9.3 Phase Plane Portraits. Classification of 2d Systems. Distinct Real Eigenvalues. Phase Portrait. Saddle: λ1 > 0 > λ2. Nodal Source: λ1 > λ2 > 0. Nodal Sink: ...

The phase portrait is a representative sampling of trajectories of the system. A trajectory is the directed path traced out by a solution. It does not include ...

It is a representative set of solutions for the system of ODEs, plotted as parametric curves (with t as the parameter) on the Cartesian plane tracing the path ...

Hand-drawn phase portraits are accordingly limited: you cannot draw a solution trajectory that touches another solution curve! Theorem 1 (Identical trajectories).

trajectories in the phase plane is called a phase portrait (see Figure 1). Below, we describe phase portraits generated by (4) for different 7 and 7 . Since ...

where x Є R. The phase portrait consists of equilibria and trajectories between them going from one equilibrium to another. The equilibria are the solutions.

Phase portraits can have many shapes. To get a general idea of them, we examine phase portraits of first- order linear differential equations, which we have ...

To sketch a phase portrait, it can be helpful to follow some or all of the following steps. 1. Find all equilibria. Where possible, use.

= To plot the phase portrait of y's Ay,. Step 1: find eigenvalues & eigenvectors of A. * If one of the eigenvalues =D or A is not diagonalizable then this is ...

The phase portrait is a picture of a collection of representative solution curves of the system in R2, which we call the phase plane. The equilibrium point of a ...