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).
$$ \dot x(t) = f(x(t - \alpha )) $$
KeywordsPeriodic Solution Negative Feedback Primary Branch Global Bifurcation Unstable Behaviour
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Unable to display preview. Download preview PDF.
© Springer-Verlag New York, Inc. 1995