This book presents recent developments in dynamical systems theory and its cross-disciplinary applications. It connects mathematical theory with practical problem-solving in fields ranging from social dynamics to oceanography. Topics include nonlinear phenomena, chaos theory, fractional calculus, and delayed systems, with applications in social systems, energy optimization, wave dynamics, neuroscience, and astronomy. The collection provides analytical and numerical approaches for understanding complex system behaviors, demonstrating how dynamical systems frameworks reveal patterns across diverse phenomena and offer powerful tools for scientists and engineers addressing real-world problems.

Prof. Dimitri Volchenkov sits in the Department of Mathematics and Statistics, Texas Tech University, Texas, USA; Prof. Siyuan Xing sits in the Department of Mechanical Engineering, California Polytechnic State University, San Luis Obispo, CA, USA; Prof. Jianzhe Huang sits in the Department of Aerospace Information and Control, Shanghai Jiaotong University, China; and Prof. Yeyin Xu sits in the School of Astronautics and Aeronautics, Xi'an Jiaotong University, China.