Floquet multipliers of symmetric rapidly oscillating solutions of differential delay equations
The authors discuss the Floquet multiplies of symmetric rapidly oscillating periodic solutions to the differential delay equation \[ \dot x(t) =\alpha f(x(t),x(t-1)) \] with the symmetries \(f(-x,y)=f(x,y) =-f(x,-y)\) in terms of zeroes of a characteristic function. A relation to the characteristic function of symmetric slowly oscillating periodic solutions is derived. Sufficient conditions are established for the existence of at least one real multiplier located outside the unit disc. As an example, a piecewise linear equation with sine-like feedback is studied detailed both analytically and numerically.
scientific article; zbMATH DE number 1854208