Identification and Control of Global Dynamical Structures for a Two-Degree-of-Freedom Airfoil System

The global dynamic structures of a nonlinear system can comprehensively predict the system’s responses and understand the underlying mechanisms. However, the amount of data and the computational cost are very high for global analysis of a system with multiple-degree-of-freedom. In the framework of space discretization, this paper proposes a methodology that captures global structures using as few data as possible. This method employs the proposed feature recognition vectors (FRVs) for attractors finding, critical slowing down (CSD) for localization of saddle on boundary, cell-to-cell mapping in backward searching way for characterization of stable manifolds. In this way, the global dynamics of a two-degree-of-freedom airfoil (TDOFA) system is investigated. As the flow velocity varies, a subcritical Hopf bifurcation occurs, resulting in a sudden transition from the equilibrium state to a high-amplitude limit cycle. Furthermore, external excitation is introduced to reshape the intrinsic global structure of the system. Through parameter adjustment, the attractor with high-amplitude oscillator can be eliminated through saddle-node bifurcations or boundary crises. This approach provides a way, from a perspective of global dynamics, to deeply understand the nature of catastrophic responses and to effectively implement global control.