Synched is free software designed to visualize synchronizing phenomena in complex networks. It includes the capability of showing in real-time the dynamics of several models, including the Kuramoto model and other more complicated generalizations. If you have suggestions of other models to be added, contact me and I will be happy to re-release Synched. I would like to particularly thank my group member and colleague Dan Larremore for his help and guidance. Synched is free to use and distribute non-commercially under a Creative Commons license.
Looking for other cool software? Check out these:
- PercoVIS, a free software tool created by Dan Larremore to visualize percolation processes in networks.
- 3DAttractors, a free software tool created by Juan G. Restrepo to visualize 3D Chaotic Dynamics.
My main resarch interests are in nonlinear dynamics and complex systems. Most of my work is in either synchronization on networks or cardiac dynamics, but I am also interested in more general bifurcation, chaos, and complexity theory. My collaborators include Juan G. Restrepo, Alain Karma, and Ed Ott, as well as my group members Dan Larremore and Dane Taylor.
Networks of coupled oscillators occur in many examples throughout science and nature and serve as a great model for emergence of collective behavior (i.e. synchronization). Im interested in phenomena that occurrs in systems with time delay, heterogeneous and non-local coupling, community structure, and higher-order (i.e. non-sinusoidal) coupling functions. Depending on the system, many interesting phenomena can occurr, including bistability, intermittent synchrony, coexistence of synchronized and unsychronized states (a.k.a. "chimera" states), hierarchical synchrony, and cluster synchrony. I am also interested in reducing the complexity of the study of such systems by finding reduced low-dimensional manifold beahviors, making analytical treatment tractable.
The heart is a complex dynamical system that exhibits nonlinear phenomena in many different ways. My interest in cardiac dynamics spans several different levels, from the spatiotemporal dynamics of both calcium- and voltage-driven alternans in patches of tissue to cellular regulation of ion channels yielding healthy cardiac behavior. Mathematical tools can provide insight into how the heart works and how to prevent certain kinds of cardiac arrhythmia.
1. Per Sebastian Skardal, Alain Karma, and Juan G. Restrepo. Unidirectional Pinning and Hysteresis of Spatially Discordant Alternans in Cardiac Tissue. Accepted: to appear in Phys. Rev. Lett. Preprint.
2. Per Sebastian Skardal and Juan G. Restrepo. Hierarchical Synchrony of Phase Oscillators in Modular Networks. Phys. Rev. E 85, 016208 (2012). PDF.
3. Per Sebastian Skardal, Edward Ott, and Juan G. Restrepo. Cluster Synchrony in Systems of Coupled Phase Oscillators with Higher-Order Coupling. Phys. Rev. E 84, 036208 (2011). PDF.
4. Per Sebastian Skardal. Spatiotemporal Chaos: Effect of Spatial Smoothing on Bifurcations in a Discrete-Time Chaotic Map. University of Colorado, Department of Computer Science, Boulder, CO 80309-0430: Elizabeth Bradley; July 2010. Technical Report CU-CS 1066-10. 123 p. PDF.
Working on several others...
Check out my CV here.
Right now (spring 2012) I'm not teaching any courses. In the past I've been an instructor for APPM 2360: Differential Equations and Linear Algebra twice and TA-ed several other courses.
Check out my FCQ ratings evaluations here.
Living in Boulder is fantastic for skiing, hiking, climbing, playing soccer, and all sorts of outdoor activities. I also like reading and travelling. If you'd like, you can check out some of my pictures here.