Stability of symmetric periodic solutions with small amplitude of ẋ(t) = αf(x(t),x(t - 1))

Discrete and Continuous Dynamical Systems

Volumn 5, Issue 1, 1999, Pages 61-82

  Dormayer, Peter ^a   Ivanov, Anatoli F ^b,c  

^a JUSTUS LIEBIG UNIVERSITY   (Germany)

^b PENNSYLVANIA STATE UNIVERSITY   (United States)

^c UNIVERSITY OF BALLARAT   (Australia)

Author keywords

Bifurcations; Floquet multipliers; Symmetric periodic solutions

Indexed keywords

EID: 0010813253     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (9)

1. S.-N. Chow and H.-O. Walther, Characteristic multipliers and stability of symmetric periodic solutions of ẋ(t) = g(x(t-1)), Transactions of the American Mathematical Society 307 (1988), 127-142.
2. 3(t)), Z. Angew. Math. Phys. (ZAMP) 37 (1986), 765-775..
3. P. Dormayer, Smooth bifurcation of symmetric periodic solutions of functional differential equations, J. Differential Equations 82 (1989), 109-155.
4. P. Dormayer, The stability of special symmetric solutions of ẋ(t) = αf(x(t - 1)) with small amplitude, Nonlinear Analysis, Theory, Methods & Applications 14 (1990), 701-715.
5. P. Dormayer, Floquet multipliers and secondary bifurcation of periodic solutions of functional differential equations (1996, 132 pp.), Habitalitation Thesis, Giessen University.
6. J.K. Hale and S.M. Verduyn Lunel, Introduction to Functional Differential Equations, vol. 99, Springer-Verlag, New York - Heidelberg - Berlin, Applied Mathematics Series, 1993.
7. A-F. Ivanov and A.N. Sharkovsky, On periodic solutions of certain classes of differential difference equations (1982), In : Oscillation and Stability of Solutions of Differential Functional Equations, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev, 25-34. (in Russian)
8. J.L. Kaplan and J.A. Yorke, Ordinary differential equations which yield periodic solutions of functional differential equations, J. Math. Anal. Appl. 48 (1974), 317-324.
9. H.-O. Walther, Bifurcation from periodic solutions in functional differential equations, Math. Z. 182 (1983), 269-289.