Poincare-Andronov-Melnikov Analysis for Non-Smooth Systems is
devoted to the study of bifurcations of periodic solutions for
general n-dimensional discontinuous systems. The authors study
these systems under assumptions of transversal intersections with
discontinuity-switching boundaries. Furthermore, bifurcations of
periodic sliding solutions are studied from sliding periodic
solutions of unperturbed discontinuous equations, and bifurcations
of forced periodic solutions are also investigated for impact
systems from single periodic solutions of unperturbed impact
equations. In addition, the book presents studies for weakly
coupled discontinuous systems, and also the local asymptotic
properties of derived perturbed periodic solutions. The
relationship between non-smooth systems and their continuous
approximations is investigated as well. Examples of 2-, 3- and
4-dimensional discontinuous ordinary differential equations and
impact systems are given to illustrate the theoretical results. The
authors use so-called discontinuous Poincare mapping which maps a
point to its position after one period of the periodic solution.
This approach is rather technical, but it does produce results for
general dimensions of spatial variables and parameters as well as
the asymptotical results such as stability, instability, and
hyperbolicity.
General
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