Characterization of the Kuramoto Model and Coupled Lorenz Systems Using Information Theoretic Techniques
Gabriel Dominik E. Sison1*, Giovanni A. Tapang1
1National Insitute of Physics, University of the Philippines, Diliman, Quezon City, Philippines
* presenting author:Gabriel Dominik Sison,
Many systems in nature are driven by mechanisms with non-obvious patterns. From the neurons in the brain, to patterns of disease incidence, it is often difficult to see how one part influences the others. One way to represent a complex system is to represent each object as a oscillator. The relationship between each object can then be represented as a coupling between two oscillators. By then characterizing the behavior of these oscillators we can then model the physical system represented by these oscillators. We can then model the couplings between these oscillators as connections in a complex network. If the couplings between the oscillators are unknown, one must turn to statistical techniques to determine the coupling based from observed data. What we now seek is to determine how well this modelling actually represents the structure of the underlying oscillator network.

In order to do we this, we constructed and simulated two different coupled dynamical systems, the Kuramoto Model and coupled Lorenz systems. We then applied correlation and mutual information on the observed amplitudes of each oscillator, and used them to characterize the behavior of the system. We then compared this behavior to the structure of the original constructed systems. We compare the results of correlation and mutual information to results of traditional methods of analyzing these systems, that of the average phase. We see that the correlation and mutual information give comparable results to the original methods

Keywords: Synchronization, coupled oscillators, Structures and organization in complex systems, Networks and genealogical trees