Five simultaneous steady states in a flipping two-compartment-system with optical antipodes

The previously given systems-theoretic model for the synthesis of optical antipodes (AD and AL) in strongly asymmetric yield, which shows mono-bistable behaviour depending on the degree of "openess" of the chemical reaction system is reconsidered for two equal compartments (subscripts 1 and 2 on A) with coupling by diffusion. In this configuration three threshold values, j1, is less than j2 is less than j3, for the influx j of the common precursor substance appear. For j is less than j1 only one steady state (s.s.) with no optical activity (ADi = ALi, i-1;2) and equal distribution of the antipodes in both compartments (AD1 = AD2, AL1 = AL2) exists. For j is greater than j 1, this totally symmetric s.s. becomes unstable and a pair of s.s. with optical activity (AD1 is less than AL1, AD2 is less than AL2 or AD1 is greater than AL1, AD2 is greater than AL2) but no spatial asymmetry emerges (parallel flipping), i.e. both compartments be8have as a whole, showing a preponderance of either the D- or the L-form. For j is greater than j2 in addition two new s.s. are possible with antiparallel flipping (AD1 is less than AL1, AD2 is greater than AL2 or AD1 is greater than AL1, AD2 is less than AL2), i.e. in one compartment the D-form has the majority and in the other one the L-form, but these are stable only beyond a third threshold value j3. A third thinkable pair with no optical activity, but different sum concentrations in both cells, does not exist in this special circuitry, but can be obtained in a slightly changed arrangement. So for j is greater than j2, 5 different (4 stable, 1 unstable) s.s., exist for the same set of parameters, one of which is chosen by the system.