Bifurcations and Chaos in piecewise Smooth Dynamical Systems

  • Mosekilde, Erik (Project Manager)
  • Zhusubaliyev, Z. (Project Participant)
  • Soukhoterin, E. (Project Manager)

Project Details

Description

Technical problems often lead to differential equations with piecewise
smooth right-hand sides. Problems in mechanical engineering, for instance,
violate the conditions of smoothness if they involve collisions, finite
clearances, or stick-slip phenomena. Systems of this type can display a
large variety of complicated bifurcation scenarios that still lack a
detailed description.
The purpose of this project is to study a range of new phenomena that can
arise in piecewise-smooth dynamical systems, including new types of direct
transitions to chaos, modified period-doubling, saddle-node and Hopf
bifurcations, truncated bifurcation series, period-tripling and-quadrupling
bifurcations, and multiple-choice bifurcations. Particular emphasis is given to the study of torus destruction in non-smooth systems.
The practical significance of these phenomena will be demonstrated
through a series of well-documented applications to switching power converters, to relay systems with and without hysteriesis and time deadzones, and to different forms of pulse-width modulated control systems.
StatusActive
Effective start/end date01/01/2000 → …