Albert C. Luo is currently a Distinguished Research Professor at Southern Illinois University Edwardsville. He is an international renowned figure in the area of nonlinear dynamics and mechanics. For about 30 years, Dr. Luo’s 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, (v) The full nonlinear theory for a deformable body. Such contributions have been scattered into 13 monographs and over 200 peer-reviewed journal and conference papers. His new research results are changing the traditional thinking in nonlinear physics and mathematics. Dr. Luo has served as an editor for the Journal “Communications in Nonlinear Science and Numerical simulation”, book series on Nonlinear Physical Science (HEP) and Nonlinear Systems and Complexity (Springer). Dr. Luo is the editorial member for two journals (i.e., IMeCh E Part K Journal of Multibody Dynamics and Journal of Vibration and Control). He also organized over 30 international symposiums and conferences on Dynamics and Control.

• Preface ix1 Introduction 11.1 Brief History 11.2 Book Layout 42 Nonlinear Dynamical Systems 72.1 Continuous Systems 72.2 Equilibriums and Stability 92.3 Bifurcation and Stability Switching 172.3.1 Stability and Switching 172.3.2 Bifurcations 263 An Analytical Method for Periodic Flows 333.1 Nonlinear Dynamical Systems 333.1.1 Autonomous Nonlinear Systems 333.1.2 Non-Autonomous Nonlinear Systems 443.2 Nonlinear Vibration Systems 483.2.1 Free Vibration Systems 483.2.2 Periodically Excited Vibration Systems 613.3 Time-Delayed Nonlinear Systems 663.3.1 Autonomous Time-Delayed Nonlinear Systems 663.3.2 Non-Autonomous Time-Delayed Nonlinear Systems 803.4 Time-Delayed, Nonlinear Vibration Systems 853.4.1 Time-Delayed, Free Vibration Systems 853.4.2 Periodically Excited Vibration Systems with Time-Delay 1024 Analytical Periodic to Quasi-Periodic Flows 1094.1 Nonlinear Dynamical Systems 1094.2 Nonlinear Vibration Systems 1244.3 Time-Delayed Nonlinear Systems 1344.4 Time-Delayed, Nonlinear Vibration Systems 1475 Quadratic Nonlinear Oscillators 1615.1 Period-1 Motions 1615.1.1 Analytical Solutions 1615.1.2 Frequency-Amplitude Characteristics 1655.1.3 Numerical Illustrations 1735.2 Period-m Motions 1805.2.1 Analytical Solutions 1805.2.2 Analytical Bifurcation Trees 1845.2.3 Numerical Illustrations 2065.3 Arbitrary Periodical Forcing 2176 Time-Delayed Nonlinear Oscillators 2196.1 Analytical Solutions 2196.2 Analytical Bifurcation Trees 2386.3 Illustrations of Periodic Motions 242References 253Index 257

Albert C. Luo is currently a Distinguished Research Professor at Southern Illinois University Edwardsville. He is an international renowned figure in the area of nonlinear dynamics and mechanics. For about 30 years, Dr. Luo’s 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, (v) The full nonlinear theory for a deformable body. Such contributions have been scattered into 13 monographs and over 200 peer-reviewed journal and conference papers. His new research results are changing the traditional thinking in nonlinear physics and mathematics. Dr. Luo has served as an editor for the Journal “Communications in Nonlinear Science and Numerical simulation”, book series on Nonlinear Physical Science (HEP) and Nonlinear Systems and Complexity (Springer). Dr. Luo is the editorial member for two journals (i.e., IMeCh E Part K Journal of Multibody Dynamics and Journal of Vibration and Control). He also organized over 30 international symposiums and conferences on Dynamics and Control.

• Preface ix1 Introduction 11.1 Brief History 11.2 Book Layout 42 Nonlinear Dynamical Systems 72.1 Continuous Systems 72.2 Equilibriums and Stability 92.3 Bifurcation and Stability Switching 172.3.1 Stability and Switching 172.3.2 Bifurcations 263 An Analytical Method for Periodic Flows 333.1 Nonlinear Dynamical Systems 333.1.1 Autonomous Nonlinear Systems 333.1.2 Non-Autonomous Nonlinear Systems 443.2 Nonlinear Vibration Systems 483.2.1 Free Vibration Systems 483.2.2 Periodically Excited Vibration Systems 613.3 Time-Delayed Nonlinear Systems 663.3.1 Autonomous Time-Delayed Nonlinear Systems 663.3.2 Non-Autonomous Time-Delayed Nonlinear Systems 803.4 Time-Delayed, Nonlinear Vibration Systems 853.4.1 Time-Delayed, Free Vibration Systems 853.4.2 Periodically Excited Vibration Systems with Time-Delay 1024 Analytical Periodic to Quasi-Periodic Flows 1094.1 Nonlinear Dynamical Systems 1094.2 Nonlinear Vibration Systems 1244.3 Time-Delayed Nonlinear Systems 1344.4 Time-Delayed, Nonlinear Vibration Systems 1475 Quadratic Nonlinear Oscillators 1615.1 Period-1 Motions 1615.1.1 Analytical Solutions 1615.1.2 Frequency-Amplitude Characteristics 1655.1.3 Numerical Illustrations 1735.2 Period-m Motions 1805.2.1 Analytical Solutions 1805.2.2 Analytical Bifurcation Trees 1845.2.3 Numerical Illustrations 2065.3 Arbitrary Periodical Forcing 2176 Time-Delayed Nonlinear Oscillators 2196.1 Analytical Solutions 2196.2 Analytical Bifurcation Trees 2386.3 Illustrations of Periodic Motions 242References 253Index 257

Albert C. Luo is currently a Distinguished Research Professor at Southern Illinois University Edwardsville. He is an international renowned figure in the area of nonlinear dynamics and mechanics. For about 30 years, Dr. Luo’s 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, (v) The full nonlinear theory for a deformable body. Such contributions have been scattered into 13 monographs and over 200 peer-reviewed journal and conference papers. His new research results are changing the traditional thinking in nonlinear physics and mathematics. Dr. Luo has served as an editor for the Journal “Communications in Nonlinear Science and Numerical simulation”, book series on Nonlinear Physical Science (HEP) and Nonlinear Systems and Complexity (Springer). Dr. Luo is the editorial member for two journals (i.e., IMeCh E Part K Journal of Multibody Dynamics and Journal of Vibration and Control). He also organized over 30 international symposiums and conferences on Dynamics and Control.

• Preface ix1 Introduction 11.1 Brief History 11.2 Book Layout 42 Nonlinear Dynamical Systems 72.1 Continuous Systems 72.2 Equilibriums and Stability 92.3 Bifurcation and Stability Switching 172.3.1 Stability and Switching 172.3.2 Bifurcations 263 An Analytical Method for Periodic Flows 333.1 Nonlinear Dynamical Systems 333.1.1 Autonomous Nonlinear Systems 333.1.2 Non-Autonomous Nonlinear Systems 443.2 Nonlinear Vibration Systems 483.2.1 Free Vibration Systems 483.2.2 Periodically Excited Vibration Systems 613.3 Time-Delayed Nonlinear Systems 663.3.1 Autonomous Time-Delayed Nonlinear Systems 663.3.2 Non-Autonomous Time-Delayed Nonlinear Systems 803.4 Time-Delayed, Nonlinear Vibration Systems 853.4.1 Time-Delayed, Free Vibration Systems 853.4.2 Periodically Excited Vibration Systems with Time-Delay 1024 Analytical Periodic to Quasi-Periodic Flows 1094.1 Nonlinear Dynamical Systems 1094.2 Nonlinear Vibration Systems 1244.3 Time-Delayed Nonlinear Systems 1344.4 Time-Delayed, Nonlinear Vibration Systems 1475 Quadratic Nonlinear Oscillators 1615.1 Period-1 Motions 1615.1.1 Analytical Solutions 1615.1.2 Frequency-Amplitude Characteristics 1655.1.3 Numerical Illustrations 1735.2 Period-m Motions 1805.2.1 Analytical Solutions 1805.2.2 Analytical Bifurcation Trees 1845.2.3 Numerical Illustrations 2065.3 Arbitrary Periodical Forcing 2176 Time-Delayed Nonlinear Oscillators 2196.1 Analytical Solutions 2196.2 Analytical Bifurcation Trees 2386.3 Illustrations of Periodic Motions 242References 253Index 257