Professor Albert C.J. Luo works at Southern Illinois University Edwardsville. For over 30 years, Dr. Luos contributions on nonlinear dynamical systems and mechanics lie in: (i) the local singularity theory for discontinuous dynamical systems; (ii)dynamical systems synchronization; (iii) analytical solutions of periodic and chaotic motions in nonlinear dynamical systems; (iv) the theory for stochastic and resonant layer in nonlinear Hamiltonian systems; and (v) the full nonlinear theory for a deformable body. Such contributions have been scattered into 20 monographs and over 300 peer-reviewed journal and conference papers. Dr. Luo has served as an editor for the journal Communications in Nonlinear Science and Numerical Simulation, and book series on Nonlinear Physical Science (HEP) and Nonlinear Systems and Complexity (Springer). Dr. Luo was an editorial member for IMeChE Part K Journal of Multibody Dynamics and Journal of Vibration and Control, and has also organized over 30 international symposiums and conferences on dynamics and control.Siyu Guo is a Ph.D. student in Mechanical Engineering, at Southern Illinois University Edwardsville. He received his B.S.from Nanjing University of Science and Technology in 2012 and his M.S. from Southern Illinois University Edwardsville in 2018. In 2017–2018, he was an FEA engineer in the Innovation & Technology Development Division of the Caterpillar Inc. in Peoria, Illinois. His research interests are on dynamical systems and discontinuous dynamical systems. Siyu has published five peer-review journal papers and five conference papers on nonlinear dynamics.

• Preface.- Introduction.- Generalized Harmonic Balance Method.- Analytical Periodic Evolutions.- Analytical Routes to Chaotic Evolutions.- Independent Periodic Evolutions.- Production and Compensation.- References.- Authors' Biographies.

Professor Albert C.J. Luo works at Southern Illinois University Edwardsville. For over 30 years, Dr. Luos contributions on nonlinear dynamical systems and mechanics lie in: (i) the local singularity theory for discontinuous dynamical systems; (ii)dynamical systems synchronization; (iii) analytical solutions of periodic and chaotic motions in nonlinear dynamical systems; (iv) the theory for stochastic and resonant layer in nonlinear Hamiltonian systems; and (v) the full nonlinear theory for a deformable body. Such contributions have been scattered into 20 monographs and over 300 peer-reviewed journal and conference papers. Dr. Luo has served as an editor for the journal Communications in Nonlinear Science and Numerical Simulation, and book series on Nonlinear Physical Science (HEP) and Nonlinear Systems and Complexity (Springer). Dr. Luo was an editorial member for IMeChE Part K Journal of Multibody Dynamics and Journal of Vibration and Control, and has also organized over 30 international symposiums and conferences on dynamics and control.Siyu Guo is a Ph.D. student in Mechanical Engineering, at Southern Illinois University Edwardsville. He received his B.S.from Nanjing University of Science and Technology in 2012 and his M.S. from Southern Illinois University Edwardsville in 2018. In 2017–2018, he was an FEA engineer in the Innovation & Technology Development Division of the Caterpillar Inc. in Peoria, Illinois. His research interests are on dynamical systems and discontinuous dynamical systems. Siyu has published five peer-review journal papers and five conference papers on nonlinear dynamics.

• Preface.- Introduction.- Generalized Harmonic Balance Method.- Analytical Periodic Evolutions.- Analytical Routes to Chaotic Evolutions.- Independent Periodic Evolutions.- Production and Compensation.- References.- Authors' Biographies.

Professor Albert C.J. Luo works at Southern Illinois University Edwardsville. For over 30 years, Dr. Luos contributions on nonlinear dynamical systems and mechanics lie in: (i) the local singularity theory for discontinuous dynamical systems; (ii)dynamical systems synchronization; (iii) analytical solutions of periodic and chaotic motions in nonlinear dynamical systems; (iv) the theory for stochastic and resonant layer in nonlinear Hamiltonian systems; and (v) the full nonlinear theory for a deformable body. Such contributions have been scattered into 20 monographs and over 300 peer-reviewed journal and conference papers. Dr. Luo has served as an editor for the journal Communications in Nonlinear Science and Numerical Simulation, and book series on Nonlinear Physical Science (HEP) and Nonlinear Systems and Complexity (Springer). Dr. Luo was an editorial member for IMeChE Part K Journal of Multibody Dynamics and Journal of Vibration and Control, and has also organized over 30 international symposiums and conferences on dynamics and control.Siyu Guo is a Ph.D. student in Mechanical Engineering, at Southern Illinois University Edwardsville. He received his B.S.from Nanjing University of Science and Technology in 2012 and his M.S. from Southern Illinois University Edwardsville in 2018. In 2017–2018, he was an FEA engineer in the Innovation & Technology Development Division of the Caterpillar Inc. in Peoria, Illinois. His research interests are on dynamical systems and discontinuous dynamical systems. Siyu has published five peer-review journal papers and five conference papers on nonlinear dynamics.

• Preface.- Introduction.- Generalized Harmonic Balance Method.- Analytical Periodic Evolutions.- Analytical Routes to Chaotic Evolutions.- Independent Periodic Evolutions.- Production and Compensation.- References.- Authors' Biographies.