This book addresses a special topic in the field of nonlinear dynamical systems, develops a new research direction of surface chaos and surface bifurcation. It provides a clear watershed for original nonlinear chaos and bifurcation research. The novel content of this book makes nonlinear system research more systematical and personalized. This book introduces the chaos and bifurcation behavior of surface dynamics in the sense of Li Yorke, the basic properties, Lyapunov exponent and Feigenbaum constant of nonlinear behavior of surface, and obtained the wave behavior of chaotic process in surface motion, the control of surface chaos and bifurcation, and the wide application of surface chaos in engineering technology. Through this book, readers can obtain more abundant and novel contents about surface chaos and surface bifurcation than the existing mixed fitting bifurcation of plane curve and space curve, which can also expand the realm and vision of research.

Auteur

Shu Tang Liu, Ph.D., second grade professor of Shandong University, doctoral supervisor.

He received the Ph. D. degree from South China University of Technology in 2002(jointing training by City University of Hong Kong and South China University of Technology). He is the winner of one hundred Excellent Doctoral Dissertations in 2004 in China (jointly organized and implemented by the academic degree office of the State Council and the Ministry of education, discipline of control theory and control engineering). He won the first prize of excellent scientific research achievements of Shandong colleges and universities.

He is also a member of the center for chaos and complex networks, a commentator of American Mathematical Reviews, a member of the American Mathematical Society, and a member of the international WSEAS automatic control academic committee. He is the reviewer of international magazines such as Complex Systems, Transactions of the American Mathematical Society, IEEE Transactions on Circuits and Systems I-Regular Paper, Automatica, Fractals, Chaos, Solitons & Fractals, Nonlinear Analysis: Real World Applications, International Journal of Bifurcation and Chaos, Science China, Chinese Science Bulletin, and Acta Automatica Sinica.

He has been engaged in scientific research in the fields of nonlinear system theory, fractal and chaos theory, nonlinear control and application, physical oceanography, marine environment and marine ecology. He published three monographs in Springer as the first author: Fractal Control Theory,Fractal Control and Its Appllicationsand Mathematical Principle and Fractal Analysis of Mesoscale Eddy, and published more than 200 papers in top journals and other journals at home and abroad.

Li Zhang, Ph.D., Associate Professor of Business School, Shandong University of Political Science and Law.

She received the B.S. degree in mathematics and applied mathematics from Jinan University in 2003, an M.S. degree from Shandong University in 2006 and the Ph.D. degree from Shandong University in 2011, China. Her current research interests are control theory of chaos, fractal in social, financial and economic systems and its applications. She, with co-authors, has published 9 journal papers like SIAM Journal on Applied Dynamical Systems, Nonlinear Dynamics, Communications in Nonlinear Science and Numerical Simulation, Fractals, International Journal of Bifurcation and Chaos and 7 conference papers.

Contenu
Introduction.- Basic Knowledge.- Spatial Periodic Orbits and Surface Chaos.- Surface Chaos and Its Spatial Lyapunov Exponent.- Surface Chaos and Its Associated Bifurcation and Feigenbaum Problem.- Prediction-Based Feedback Control of Surface Chaos for Convection System with A Forced Term.- Spatial Static Bifurcation and Control of 2-D Discrete Dynamical System.- Holistic Compression Control and Surface Chaos.- Linear Generalized Synchronization of Surface Chaos.- Generalized Feedback Synchronization of Surface Chaos.- Surface Determining Wave Behavior of A Delay 2-D Discrete System.- Nonlinear Analysis of The Process From The Wave To Surface Chaos.- Nuclear Fission and Surface Chaos.- Uniformity and Surface Chaos of Spatial Physics Kinematic System.- Uniformity of Physical Motion Systems and Surface Chaos.- Surface Chaos Behavior of Molecular Orbit.- Surface Chaotic Theory and the Growth of Harmful Algal Bloom.- Surface Chaos-Based Image Encryption Design.- The Relationships Among Spatial Body Chaos, Cosmic Black Hole and Galaxy