Marginal states in a cubic autocatalytic reaction

Marginal steady state belongs to a special class of states in nonlinear dynamics. To realize this state we consider a cubic autocatalytic reaction A + 2B -> 3B in a continuous-stirred-tank-reactor, where the flow rate of the reactant A can be controlled to manipulate the dynamical behavior of the open system. We demonstrate that when the flow rate is weakly noisy the autocatalytic reaction admits of a steady state which is marginal in nature and is surrounded by infinite number of periodic trajectories. When the uncatalyzed reaction A -> B is included in the reaction scheme, there exists a marginal steady state which is a critical state corresponding to the point of transition between the flow branch and the equilibrium branch, similar to gas-liquid critical point of transition. This state loses its stability in the weak noise limit. (C) 2011 American Institute of Physics. [doi:10.1063/1.3640012]