**报告题目****：****Controlling Complex Nonlinear Dynamical Networks**

**报告人****：**Ying-Cheng Lai(来颖诚教授)

**报告内容****：**Recent frameworks of controllability of complex networks were exclusively for linear dynamics. We begin by demonstrating that, even when a linear dynamical network is structurally controllable, it may not be physically controllable as the energy required for control can diverge. We introduce the notion of physical controllability to quantify this phenomenon and establish that the control energy exhibits an algebraic scaling behavior. These results point at the practical difficulty in controlling complex networks, even under the assumption of linear dynamics. We then turn to *complex, nonlinear dynamical networks* and articulate a general control framework whereby we nudge the system from attractor to attractor through small perturbations to a set of experimentally feasible parameters. This principle enables us to formulate a general controllability framework for nonlinear dynamical networks. In particular, given a set of system performance indicators, we classify all the accessible attractors into three categories: undesirable, desirable, and intermediate attractors. A nonlinear network is controllable if there is a control path from any undesirable attractor to the desirable attractor under finite parameter perturbations. Regarding each attractor as a node and the control paths as directed links or edges, we can construct an “attractor network” that determines the controllability of the original nonlinear network. A consequence is that, due to the interplay between nonlinearity and stochasticity, noise can facilitate control of nonlinear dynamical networks, leading to the phenomenon of noise-enhanced controllability. We illustrate these ideas using a class of synthetic biological networks. Finally, we discuss the more recent ideas of feedback-vertex set based control, closed-loop control of nonlinear dynamical networks, as well as controlling tipping point in complex mutualistic networks.

The main collaborator in this series of works is Prof. Wenxu Wang from Beijing Normal University. Former students Dr. Yuzhong Chen, Dr. Riqi Su, and Dr. Lezhi Wang at ASU contributed significantly to these works. Other collaborators include Prof. Zi-Gang Huang from Xi’an Jiao Tong University, Prof. Xiao Wang from ASU, Prof. Celso Grebogi from University of Aberdeen, and Prof. Wei Lin from Fudan University.

**报告人简介****：**Ying-Cheng Lai is a professor of Arizona State University.He received B.S. and M.S. degrees in Optical Engineering from Zhejiang University in 1982 and 1985, and M.S. and Ph.D. degrees in Physics from University of Maryland at College Park in 1989 and 1992, respectively. He joined the University of Kansas in 1994 as an Assistant Professor of Physics and Mathematics and became an Associate Professor in 1998. In 1999, he came to Arizona State University as an Associate Professor of Mathematics and an Associate Professor of Electrical Engineering. He was promoted to Professor of Mathematics and Professor of Electrical Engineering in 2001. In 2005, he switched full-time into Electrical Engineering. In 2009, Y.-C. Lai was named the Sixth Century Chair in Electrical Engineering by the University of Aberdeen, Scotland, UK. In January 2014, he was awarded an endowed Chair Professorship of Electrical Engineering at Arizona State University.

Y.-C. Lai has authored and co-authored approximately 460 papers, with about 430 in refereed journals. He has directed 20 Ph.D. and 20 Master theses and supported 14 post-doctoral fellows. He has given approximately 230 invited lectures and colloquia all over the world. His papers have been cited more than 18,000times. His current Google-Scholar based H-index is 66 and i10 index is 300.

Y.-C. Lai currently serves on the Editorial Boards of Physical Review E and Philosophical Transactions of Royal Society A, and is an Associated Editor of Scientific Reports and International Journal of Bifurcation and Chaos. From 2010-2014, he was a Co-Editor of Europhysics Letters.

**报告时间****：**2018年1月5日（周五）下午14:30-15:30

**报告地点：**6教南楼528