A 3D Nonlinear Filippov System with a Symmetric Pair of T-Singularities

Teixeira singularity (TS) is the transverse intersection point of invisible quadratic tangency lines in 3D piecewise-smooth systems, which significantly impacts both local and global dynamics. This paper considers the 3D nonlinear Filippov system composed of Yang system and Sprott-C system with a symmetric pair of TSs. In parameters space, this Filippov system exhibits rich bifurcation phenomena, such as the boundary equilibrium bifurcations and a symmetric pair of sliding transcritical bifurcations. By constructing the Poincaré map and analyzing the number of fixed points, we present the conditions for the existence of crossing limit cycles. Furthermore, we observe the phenomenon of compound bifurcation occurring at TS, namely the TS bifurcation. This bifurcation results from the combination of transcritical bifurcation of sliding dynamics and Bogdanov–Takens bifurcation of crossing dynamics. Finally, a new chaotic attractor, which consistently surrounds two TSs, is found through numerical analysis.