Non-linear Systems - UCI Mathematics
www.math.uci.edu › ~ndonalds › math3dNon-linear Systems Linearization Definition. Suppose P = (x0,y0) is an isolated critical point of the system (dx dt = f(x,y) dy dt = g(x,y) and that f and g are differentiable at P. The linearization of the system at P is the linear system (du dt = fx(P)u+ fy(P)v dv dt = gx (P)u+ gy P)v Written in matrix format: du/dt dv/dt = fx(x0,y0) fy(x0,y0) gx(x0,y0) gy(x0,y0) u v
Non-linear Systems - UCI Mathematics
https://www.math.uci.edu/~ndonalds/math3d/nonlinear.pdfQuestion Find all the critical points of the non-linear system dx dt = x y x 2 + xy dy dt = x 2 y and identify their types. The sketch a possible phase-portrait for the system. Solution To find the critical points we need to find all solutions to the simulatanous equations x y x2 + xy = 0 x2 y = 0 In general there is no guaranteed method for doing this, so be creative!
9.6 Solving Nonlinear Systems of Equations
www.jacksonsd.org › cms › libApproximating Solutions of a Nonlinear System Approximate the solution(s) of the system to the nearest thousandth. y = —1 2 x2 Equation 1+ 3 y = 3x Equation 2 SOLUTION Sketch a graph of the system. You can see that the system has one solution between x = 1 and x = 2. Substitute 3x for y in Equation 1 and rewrite the equation. 3x = —1 2