18.03 Lecture Notes - Lecture 35: Phase Portrait, Normal Mode, Phase Plane
Document Summary
Linear phase portraits: eigenvalues rule (usually: eigenvalues rule, trace-determinant plane, marginal cases, stability. [1] phase portrait: this means the (x,y) plane (the "phase plane") with trajectories of solutions of u" = au drawn on it (with direction of time indicated). These homogeneous linear equations exhibit a nice variety of phase portraits, as shown by the linear phase portraits mathlets. We"ll classify the linear phase portraits according to the eigenvalues of the matrix a . If the number of rabbits in macgregor"s field is twice the number in. This is not meaningful in itself in our population model, but we can draw it in the phase plane. And the two together provide the general solution. For large t , the v_1 component is much bigger than the v_2 component. For small t , the v_1 component is much smaller than the v_2 component. So near the origin the trajectories become asymototic to the eigenline with smaller eigenvalue.
