Andronov–Hopf Bifurcation in Control Systems with Nonsmooth Functions

The paper discusses the problem of Andronov–Hopf bifurcation in differential equations containing small non-smooth nonlinearities. Many problems of nonlinear dynamics, mechanics, control theory, etc. lead to such a problem. In this regard, it is of relevance to develop analogues of theorems of the classical bifurcation theory for equations with nonsmooth functions. New characteristics of Andronov–Hopf bifurcation are proposed, including those for problems in which the bifurcation parameter corresponds to a small parameter at nonsmooth nonlinearity. An approach for obtaining asymptotic formulas for bifurcation solutions and calculation of the corresponding coefficients is given.