Limit cycles and discontinuous entropy production changes in the reversible Oregonator

Abstract

We show that the chemical entropy production in the reversible Oregonator changes discontinuously at critical values of the concentration parameter at which points a limit cycle bifurcates out of an unstable steady state. The discontinuities in the entropy production are reminiscent of the behavior of the entropy change accompanying a first order phase transition in thermodynamics. They appear to be an example of dynamic phase transitions. For this model, by using Poore’s algorithm, we show that in the case of f=1 the limit cycle is orbitally asymptotically unstable and the bifurcation is subcritical, but in the case of f=0.5 the limit cycle bifurcation at the higher critical concentration of P is subcritical whereas the one at the lower critical concentration of P is supercritical. Therefore, a discontinuous change in chemical entropy production accompanies subcritical Hopf bifurcations and possibly a supercritical Hopf bifurcation. It is conjectured that if a bifurcation is subcritical, attractors of different topological dimensions have different characteristic entropy productions in the same manner as two different states of aggregation of matter have different entropies associated with them.