14 July 2019
Bifurcation Theory and its Applications: From Biology to Greek Ornamental Design
Most complex physical, biological and other systems often depend on a limited number of parameters (i.e., growth, death, predation or competition rates in biological systems) that determine qualitative behavior of the system. The parameters may vary within specific ranges. Bifurcation theory provides methods to understand the qualitative behavior of a system and its variation as the parameters vary, especially when it comes to changes between equilibrium states of the system. It helps to formulate criteria in order to identify “critical boundaries” that one may wish to either approach, or stay away from.
In this seminar, the following topics (supplemented with numerous examples from biology) will be covered:
Introduction to non-linear dynamical systems
Introduction to bifurcation theory
Introduction to co-dimension of bifurcations and phase-parameter portraits of dynamical systems
Understanding the nature of equilibria, including bifurcations of equilibria in continuous and discrete time systems
Understanding the nature of oscillations, including bifurcations of equilibria and periodic orbits
Introduction to various types of bifurcations, such as homoclinic and heteroclinic bifurcations
Introduction to Hamiltonian systems
Application of Hamiltonian systems to understanding ancient Greek ornamental designs such as the one depicted in the photo above.
Faina Berezovskaya, Howard university
Students doing work in Math, Biology, Pre-Med.
USD 1500: Includes room and board as well as excursions
Extensive range of scholarships and discounts for registrations in more than one seminar (see our Tuition and Registration page)