Plenary Lecture

Nonlinear Control and Synchronization of Multistable Dynamical Systems

Professor Alexander Pisarchik
Centro de Investigaciones en Optica, A.C.
Mexico.

Abstract: Nonlinear dynamical systems are known to exhibit a rich variety of different long-term behaviors such as stationary points, limit cycles, quasiperiodic, and chaotic motion. In a complex system several equilibrium states (attractors) may coexist for a given set of system parameters. Chaos and multistability are the most excited phenomena in nonlinear dynamics. Multistability has been found in almost all research areas in natural science, such as mechanics, optics, electronics, environmental science and neuroscience. Multistability also appears in systems subject to time-delayed feedback and in coupled systems. Due to complexly interwoven basins of attraction, multistable systems are extremely sensitive to noise, parameter perturbations or small changes in initial conditions. This can create inconvenience in many practical situations; for instance, when one desires to design a commercial device with predetermined characteristics. Therefore, control of multistability is an important problem in applied nonlinear science and engineering. The significant progress in controlling nonlinear dynamics and chaos encourages the creation of methods for controlling multistability. Synchronization of multistable systems is another long-standing and challenging problem of a broad interdisciplinary interest, both from the point of view of fundamental research and for practical applications including secure communication. This talk is devoted to new achievements in resolving these two important problems on examples of different dynamical systems, from iterative maps to differential equations and experiments with electronic circuits and lasers.

Brief Biography of the Speaker:
Alexander N. Pisarchik graduated from Physics Department of the Belarus State University in Minsk in 1976 and carried out doctoral research in Optics and Quantum Electronics at the Institute of Physics of the Belarus Academy of Sciences where in 1990 he obtained the Ph.D. in Physics and Mathematics. In 1997 he completed the special courses on Nonlinear Dynamics in Physiology and Medicine at the McGill University, Montreal, Canada and Time Evolution of Complex Systems in Lisbon, Portugal. In 1983-88 he was the Assistant Director of the Molecular Kinetics Laboratory in the Institute of Physics, and in 1989-92 he was the Vice-Director of the same laboratory. He was awarded by several research grants from governments and universities of different countries and worked as a Researcher at Universite Libre de Brusseles in 1992, Universitat Autonoma de Barcelona in 1993-99 and 2006-7 and University of Iceland in 1995. Since 1999 he works as a Research Professor at the Center of Optical Research in Leon, Guanajuato, Mexico.
Prof. Pisarchik is the member of the National System of Researchers (SNI, level III), Society for Industrial and Applied Mathematics, American Association for the Advancement of Science, National System of Evaluators in Science and Technology, Mexican Physical Society and Academy of Optics. He has received various recognitions, including the First Prize of the National Academy of Sciences of Belarus for his studies of Nonlinear Dynamics in Complex Systems (1999). He was the organizer and Chair of the International Conference on Control and Synchronization of Dynamical Systems which was held in Leon, Mexico in 2005. His main research interests include the chaos theory and applications to lasers and other dynamical systems, control and synchronization, multistability, chaotic cryptography for secure communication. He is the author of more than 200 scientific publications and 4 patents and presented 36 invited lectures, the Guest Editor of the Proceedings of the 6th WSEAS Conference (2002), the International Conference on Control and Synchronization of Dynamical Systems published in Journal of Physics: Conference Series (2005), and the theme issue on Multistability in Dynamical Systems assigned for publication in International Journal of Bifurcation and Chaos in 2008. He is the Editorial Board Member of The Open Electrical and Electronic Engineering Journal and the Editor of the book Recent Advances in Laser Dynamics: Control and Synchronization which will be published by Research Singpost in 2008.