26
Views
8
CrossRef citations to date
0
Altmetric
Original Articles

Smoothness loss of periodic solutions of a neutral functional differential equation: On a bifurcation of the essential spectrum

Pages 255-273 | Published online: 01 Jul 2010

  • Ascher , U. M. and Spiteri , R. J. 1994 . Collocation software for boundary value differential-algebraic equations . SIAM Journal of Scientific Computing , 15 : 938 – 952 .
  • Bhatt , S. and Hsu , C. 1966 . Stability criteria for second order dynamical systems with time lag . Journal of Applied Mechanics , 33 : 113 – 118 .
  • Campbell , S. A. 1997 . Resonant codimension two bifurcation in a neutral functional differential equation . Nonlinear Analysis, Theory, Methods & Applications , 30 (7) : 4577 – 4584 . Proc. 2nd World Congress of Nonlinear Analysts
  • Chen , Y. 1992 . The existence of periodic solutions for a class of neutral differential difference equations . Journal of the Australian Mathematical Society Series B , 33 : 528 – 616 .
  • Engelborghs , K. , Luzyanina , T. and Roose , D. 1998 . Bifurcation analysis of periodic solutions of neutral functional differential equations: a case study . International Journal of Bifurcation & Chaos , 8 (10) : 1889 – 1905 .
  • Gopalsamy , K. , Li , J. and He , X.-Z. 1995 . On the construction of periodic solutions of Kaplan-Yorke type for some differential delay equations . Applicable Analysis , 59 : 65 – 80 .
  • Hale , J. K. 1977 . “ Theory of Functional Differential Equations ” . In Mathematical Sciences , Vol. 3 , Berlin : Springer-Verlag .
  • Hale , J. K. 1995 . “ Effects of delays on dynamics ” . In Topological Methods in Differential Equations and Inclusions , Edited by: Granas , A. , Frigon , M. and Sabidussi , G. 191 – 238 . Dordrecht : Kluwer Academic .
  • Hale , J. K. and Verduyn Lunel , S. M. 1993 . “ Introduction to Functional Differential Equations ” . In Mathematical Sciences , Vol. 99 , Berlin : Springer-Verlag .
  • Kaplan , J. L. and Yorke , J. A. 1974 . Ordinary differential equations which yield periodic solutions of differential delay equations . Journal of Mathematical Analysis and Applications , 48 : 317 – 324 .
  • Kolmanovskii , V. B. and Myshkis , A. 1999 . “ Introduction to the Theory and Application of Functional Differential Equations ” . In Mathematics and its Applications , Vol. 463 , Dordrecht : Kluwer Academic .
  • Kolmanovskii , V. B. and Nosov , V. R. 1986 . “ Stability of Functional Differential Equations ” . In Mathematics in Science and Engineering , Vol. 180 , New York : Academic Press .
  • Li , J. and He , X.-Z. 1995 . “ Proof and generalization of Kaplan-Yorke's conjecture on periodic solutions of differential delay equations ” . In Kunming Institute of Technology , Center of Nonlinear Sciences Studies . Technical Report
  • Luzyanina , T. , Engelborghs , K. , Lust , K. and Roose , D. 1997 . Computation, continuation and bifurcation analysis of periodic solutions of delay differential equations . International Journal of Bifurcation & Chaos , 7 (11) : 2547 – 2560 .
  • Murray , R. M. , Jacobson , C. A. , Casas , R. , Khibnik , A. I. , Johnson , C. R. , Bitmead , R. , Peracchio , A. A. and Proscia , W. M. 1997 . “ System identification for limit cycling systems: a case study for combustion instabilities ” . In Caltech CDS Technical Report cds 97 – 012 . Caltech
  • Nussbaum , R. D. 1979 . Uniqueness and nonuniqueness for periodic solutions of x'(t) =- g(x(t - 1)) . Journal of Differential Equations , 34 : 25 – 54 .
  • Paul , C. A. H. December 1995 . A user-guide to Archi--an explicit Runge-Kutta code for solving delay and neutral differential equations , Vol. 283 , December , The University of Manchester, Manchester Centre for Computational Mathematics . Technical Report

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.