This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
an der Heiden, U. (1979): Periodic solutions of second order differential equations with delay. J. Math. Anal. Appl. 70, 599–609
Bélair, J., Mackey, M.C. (1989): Consumer memory and price fluctuations in commodity markets: an integrodifferential model. J. Dyn. Diff. Equations 1, 299–325
Busenberg, S., Travis, C.C. (1982): On the use of reducible functional differential equations. J. Math. Anal. Appl. 89, 46–66
Busenberg, S., Hill, T. (1988): Construction of differential equation approximations to delay differential equations. Appl. Anal. 31, 35–56
Cao, Y. (1989): The discrete Lyapunov function for scalar differential delay equations. J. Differential Equations. To appear
Chow, S.-N., Diekmann, O., Mallet-Paret, J. (1985): Multiplicity of symmetric periodic solutions of a nonlinear Volterra integral equation. Japan J. Appl. Math. 2, 433–469
Chow, S.-N., Hale, J.K. (1982): Methods of Bifurcation Theory. Springer-Verlag
Chow, S.-N., Lin, X.-L., Mallet-Paret, J. (1989): Transition layers for singularly perturbed delay differential equations with monotone nonlinearities. J. Dynamics Diff. Eqns. 1, 3–43
Chow, S.-N., Mallet-Paret, J. (1983): Singularly perturbed delay differential equations. In Coupled Oscillators (Eds. J. Chandra and A. Scott), North-Holland, 7–12
de Oliveira, J.C., Hale, J.K. (1980): Dynamic behavior from the bifurcation function. Tôhoku Math. J. 32, 577–592
Hale, J.K. (1979): Nonlinear oscillations in equations with delays. Lect. Appl. Math. 17, 157–185. Am. Math. Soc.
Hale, J.K. (1985): Flows on centre manifolds for scalar functional differential equations. Proc. Royal Soc. Edinburgh 101A, 193–201
Hale, J.K. (1986): Local flows for functional differential equations. Contemporary Mathematics 56, 185–192. Am. Math. Soc.
Huang, W. (1990): Global geometry of the stable regions for two delay differential equations. To appear
Ivanov, A.F., Sharkovsky, A.N. (1990): Oscillations in singularly perturbed delay equations. Dynamics Reported. To appear
Lenhart, S.N., Travis, C.C. (1985): Stability of functional partial differential equations. J. Differential Equations 58, 212–227
Longtin, A. (1988): Nonlinear oscillations, noise and chaos in neural delayed feedback. Ph. D. Thesis, McGill University, Montreal
Mallet-Paret, J. (1988): Morse decomposition for delay differential equations. J. Differential Equations. 72, 270–315
Mallet-Paret, J., Nussbaum, R. (1986): Global continuation and asymptotic behavior for periodic solutions of a delay differential equation. Ann. Math. Pura Appl. 145, 33–128
Nussbaum, R. (1973): Periodic solutions of analytic functional differential equations are analytic. Mich. Math. J. 20, 249–255
Vallée, R., Dubois, P., Côté, M., Delisle, C. (1987): Second-order differential delay equation to describe a hybrid bistable device. Phys. Rev. A 36, 1327–1332
Vallée, R., Marriott, C. (1989): Analysis of an N th-order nonlinear differential delay equation. Phys. Rev. A 39, 197–205
Zhao, Y., Wang, H., Huo, Y. (1988): Anomalous behavior of bifurcation in a system with delayed feedback. Phys. Letters A 133, 353–356
Editor information
Additional information
To Kenneth Cooke on his 65th birthday
Rights and permissions
Copyright information
© 1991 Springer-Verlag
About this paper
Cite this paper
Hale, J.K. (1991). Dynamics and delays. In: Busenberg, S., Martelli, M. (eds) Delay Differential Equations and Dynamical Systems. Lecture Notes in Mathematics, vol 1475. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083476
Download citation
DOI: https://doi.org/10.1007/BFb0083476
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54120-2
Online ISBN: 978-3-540-47418-0
eBook Packages: Springer Book Archive