Nov 16, 2022 · In this section we will give a brief introduction to the phase plane and phase portraits. We define the equilibrium solution/point for a homogeneous system of differential equations and how …

The phase portraits of these linear systems display a startling variety of shapes and behavior. We’ll want names for them, and the names I’ll use differ slightly from the names used in the book and in some …

Phase Portraits of Two-Dimensional Differential Systems of Equations - by Lara Kassabian. If you have any questions or comments, tweet me @teslarak. Graph phase portraits of any two-dimensional …

On the phase portrait, the trajectory/solution matching up with initial condition given is traced, try a diferent initial condition or diferent model parameters to see how the phase portraits and trajectories …

Nov 27, 2025 · Learn about phase portraits for your IB Maths AI course. Find information on key ideas, worked examples and common mistakes.

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 already studied in detail.

Compare the three different methods of determining the behavior of solutions. Method 1: Solve the Diff Eq, Get the Solution Formula, Sketch Solution Graphs vs t, and Determine the Dynamic Behavior of …

Classification of 2d Systems Distinct Real Eigenvalues. Phase Portrait Saddle: 1. > 0 > 2. Nodal Source: 1. 2. > 0 Nodal Sink: 1. 2. < 0. Complex Eigenvalues. Center: ↵ =0 Spiral Source: ↵>0 Spiral …

ystem with X(t) = T C(t) will conserve the banana phase portrait. However, the eigenvectors will be diferent in the canonical forms system to the original system. Regardless of this, T will always be an …

Parallel Lines: one zero and one negative real eigenvalue (ex 0 and -5). NOTE: arrows point away from line if positive eigenvalue.