MS44 ~ Wednesday, May 24, 1995 ~ 10:00 AM

Theory and Applications of Non-Lipschitz Dynamics

Although dynamical systems have been used to model energy transformations, increasingly, they have also been recognized for their ability to model information processing, and biological systems. A significant limitation is their rigid, "deterministic" behavior in contradistinction to the plasticity of the real world. Dependence upon initial conditions forces the dynamics to "remember" them to infinity, thus precluding them from adapting to new "environmental" challenges. The reason for this is the requirement of Lipschitz conditions for differential equations: that all derivatives exist, are bounded, and have unique solutions. If Lipschitz conditions are removed, the system becomes free of deterministic dependence on initial conditions, and is allowed to have multiple solutions. With non-Lipschitzian dynamics, more complex, spatio-temporal, phenomenological models can be obtained.

Organizer: Joseph P. Zbilut, Rush Medical College

Non-Lipschitzian Approach to Discrete Event Dynamics
Michail Zak, Jet Propulsion Laboratory
Physiological Non-Lipschitz Systems
Joseph P. Zbilut, Organizer and Charles L. Webber, Jr., Loyola Stritch School of Medicine
Non-determinism and Neutron Stars
David D. Dixon, University of California, Riverside
An Algorithm for Fast Global Optimization using Non-Lipschitzian Dynamics
Jacob Barhen, Jet Propulsion Laboratory