Online Course Catalog

The use of computational tools for continuation and bifurcation analysis of characteristic classes of dynamical systems trajectories has revolutionized the field of nonlinear dynamics and offers distinct advantages to bruteforce simulation. This methodology has extended the reach of methods of complex systems analysis to a wide range of applications in engineering, physics, chemistry, and biology.

This course demonstrates the construction of efficient numerical algorithms for continuation and bifurcation analysis of equilibria and (multi-segment) periodic trajectories in continuous-in-time (hybrid) dynamical systems. It further provides a detailed introduction to the problem of manifold covering, i.e., the development of a numerical atlas of an implicitly defined embedded hypersurface in a high-dimensional space. The course includes extensive introduction to high-level MATLAB programming concepts and demonstrates the implementation and use of the MATLAB-based continuation package COCO.

4 hours

Undergraduate Degree and a course in Analysis of Nonlinear Systems (ME 546) or equivalent.

• Mechanical Science and Engineering