[Introduction|Background|Analysis]

Conclusions

This model is of the autocatalytic behavior in chemical systems. In our analysis, we only allowed one parameter to be varied, gamma2. However, simply by varying this one feed concentration, we discovered many interesting solutions to the model.

At large values of gamma2 (~.2), there is a single steady state in the reaction for all values of lambda. This represents the point in which the reaction stops, probably because of a limiting reagent.

For middle range values (~.15), we can see the appearance of periodic solutions for low residence time (lambda). These solutions represent a constantly reacting mixture, as the autocatalytic system continuously catalyses itself ad infinitum.

For low values of gamma2, (~.12), the model's behavior becomes erratic, as periodic solutions appear for low lambda, and dual stable steady states appear for large lambda. The dual steady states are probably points in which the reaction stops because of lack of both reactants in sufficient quantity.

It is interesting to note what happens when gamma2 drops below .1. The graph of v versus lambda becomes very erratic:


gamma2 = .06

This particular solution shows relatively erratic behavior, most values of lambda have 2 solutions, at low values of lambda (<.04) some values have what looks like 4 solutions. As gamma2 decreases below this point, the solutions become even stranger.


Ethan Deneault (eand@wpi.edu)