Bifurcations at Infinity in General 3D Piecewise-Smooth Quadratic Vector Fields

This paper investigates bifurcations at infinity, in general, Three-Dimensional (3D) piecewise-smooth quadratic vector fields. We derive the expression for the sliding vector field in the switching region at infinity utilizing the Poincaré compactification and the Filippov convention. Then, we establish the parameter conditions under which the piecewise smooth system exhibits local codimension-0 singularities, regular points on the discontinuity boundary, and codimension-1 singularities at infinity. These findings offer valuable insights into the complex dynamics of piecewise smooth nonlinear vector fields. Finally, the main results are applied to two models of 3D variable-boostable chaotic flows, whose vector fields contain only square (e.g. [Formula: see text], [Formula: see text] and [Formula: see text]) or cross-product terms (e.g. [Formula: see text], [Formula: see text] and [Formula: see text]), and the phase portraits of the dynamic behaviors at infinity are described.