Rate-Dependent Bifurcations and Isolating Blocks in Nonautonomous Systems

Thumbnail Image

Persistent link to this item

View Statistics

Journal Title

Journal ISSN

Volume Title


Rate-Dependent Bifurcations and Isolating Blocks in Nonautonomous Systems

Published Date




Thesis or Dissertation


We examine rate-dependent tipping and the behavior of solutions to nonautonomous systems from a topological perspective. We analyze an example of a rate-dependent bifurcation in which steady solutions begin to spiral, yet remain in a bounded region around a moving equilibrium. This example motivates us to develop a theory of isolating blocks for invariant sets in nonautonomous systems. Our examination of these isolating blocks reveals that solutions in rate-dependent systems are structurally stable; the rate-dependent forcing may have some amount of noise while the underlying behavior of solutions to the system remains the same. We also find isolating blocks useful for placing bounds on critical values for rate-dependent tipping in nonautonomous systems. Finally, we introduce rate-dependent tipping for discrete maps.


University of Minnesota Ph.D. dissertation. 2017. Major: Mathematics. Advisor: Richard McGehee. 1 computer file (PDF); 83 pages.

Related to




Series/Report Number

Funding information

Isbn identifier

Doi identifier

Previously Published Citation

Suggested citation

Hahn, Jonathan. (2017). Rate-Dependent Bifurcations and Isolating Blocks in Nonautonomous Systems. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/192674.

Content distributed via the University Digital Conservancy may be subject to additional license and use restrictions applied by the depositor. By using these files, users agree to the Terms of Use. Materials in the UDC may contain content that is disturbing and/or harmful. For more information, please see our statement on harmful content in digital repositories.