)
9. Krisztin, T., Walther, H.O., Wu, J.: Shape, smoothness and invariant stratification of an attracting set for delayed monotone positive feedback. In: Fields Institute Monographs, vol. 11. A.M.S., Providence (1999)
10. Mallet-Paret, J., Sell, G.: Systems of differential delay equations: Floquet multipliers and discrete Lyapunov functions. J. Diff. Eqs. 125, 385-440 (1996)
11. Mallet-Paret, J., Sell, G.: The Poincaré-Bendixson theorem for monotone cyclic feedback systems with delay. J. Diff. Eqs. 125, 441-489 (1996)
12. Walther, H.O.: Convergence to square waves for a price model with delay. Discr. Contin. Dynam. S. 3, 1325-1342 (2005)
13. Walther, H.O.: An invariant manifold of slowly oscillating solutions for xx(t) = - μ x(t)+f(x(t-1)). J. Reine Angew. Math. 414, 67-112 (1991)
14. Walther, H.O.: The 2-dimensional attractor of x'(t)= -μ x(t)+f(x(t-1)). Memoirs A.M.S. 544 (1995)