F xs ys qf x ylxsysx qyf x y

Now let us consider the three terms in the right hand expression of this equation. The first term on the right hand side is identically zero, because (xs, ys) is a steady state. The second term is the partial derivative off (x, y) with respect to x, evaluated at the steady state. To help simplify what we have to write, we will use subscripts for partial derivatives and, with a slight abuse of notation, replace the second and third terms on the right hand side of Eq. (2.45) by fx(xs, ys)x and fy (xs, ys)y. A similar argument shows that g(x, y) « gx(xs, ys)x + gy(xs, ys)y. The point of all this work is that we can now replace the nonlinear differential equation (2.44) by a linear system that characterizes the deviations from the steady state

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