In this paper, we characterize the topological structure of orbits of the Rabinovich system ẋ = hy − v 1 x + yz, ẏ = hx − v 2 y − xz and ż = v 3 z + xy having an invariant algebraic surface.

In this paper, we characterize the dynamics of the Chen system ẋ = a(y - x), ẏ = (c - a)x - xz + cy, ż = xy - bz which has an invariant algebraic surface.

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In this paper, we characterize all dynamics of the Lorenz system ẋ=s(y−x), ẏ=rx−xz−y, ż=xy−bz having an invariant algebraic surface.

With the help of Abel differential equations we obtain a new class of Darboux integrable planar polynomial differential systems, which have degenerate infinity. Moreover such integrable systems may have algebraic limit cycles. Also we present the explicit expressions of these algebraic limit cycles for quintic systems.