The effect of oxygen on time-dependent bifurcations in the Belousov-Zhabotinsky oscillating chemical reaction in a batch.

We have studied the effect of oxygen on the time-dependent bifurcations of transient oscillations in the Belousov-Zhabotinsky oscillating chemical reaction in a closed system. Experiments show that oscillations disappear through different bifurcations depending on the oxygen concentration in gas phase above the reaction solution. Oscillations disappear through the time-delayed Hopf bifurcation at low oxygen concentrations, whereas at high oxygen concentrations they disappear through the time-dependent SNIPER (saddle-node infinite period) bifurcation.

Complex mixed-mode periodic and chaotic oscillations in a simple three-variable model of nonlinear system.

A detailed study of a generic model exhibiting new type of mixed-mode oscillations is presented. Period doubling and various period adding sequences of bifurcations are observed. New type of a family of 1D (one-dimensional) return maps is found.

Scalings of mixed-mode regimes in a simple polynomial three-variable model of nonlinear dynamical systems.

We describe scaling laws for a control parameter for various sequences of bifurcations of the LSn mixed-mode regimes consisting of single large amplitude maximum followed by n small amplitude peaks. These regimes are obtained in a normalized version of a simple three-variable polynomial model that contains only one nonlinear cubic term. The period adding bifurcations for LSn patterns scales as 1/n at low n and as 1/n2 at sufficiently large values of n.