## Differential Equations – Phase Plane

The time dependence of the solution can be shown by adding arrows to the trajectories. In this case, all but two of the solutions are moving away from the equilibrium point.

## How do you determine phase portraits?

The eigenvalues or the trace and determinant (trace = sub>1/sub> x sub>2/sub>, determinant = sub>1/sub> x sub>2/sub>) of a system of ODEs can determine the phase portrait behavior of the system, which can indicate the system’s stability.

## How do you graph a phase plane?

We draw a vector starting at (x0,y0) in the direction f(x0,y0)i g(x0,y0)j at each point (x0,y0) in the xy-plane to sketch the phase plane of such a system.

## How do you make a phase portrait in Maplestory?

Click anywhere in the direction field to create a phase portrait through that point, then select the Click and Drag Manipulator ( ) from the Plot menu or plotting toolbar. The Erase Phase Portrait button erases all orbits and field arrows.

## What is the phase trajectory?

A non-closed phase trajectory is divided into two parts u2014 positive and negative semi-trajectories u2014 by a point w in phase space, which represents how the state of a dynamical system changes with time.

## What is a phase line diagram?

A phase line diagram is simply a summary of the solution behavior in a direction field; however, an independently created phase line diagram can be used to enrich the detail in a direction field. Fact 3 is used to create additional threaded solutions by translation from an initial threaded solution.

## What is phase plane in differential equation?

The phase plane method is a graphical method for determining the existence of limit cycles in differential equation solutions. The differential equation solutions are a family of functions that can be graphically plotted in the phase plane like a two-dimensional vector field.

## What is the phase plot?

The Bode phase plot is a graph of the transfer function’s phase, commonly expressed in degrees, as a function of, plotted on the same logarithmic -axis as the magnitude plot, but with the value plotted on a linear vertical axis.