The effect of symmetry-breaking on the parameterically excited pendulum

摘要: Abstract The effect of the symmetry-breaking on parameterically excited pendulum including a bias term is investigated. At first, our numerical simulations show that area safe region unexcited (without damping and without forcing) will decrease with increasing term. Due to variation, critical homoclinic bifurcation increase, where transversal intersection occurs between stable unstable manifolds in Poincare map be enlarged. Second, as increases, analysis demonstrates number type attractors map, phase portraits, basins attraction, diagrams produce considerable variation. In particular, stability lose once exceeds value. this case there no longer any steady state existing. These results suggest much attention should paid controlling term, especially when main device applied some practical systems.