Stability of Yang-Mills fields system in the homogeneous (anti)self-dual background field

Stability of Yang-Mills fields system in the background field is investigated based on the Toda criterion, Poincare sections, and the values of the maximal Lyapunov exponents. The existence of the region of regular motion at low densities of energy is demonstrated. Critical energy density of the order-chaos transition is analyzed for different values of the model parameter. The text was submitted by the authors in English.