Subharmonic bifurcation and chaos of a carbon nanotube supported by a Winkler and Pasternak foundation

Abstract

In this paper, by employing both analytical and numerical methods, global dynamic responses including subharmonic bifurcations and chaos are investigated for a carbon nanotube supported by a Winkler and Pasternak foundation. The criteria of chaos arising from transverse intersections for stable and unstable manifolds of homoclinic orbits are proposed with the Melnikov method. The critical curves separating the chaotic and nonchaotic regions are plotted in the parameter plane. The parameter conditions for subharmonic bifurcations are also obtained by the subharmonic Melnikov method. It is proved rigorously that the route to chaos for this model is infinite subharmonic bifurcations. The stability of subharmonic bifurcations is also studied by the characteristic multipliers. Numerical simulations are given to confirm the analytical results.