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A new class of quadratic systems. (English) Zbl 0733.58037

The qualitative features of the phase portraits of the class of quadratic systems given by

x ˙=ax+by+(Dx+Ey)(Ax+By),y ˙=cx+dy+(Dx+Ey)(Cx+Ay),

is studied. For example, it is shown that if such a system has at most two critical points at infinity, then either it has a center or it has at most one periodic orbit. If there is a unique periodic orbit it is a hyperbolic limit cycle. A nice application of the theory developed in the paper is made to a quadratic system which arises in the study of shear flow of a non-Newtonian fluid.


MSC:
37G15Bifurcations of limit cycles and periodic orbits
34C05Location of integral curves, singular points, limit cycles (ODE)