Richard Eykholt

Richard Eykholt

Associate Professor

B.A., M.S., Ph.D., University of California – Irvine (1978,1980,1984)

Chaos and Nonlinear Dynamical Systems

My basic area of research is the theory of chaos and nonlinear dynamics. I do applied work analyzing real-world systems, such as weather systems and streamflows, and basic theoretical work developing new techniques for analyzing chaotic systems.

Currently, the main focus of my research is a collaboration with a faculty member in the Department of Civil Engineering. This research began as an examination of the extent to which streamflows are predictable, rather than stochastic. We began by developing new techniques for analyzing small noisy data sets and then applied these techniques to the study of predictability in ordinary streamflows. In particular, we have been able to answer the question of why rainfall is chaotic, and, thus, partially predictable, but most streamflows appear to be stochastic. Now that we understand why the predictability is hidden for streamflows, we want to see if it is possible to extract this hidden predictability. In addition, we wish to study intermittent streamflows, such as occur in desert areas such as Arizona. This latter project will require the development of new techniques for analyzing data sets consisting of small series of data separated by long strings of zeros.

The other focus of my current research is improving techniques for distinguishing chaos from stochasticity in general. In the recent past, I have improved the ability of existing techniques for making this distinction, and I have several ideas for improving the new technique even further. I believe that this improved technique also has the potential to be used for analyzing certain properties of chaotic systems, and I wish to explore this potential as well.

In the past, I have collaborated with researchers in the Department of Atmospheric Science on analyzing chaos and predictability in the weather and climate. Although I am not pursuing this research area at the moment, it might be possible to pursue such projects if a student has the appropriate background.

 

Selected Publications

  • J. D. Salas, H. S. Kim, R. Eykholt, Paolo Burlando, and Tim Green, “Aggregation and Sampling in Deterministic Chaos: Implications on the Dynamics of Hydrological Processes,” Nonlinear Processes in Geophysics 12, 557 (2005).
  • H. S. Kim, R. Eykholt, and J. D. Salas, “Nonlinear Dynamics, Delay Times, and Embedding Windows,” Physica D 127, 48 (1999).
  • H. S. Kim, R. Eykholt, and J. D. Salas, “Delay Time Window and Plateau Onset of the Correlation Dimension for Small Data Sets,” Phys. Rev. E 58, 5676 (1998).