Chaotic responses of a deformable system under parametric and external excitations

This paper explores the effect of the deformability that certain systems undergo on their chaotic behavior, in the case where they are driven by both direct and parametric forces. The deformability of a system is accounted for by allowing its substrate potential to depend explicitly on a parameter that can varies continuously in a given range. The Remoissenet and Peyrard (RP) potential that we use additionally generates heteroclinic orbits, which enables an analytical approach of Melnikov’s type to the problem. The system is also investigated numerically by constructing Poincaré surfaces of sections and bifurcation diagrams and by computing Lyapunov exponents. It is found that the complexity of the model’s dynamics increases with the increase of the potential wells’ width. The analytical Melnikov’s type result is inconclusive with respect to this effect of the shape of the potential, but agree well with numerical analysis for fixed value of the shape parameter.