Abstract
In this chapter we study the nonlinear equation
where f: ℝ→ℝ is a continuous function. The positive parameter α is called the time lag. Equation (1.1) is the prototype for nonlinear delayed feedback. We shall see that the lag α can cause much more complex behaviour of solutions than in the ODE case α=0 where only monotone solutions converging to equilibria or infinity are possible. In particular, we shall prove the existence of periodic solutions (Section 5).
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© 1995 Springer-Verlag New York, Inc.
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Diekmann, O., Verduyn Lunel, S.M., van Gils, S.A., Walther, HO. (1995). The prototype equation for delayed negative feedback: periodic solutions. In: Delay Equations. Applied Mathematical Sciences, vol 110. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4206-2_16
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DOI: https://doi.org/10.1007/978-1-4612-4206-2_16
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-8696-7
Online ISBN: 978-1-4612-4206-2
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