RECENT DEVELOPMENTS IN DIMENSION REDUCTION METHODS FOR HIGH-DIMENSION DYNAMICAL SYSTEMS

The currentachievements in dimension reduction of nonlinear dynamic systemsare reviewed. The basic concepts, features and limitations areelucidated for the existing dimension reduction methods ofnonlinear dynamic systems. In addition to the typical dimensionreduction methods (such as the model reduction method based oncenter manifold theorem, the Lyapunov-Schmidt method, the Galerkinmethod and the method of proper orthogonal decomposition), themethods in terms of normal form and slow-fast dynamics are brieflypresented. Finally, new ideas on the dimension reduction ofhigh-dimensional dynamical systems are proposed, and futureresearch directions are discussed.