Bifurcations in an economic model with fractional degree

A planar ODE system which models the industrialization of a small open economy is considered. Because fractional powers are involved, its interior equilibria hardly found by solving transcendental equation and routine qualitative analysis not applicable. We qualitatively discuss equation, eliminating term to polynomialize expression extreme value, so that we can compute polynomials obtain number in all cases complete their analysis. Orbits near origin, at cannot be extended differentiably, investigated using GNS method. Then display bifurcations such as saddle-node bifurcation, transcritical bifurcation codimension 2 on one-dimensional center manifold. Furthermore, prove nonexistence closed orbits, homoclinic loops heteroclinic loops, exhibit global orbital structure analyze tendency development.