We consider diierential equations _ x = f (x;) where the parameter = "t moves slowly through a bifurcation point of f. Such a dynamic bifurcation is often accompanied by a possibly dangerous jump transition. We construct smooth scalar feedback controls which avoid these jumps. For transcritical and pitchfork bifurcations, a small constant additive control is usually suucient. For Hopf bifurcati...

We study noise-induced switching of a system close to bifurcation parameter values where the number of stable states changes. For non-Gaussian noise, the switching exponent, which gives the logarithm of the switching rate, displays a non-power-law dependence on the distance to the bifurcation point. This dependence is found for Poisson noise. Even weak additional Gaussian noise dominates switch...

Oneand two-parameter Hopf bifurcation behavior is analyzed for several variants of the Citri-Epstein mechanism of the chlorite-iodide reaction. The coefficients of an equation for the amplitude of oscillations (the universal unfolding of the Hopf bifurcation) are evaluated numerically. Local bifurcation diagrams and bifurcation sets are derived from the amplitude equation. Suband supercritical ...

The saddle-node Hopf bifurcation (SNH) is a generic codimensiontwo bifurcation of equilibria of vector fields in dimension at least three. It has been identified as an organizing centre in numerous vector field models arising in applications. We consider here the case that there is a global reinjection mechanism, because the centre manifold of the zero eigenvalue returns to a neighbourhood of t...

In two-parameter systems with symmetry two steady state bifurcation points of diierent symmetry types coalesce generically within one point. Under certain group theoretic conditions involving the action of the symmetry group on the kernels, we show that secondary Hopf bifurcation is borne by the mode interaction. We explain this phenomenon by using linear representation theory. For motivation a...

Numerical simulation of the bifurcation of Bingham fluid streamline topologies in rectangular double-lid-driven cavity, with varying aspect (height to width) ratio A, is presented. The lids on the top and bottom move at the same speed but in opposite directions so that symmetric flow patterns are generated. Similar to the Newtonian case, bifurcations occur as the aspect ratio decreases. Special...

The study of premixed laminar flames is a central question in combustion theory. Here the differential equations describing steady flame propagation are investigated mathematically. The emphasis is on analytic results, hence a simple model, a onestep exothermic reaction with linear or radiative heat loss is studied. The equations governing our model can be considered as travelling wave equation...

Stability analysis of a baseline power system architecture for modern aircraft is addressed. Power electronic converters are widely used in modern aircraft power distribution systems. Due to their inherent nonlinear characteristics, instabilities may arise while integrating individual subsystems together. Bifurcation analysis is used to identify the type, multiplicity and stability of system tr...

Complex dynamics in the reduced swing equations of a power system are investigated. As the change of bifurcation parameter μ, the system exhibits complex bifurcations, such as saddle-node bifurcation, Hopf bifurcation, cyclic fold bifurcation and torus bifurcations and complex dynamics, such as periodic orbits, quasiperiodic orbits, period-doubling orbits and chaotic attractors which link with ...

We study the slow–fast dynamics of a system with double-Hopf bifurcation and slowly varying parameter. The model consists coupled Bonhöffer–van der Pol oscillators excited by periodic slow-varying AC source. consider two cases where parameter passes or crosses bifurcation, respectively. Due to system’s multistability, bursting solutions are observed in each case: single-mode two-mode bursting. ...