Spatiotemporal nonlinear dynamics and chaos in a mechanical Duffing-type system

This paper investigates spatiotemporal nonlinear dynamics and chaos in a dissipative mechanical Duffingtype system subjected to external stimulus. A nonlinear wave equation with cubic nonlinearity governs the system dynamics. A perturbation description is employed to build mathematical tools that represent different aspects of system dynamics, from local to global behaviors. Lyapunov exponents are defined from the different perturbations allowing the evaluation of local, convective and mean exponents. Different dynamical regimes are investigated considering homogeneous and heterogeneous spatial stimuli. Distinct dynamical responses are observed including periodic, quasi -periodic and chaotic behaviors. A novel concept of chaotic wave is employed to explain the spatial transport of chaos through the media considering heterogeneous conditions. Chaotic wave velocity is measured by the convective Lyapunov exponents.