General 2-D Quadratic Map

xn+1 = a1 + a2xn + a3xn2 + a4xnyn + a5yn + a6yn2

yn+1 = a7 + a8xn + a9xn2 + a10xnyn + a11yn + a12yn2

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Systems of this sort can model a very wide range of phenomena

Values of a are control knobs that change the dynamical behavior