### Wednesday, May 21

*(This session will run until 1:00 PM)*

10:00 AM-12:00 PM

*Wasatch A & B - Level B*

## MS39

Spatially Discrete Dynamical Systems - Theory and Applications

Spatially discrete dynamical systems are either infinite-dimensional systems which possess a discrete spatial structure, generally modeled on a regular lattice, or finite dimensional systems which could be cellular neural networks (CNN) or cellular automata. The time variable can be either discrete or continuous. Such systems arise as models in a wide variety of applications, including image processing, material science, and biology. They moreover represent a new direction in mathematics, giving rise to challenging mathematical problems of pattern formation, spatial chaos, traveling waves, and synchronization. The talks in mathematical theory and applications on similar problems will clearly demonstrate the continuity between applications, scientific computing, and mathematics.

**Organizers: John Mallet-Paret, Brown University; and Shui-Nee Chow, Georgia Institute of Technology**

**10:00 Transition from Slow Motion to Pinning in Lattice Equations**
- Christopher P. Grant, Brigham Young University
**10:30 Modeling Biological Systems by Means of Nonlinear Electronic Circuits **
*Alberto P. Munuzuri* and L. O. Chua, University of California, Berkeley; and V. Perez-Munuzuri, University of Santiago de Compostela, Spain
**11:00 Traveling Waves in Lattice Dynamical Systems **
- Wenxian Shen, Auburn University
**11:30 Information Propagation, Pattern Formation and Reaction-Diffusion with Cellular Neural Networks**
*Patrick Thiran*, Swiss Federal Institute of Technology, Switzerland; and Gianluca Setti, University of Bologna, Italy
**12:00 Traveling Waves, Equilibria, and the Computation of Spatial Entropy for Spatially Discrete-Reaction Diffusion Equations**
- John W. Cahn, National Institute of Standards and Technology; Shui-Nee Chow, Georgia Institute of Technology; John Mallet-Paret, Organizer; and
*Erik S. Van Vleck*, Colorado School of Mines

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*MMD, 4/10/97*