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 systems

New 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 systems

New theory for Dynamical Systems Synchronizations

• Continuous system synchronization

• Single constraint synchronization

• Multiple-constraints synchronization

• Synchronization to edge

• Function synchronization

• Discrete systems synchronization

• Companion and synchronization

New 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 method

Singularity 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

Two-dimensional Quadratic Dynamical Systems

• Univariate Vector Fields

• Bivariate Vector Fields