Nonlinear Dynamics from High Order Interaction

The research work for this book was supported by Jiangsu University of Science and Technology. Nonlinearity is the inherent essence of most natural and engineering systems. From chaotic oscillations in mechanical structures and turbulent flows in fluid dynamics to complex fluctuation behaviors in quantum systems, biological networks and social economic systems, low-order linear and weakly nonlinear theories can no longer fully explain the intricate dynamic evolution laws of complex systems. Most real-world dynamic processes are dominated by high-order nonlinear interactions among system components, which induce abundant novel phenomena such as multi-stability, limit cycle bifurcation, chaotic transition, resonance mutation and synchronous aberration. These high-order dominant behaviors have become the core bottleneck restricting theoretical innovation, mechanism interpretation and precise control of complex dynamic systems. It is against this research background that this monograph systematically sorts out the basic theory, analytical methods, mechanism laws and engineering applications of nonlinear dynamics driven by high-order nonlinear interactions.