Lattice Dynamical Systems

*Sponsored by SIAM Activity Group on Dynamical Systems (Invited Minisymposium)*

10:30 AM-12:30 PM

*Room: Capitol Center*

Lattice differential equations are infinite systems of ODE's, modeled on an underlying spatial lattice with some regular structure, for example, the integer lattice in the plane. Such systems arise as models in many applications, including material science, image processing, and biology. As mathematical problems they in one sense lie between ODE's and PDE's, but very often they exhibit new phenomena not found in either of these fields. They raise a host of challengs to the researcher, and are of broad interest to scientists and mathematicians.

**Organizer: John Mallet-Paret**

*Brown University*

**10:30-10:55 Traveling Wave Solutions to Lattice Differential Equations**

*Christopher E. Elmer*, National Institute of Standards and Technology; and Erik S. Van Vleck, Colorado School of Mines

**11:00-11:25 On a Discrete Convolution Model for Phase Transitions**

*Adam Chmaj*, Utah State University; and Peter W. Bates, Brigham Young University

**1130-11:55 Traveling Waves in Cellular Neural Networks and Periodic Bistable Structures**

- Wenxian Shen, Auburn University

**12:00-12:25 Traveling Fronts in Discrete Space and Continuous Time**

- K. P. Hadeler, Universität Tübingen, Germany; and
*Bertram Zinner*, Auburn University

*tjf, 1/20/99, MMD, 1/27/99*