A simple mathematical model of bistability

In case of bistability, it is logical to expect that if the steady state value of any quantity X is related to certain parameter Y, then a cubic relation of the type 

It may be noted that along AB and FF, one gets only one value of Y for a particular value of X. There are three values of Y corresponding to states BC, CD and DF when X lies in the region denoted by - . These correspond to multiple steady states. In many physico-chemical systems, one of the solutions along CD is not permissible on account of theoretical constraints as in electro-kinetic phenomenon. In such cases, bistability and hysterisis are obtained. The points C and D where the nature of the solution changes is called the bifurcation point. 

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