| Popis: |
We study the delay equation $\dot{x}(t)=-\mu x(t)+f(x(t-1))$ with $\mu>0$ and a nonmonotone $C^1$-function $f$ obeying $x f(x)>0$ (positive feedback) outside a small neighbourhood of zero. By means of a computer-assisted method we prove the existence of asymptotically orbitally stable periodic solutions. The main idea behind our proof is the reduction of the infinite-dimensional dynamics to a finite-dimensional map. In particular, for two classes of nonlinearities $f$ we construct two types of solutions, the dynamics of which is reduced to a one- and a two-dimensional map, respectively. |
