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, Ed Ott, Jie (Rio) Sun, Dan Larremore, and Dane Taylor.
Networks of coupled oscillators occur in many examples throughout science and nature, e.g. cardiac pacemaker cells and circadian rhythms, and serve as a great model for emergence of collective behavior (i.e. synchronization). Im interested in studying problems where the network properties influence the oscillator dynamics and yield novel phenomena. Some examples of these problems include when network topology is modular (i.e. has many "communities") and when network properties are correlated with individual oscillator dynamics. Oscillator systems are also a good tool for studying general topics in math, physics, and networks science like dynamic bifurcation theory and the connection between adaptive systems and large-scale phenomena.
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. Periodic Behavior in Cardiac Tissue: Dynamics of Spatially Discordant Calcium Alternans. PhD Dissertation, University of Colorado Boulder (2013). PDF.
2. Per Sebastian Skardal, Dane Taylor, and Juan G. Restrepo. Complex Macroscopic Behavior in Systems of Phase Oscillators with Adaptive Coupling. Physica D (2013), 10.1016/j.physd.2013.01.012. PDF.
3. Per Sebastian Skardal, Jie Sun, Dane Taylor, and Juan G. Restrepo. Effects of Degree-Frequency Correlations on Network Synchronization: Universality and Full Phase-Locking. Europhysics Letters 101, 20001 (2013). PDF.
4. Per Sebastian Skardal and Juan G. Restrepo. Synchronization of Kuramoto Oscillators in Networks of Networks. Proceedings of the 2012 International Symposium on Nonlinear Theory and its Applications. October 22 - 26, 2012, Palma, Mallorca, Spain. PDF.
5. Per Sebastian Skardal, Alain Karma, and Juan G. Restrepo. Unidirectional Pinning and Hysteresis of Spatially Discordant Alternans in Cardiac Tissue. Physical Review Letters 108, 108103 (2012). PDF.
6. Per Sebastian Skardal and Juan G. Restrepo. Hierarchical Synchrony of Phase Oscillators in Modular Networks. Physical Review E 85, 016208 (2012). PDF.
7. Per Sebastian Skardal, Edward Ott, and Juan G. Restrepo. Cluster Synchrony in Systems of Coupled Phase Oscillators with Higher-Order Coupling. Physical Review E 84, 036208 (2011). PDF.
8. 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.
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 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.
Right now (spring 2013) I'm teaching APPM 2350: Calculus III. In the past I've been an instructor for APPM 2350: Calculus III twice and APPM 2360: Differential Equations and Linear Algebra twice, as well as a TA for 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 (outdated) pictures here.