Rare periodic and chaotic attractors and typical bifurcation groups in driven double-well and many-well potential oscillatory systems

The paper illustrates the application of the method of complete bifurcation groups (MCBG) and the concept of rare attractors (RA) for driven double-well and many-well potential oscillatory systems. Some new regular and chaotic RAs have been obtained for archetypical driven nonlinear systems with linear dissipation and harmonic external force. The existence of stable solutions near unstable equilibrium position is performed as well.