Chaotic behavior of a class of nonlinear differential delay equations (Q1060337)

The author studies the chaotic behavior, in the sense of Li and Yorke, for a class of nonlinear differential delay equations of the type \(x'(t)=-f_{\mu}(x(t-1)),\) where \(f_{\mu}: R\to R\) is a continuous odd function satisfying (i) \(f_{\mu}(x)=\mu\), for \(\delta <x<1-\delta\), (ii) \(f_{\mu}(x)=sign(x)\), for \(| x| \geq 1\), (iii) \(f_{\mu}(x)=-\mu\), for \(\delta -1<x<-\delta\), and (iv) \(\mu\in (2,3)\), \(0<\delta \ll 1/2\). In particular, he proves that the equation has infinitely many periodic as well as infinitely many aperiodic solutions.