ABSTRACT
Instability, oscillations, or chaos occur in a very small fraction of the chemical systems studied experimentally. Stability analysis shows that instability can usually be attributed to certain kinds of positive feedback cycles. A change in the concentration of one species causes a change in another concentration around the loop. If the species in a large negative feedback cycle are involved in smaller destabilizing positive feedback cycles, Hopf bifurcations usually occur. Without the large negative cycle, saddle node bifurcations usually occur. The flow in the reactions at steady state is the sum of fundamental network flows called extreme currents. Different extreme currents are important in different regions of parameter space. This chapter sketches out the main features of the bifurcation surfaces when the parameters range over many orders of magnitude and the equations have a number of different approximate limiting cases which are solvable.
