Constructed complex motions and chaos.

Constructed motions and dynamic topology are new trends in solving nonlinear systems or system interactions. In nonlinear engineering, it is significant to achieve specific complex motions to satisfy expected dynamical behaviors (e.g., nonlinear motions, singularities, bifurcations, chaos, etc.), and complex motion application and control. To achieve such expected motions and global dynamical behaviors, mapping dynamics, constructed networks, random/discontinuous dynamic theorems, etc., are applied to quantitatively determine the complex motions. These theories adopt the symbolic dynamic abstracts and topological structures with nonlinear dynamics to investigate constructed complex motions to satisfy expected dynamical behaviors.