On bifurcations in the neighborhood of a singular point of triple sewn focus type

Background. Although piecewise smooth dynamical systems have been studied in a large number of scientific works, their bifurcations have been scarcely investigated. The paper examines piecewise smooth planar vector fields in the neighborhood of a singular point of «triple sewn focus» type on the junction of their lines of discontinuity. Our aim is to describe bifurcations of that vector fields. Materials and methods. We make use of methods of the bifurcation theory, linear and nonlinear functional analysis. Results and conclusions. Vector fields with a singular point of «triple sewn focus» type form a submanifold of codimension two in the Banach space $X^r$ of piecewise smooth vector fields. The paper gives explicit formulae for functions setting that submanifold. We describe the partition of the space $X^r$ into topological equivalence classis.