Abstract—We study a class of switching systems whose dynamics are characterized by an inner switching feedback loop and an outer continuous control loop. The loops have two widely separated time scales, performing fast-scale and slow-scale dynamics accordingly. Treating the two time scales separately, the stability of the systems can be studied, with results focusing on fast-scale bifurcation a...

Bifurcation problems in which periodic boundary conditions (PBC) or Neumann boundary conditions (NBC) are imposed often involve partial differential equations that have Eu-clidean symmetry. In this case posing the bifurcation problem with either PBC or NBC on a finite domain can lead to a symmetric bifurcation problem for which the manifest symmetries of the domain do not completely characteriz...

In this paper, a stage-structured epidemic model with a nonlinear incidence is investigated. By carrying out global qualitative and bifurcation analysis, it is shown that the model exhibits the bistability and undergoes the Hopf bifurcation and the Bogdanov-Takens bifurcation. Moreover, several numerical simulations are given to support the theoretical analysis.

Bifurcations observed in a phase converter circuit are investigated. We obtain a codimension two bifurcation which is intersection of period-doubling bifurcations. Periodic solutions generated by these bifurcations become chaotic states through a cascade of a codimension three bifurcation which is intersection of D-type of branching and period-doubling bifurcation.

Global and local bifurcations are extremely important since they govern the transitions between different qualitative regimes in dynamical systems. These transitions or tipping points, which are ubiquitous in nature, can be smooth or catastrophic. Smooth transitions involve a continuous change in the steady state of the system until the bifurcation value is crossed, giving place to a second-ord...

BACKGROUND Bifurcation lesions are frequent among patients with symptomatic coronary disease treated by percutaneous coronary intervention. Current evidence recommends a conservative (provisional) approach when treating the side branch (SB). OBJECTIVES The TRYTON (Prospective, Single Blind, Randomized Controlled Study to Evaluate the Safety & Effectiveness of the Tryton Side Branch Stent Used...

A bifurcation occurs when an elastic filament rotates in a viscous fluid at frequency ω (bifurcation parameter). We use the immersed boundary (IB) method to study the interaction between the elastic filament and the surrounding viscous fluid as governed by the incompressible Navier–Stokes equations, and to determine the nature of the bifurcation, which turns out to be subcritical.

In this paper, we discuss some recent developments in the understanding of generic bifurcation from periodic solutions with spatiotemporal symmetries. We focus mainly on the theory for bifurcation from isolated periodic solutions in dynamical systems with a compact symmetry group. Moreover, we discuss how our theory justiies certain heuristic assumptions underlying previous approaches towards p...