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From sine waves to square waves in delay equations

Published online by Cambridge University Press:  14 November 2011

S.-N. Chow ,
J. K. Hale  and
W. Huang
S.-N. Chow
Affiliation:
Center for Dynamical Systems and Nonlinear Studies, Georgia Institute of Technology, Atlanta, GA 30332-0160, U.S.A.
J. K. Hale
Affiliation:
Center for Dynamical Systems and Nonlinear Studies, Georgia Institute of Technology, Atlanta, GA 30332-0160, U.S.A.
W. Huang
Affiliation:
Center for Dynamical Systems and Nonlinear Studies, Georgia Institute of Technology, Atlanta, GA 30332-0160, U.S.A.
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Synopsis

Suppose fλ: ℝ→ℝ, fλ(0) = 0 and the fixed point zero undergoes a generic supercritical period doubling bifurcation at λ = 0. We characterise those small values of ε > 0, λ ∈ ℝ for which there are periodic solutions of period approximately two of the equation

As ε → 0, these solutions approach square waves.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 120 , Issue 3-4 , 1992 , pp. 223 - 229
Copyright
Copyright © Royal Society of Edinburgh 1992

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