Analysis of Bifurcated Superstructure of Nonlinear Ocean System

Abstract

An intricate universal superstructure in bifurcation sets and routes to chaos of a nonlinear moored ocean system subjected to monochromatic wave excitations are investigated analytically and demonstrated numerically in detail herein. System nonlinearities include complex geometric restoring force and coupled fluid-system exciting forces. Primary and secondary resonance regions are identified by employing variational analysis techniques for local stability. Tangent and periodic doubling bifurcations are examined to reveal the underlying intricate superstructure. Numerical results of this complex system uncover a steady-state superstructure in the bifurcation sets that exhibit a similar bifurcation pattern of coexisting solutions in the subharmonic, ultraharmonic, and ultrasubharmonic domains. Within this superstructure it is illustrated that strange attractors appear when a period doubling sequence is infinite, and when abrupt changes in the size of an attractor occur near tangent bifurcations.