The dynamics of stochastic and resonant layers in a periodically driven pendulum

The analytical conditions for both the onset of a new resonance in stochastic layers and the presence of resonant layers in a periodically driven pendulum are presented. The stochastic layers in the vicinity of the homoclinic orbit and the resonant layers formed near the resonant separatrix are illustrated through the Poincare mapping sections. The similarity between stochastic layers and resonant layers is observed. The mechanism of resonant layers characterized by sub-resonance in nonlinear dynamics can be further investigated through such similarity.