Manifold dynamics and periodic orbits in a multiwell potential

In this article, we explore the dynamics as well as the geometry of the invariant manifolds that determine the escapes from a multiwell potential. We also present the network of both symmetric and asymmetric solutions of the system, while at the same time we extract valuable information about the periodic solutions, such as their locations, multiplicity, and linear stability. •We investigate the manifold dynamics of a multiwell potential.•We search for both simple symmetric and asymmetric periodic solutions of the system•The positions along with the linear stability of the periodic solutions are determined.