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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 \[ \dot x=ax+by+(Dx+Ey)(Ax+By),\quad \dot y=cx+dy+(Dx+Ey)(Cx+Ay), \] 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:

37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
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References:

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