Part of the Applied Mathematical Sciences book series (AMS, volume 110)
The prototype equation for delayed negative feedback: periodic solutions
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).
$$ \dot x(t) = f(x(t - \alpha )) $$
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© Springer-Verlag New York, Inc. 1995