Orbital stability and homoclinic bifurcation in a parametrized deformable double-well potential

The motion of a particle in a one-dimensional deformable double-well potential is studied. In a case study related deformable potential that permits theoretical adaptation of the model to various physical situations, the existence and the stability of periodic motion as well as the routes toward chaos upon the potential parameter are investigated. It is demonstrated that the shape of the potential is crucial in controlling the orbital stability of the system. The occurrence of chaotic motions is found to be quite sensitive to the shape parameter of the potential. These instability and chaotic behaviors result from a delicate balance between the damping, the periodic force and the total nonlinearity induced by the variable shape potential.