A numerical verification method for a periodic solution of a delay differential equation
The authors develop a new numerical verification method for a system of delay differential equations: \[ \begin{aligned} \dot x(t) & = -y(t)-z(t), \dot y(t)=x(t)+(0.2)y(t)+u(t)\\ \dot z(t) & = 0.2 + z(t)(x(t)-5.7), u(t)=k(y(t-\tau)-y(t)). \end{aligned} \] By using this system of equations corresponding to the original Rössler system, they derive sufficient conditions for the existence of the solution. They describe the verification procedure in detail with conditions and provide a numerical example.
numerical computation with guaranteed accuracy
scientific article; zbMATH DE number 5798205