Albert C. J. Luo

List of achievements and new developments.Analytical Methods and Semi-analytical methods for Nonlinear Dynamics• Generalized harmonic balance method• Analytical solutions of periodic motions• Analytical bifurcation trees to chaos• Infinite homoclinic orbits• Analytical quasi-periodic motions• Analytical nonlinear frequency-amplitude analysis• Implicit mapping dynamics• Implicit mapping methods• Ying solutions of nonlinear discrete systems• Yang solutions of nonlinear discrete systems• Analytical solutions of Time-delay systemsNew Theories for Nonlinear Deformable-body Dynamics• Nonlinear cable Theory• Nonlinear soft-web theory• Nonlinear network theory• Nonlinear plate theory• Nonlinear membrane theory• Nonlinear shell theory• Nonlinear beam theory• Nonlinear rod theory • Large damage theory• Incremental energy equivalence theory New Theories and Methods for Discontinuous Dynamical Systems• Local singularity theory of flow at the boundary• Flow switchability theory at the boundary• Flow switchability theory at the boundary• Flow barrier theory• Domain flows switchability and attractivity• Boundary flow switchability and attractivity• Edge flow switchability and attractivity• Strange attractor fragmentation• Constructed periodic motions and chaos• Constructed periodic motions and bifurcations• Constructed chaos• Switched dynamical systemsNew theory for Dynamical Systems Synchronizations • Continuous system synchronization• Single constraint synchronization• Multiple-constraints synchronization• Synchronization to edge• Function synchronization• Discrete systems synchronization• Companion and synchronizationNew theories and criteria in Nonlinear Hamiltonian Systems• Stochastic layer theory• Resonant layer theory• Chaotic motions in stochastic layers• Chaotic motions in resonant layers• Energy incremental methodSingularity theory for continuous polynomial nonlinear systems• New bifurcations and global dynamics• Limit cycles and homoclinic orbits• Infinite-equilibriums and switching bifurcations Bifurcation dynamics of discrete polynomial nonlinear systems• New bifurcations and global dynamics• Infinite-fixed points and switching bifurcations