Ordinary Differential Equations and Dynamical Systems arise in many different contexts throughout Mathematics and Science (social and natural), which describe the change rate or the evolutionary processes given implicitly by a relation. Their focus is not on finding precise solutions to the equations since it is often hopeless, but rather to answer questions like "Will the system settle down to a steady state in the long term, and if so, what are the possible steady states in the qualitative or topological structure? ", or "Does the long-term behavior of the system depend on its initial condition and small perturbations?" etc.
The group of Ordinary Differential Equations and Dynamical Systems at Shanghai Jiao Tong University focuses on qualitative theory, bifurcation theory, integrability, chaos and its applications in biology, celestial mechanics, medicine, physics and so on.