Stability and fold bifurcation in a system of two coupled demand-supply models

A model of two coupled demand-supply systems, depending on 4 parameters is considered. We found that the dynamical system associated with this model may have at most two symmetric and at most two nonsymmetric equilibria as the parameters vary.
The topological type of equilibria is established and the locus in the parameter space of the values corresponding to nonhyperbolic equilibria is determined.
We found that the nonhyperbolic singularities can be of fold, Hopf, double-zero (Bogdanov–Takens) or fold-Hopf type.
In addition, the fold bifurcation is studied using the normal form method and the center manifold theory.