Introduction

Our summer school is intended to provide graduate students and researchers in the fields of behavioral neuroscience and life sciences an exposure to the theory and applications of nonlinear dynamics.  In contrast to traditional summer schools in nonlinear dynamics, our school merges theory and experiment in a hands-on manner. More explicitly, our school does not require broad knowledge of mathematics as a prerequisite, but will emphasize a geometric understanding of how nonlinear dynamic systems work. During the first three days the participants will be instructed in the theory of low-dimensional dynamical systems with a focus on modeling. In parallel, they will apply their new-found skills in the computational laboratories to develop an intuition for nonlinear concepts. The participants will get acquainted with software tools for modeling and analysis of dynamic systems and will bring both - skills and software - back to their home institutions. In the second half of the school, various lecturers will provide introductions to the modeling of nonlinear phenomena in movement sciences, cognitive neurosciences and music perception. In parallel, these phenomena will be experimentally explored in the Movement & Perception laboratories through data collection and analysis. The primary learning objective of our summer school is to gain hands-on insight into the principles of nonlinear dynamics and their transfer to the life sciences.

Dates:                      July 16 - 21, 2007
Location:                 Luminy, Marseille

Plenary Lecture:    Hermann Haken      (July 18, 2007.  See below for details)

Target audience

Graduate students and researchers in the life, movement and neural sciences. Mathematical prerequisite: High school knowledge. The student with a familiarity of basic functions (polynomials, sine and cosine, exponentials) and their derivatives will benefit the most from the summer school.

Objectives

To provide a course in nonlinear dynamics which is accessible to scientists with only basic mathematical training. An emphasis will be placed onto, first, the geometric understanding and visualization of low-dimensional systems, and second, the application of the corresponding concepts to real-world phenomena in movement and cognition.

Our specific aims are
 

• Identify key concepts in nonlinear dynamics (fixed points, limit cycle, stability, phase space geometry, bifurcations) 
• Provide basic mathematical tools in modeling and analysis of dynamic systems 
• Provide basic computational tools for modeling and analysis 
• Identify how concepts in nonlinear dynamics are used in applied research of the movement and cognitive sciences 
• Provide hands-on expertise in the computational laboratory and experiment
• Provide software package with computational tools for nonlinear modeling and analysis for use in the participants' home laboratory 

Plenary lecture

Prof. emer. Dr. rer. nat. Dr. h.c. mult. Hermann Haken will deliver a Plenary Lecture within the framework of our Summer School. Hermann Haken is the founder of the interdisciplinary field of research Synergetics, which provides an understanding of emergent phenomena in selforganizing complex systems. In particular, synergetics searches for general principles governing selforganization irrespective of the nature of the individual parts of the systems that may belong to a variety of disciplines such as physics (lasers, luids, plasmas), metereology, chemistry (pattern formation by chemical reactions, including flames), biology (morphogenesis, evolution theory) movement science, brain activities, computer sciences (synergetic computer), sociology (e.g. city growth) psychology and psychiatry (including Gestalt psychology).