Wandering solutions of delay equations with sine-like feedback (Q2718315)

The paper deals with delay equation \(\dot x(t)= f(x(t-1))\), where \(f\) is a real-valued function. This problem has been motivated by the numerical study of bifurcations of periodic solutions of the equation \(\dot x(t)= -\alpha \sin(x(t-1))\), which exhibits successive period-doubling bifurcations from the second branch as the parameter \(\alpha >0\) is varied. The author develops a framework for the description of erratic behavior of solutions of sine-like delay differential equations, and derives explicitly equations with solutions ``wandering up and down'' between arbitrary prescribed levels.