On Stability of Physics Systems

Within the framework of the hypothesis offered by authors about a complex-valued nature of physical quantities the stability of basic equations of the classical physics concerning complex-valued perturbations of parameters and boundary conditions is explored. The conducted examination of nonlinear equations and, what is more important, of linear differential equations shows violation in some cases of the continuous dependence of the solution on the change of imaginary parts of parameters and boundary conditions in the neighborhood of zero. In other words, it was revealed that a small imaginary part may drive the real solution. It may be concluded that a small imaginary part, even if unobservable, is still an inherent characteristic of a physical quantity, being yet something like a hidden parameter, and manifests itself only indirectly forcing the system to move in this or that direction, which may be taken as a basis for experimental testing of the put forward hypothesis about a complex-valued nature of physical quantities.