## 5 Reputation

2 years, 100 days

## How to draw phase portrait of nonlinear ...

Maple

I am slightly new to maple and have the following problem... I need to draw phase portrait of nonlinear dynamical system (differential equasion: ), where function is a hysteresis loop with parameters b=2, c=1.

Solving:

Split phase plane it two areas:

A:

B:

Finally I have two differencial equasions.

1. For A area:

2. For B area:

In a textbook this phase portrait looks like:

I know how to draw phase portrait of the first differencial equasion:

```restart; with(plots); with(plottools); with(DEtools):
initialset := {seq(seq([x1(0) = a, y1(0) = b], a = -2 .. 2), b = -2 .. 2)};
DE := [diff(x1(t), t) = y1(t), diff(y1(t), t) = 1-x1(t)];
phaseportrait([DE[]], [x1, y1], t = -5 .. 5, initialset, x1 = -3 .. 3, y1 = -3 .. 3, stepsize = .1, color = green, numpoints = 600, thickness = 2, linecolor = black, title = "first de");```

I know how to draw phase portrait of the second differencial equasion:

```restart; with(plots); with(plottools); with(DEtools):
initialset := {seq(seq([x1(0) = a, y1(0) = b], a = -2 .. 2), b = -2 .. 2)};
DE := [diff(x1(t), t) = -y1(t), diff(y1(t), t) = 1+x1(t)]
phaseportrait([DE[]], [x1, y1], t = -5 .. 5, initialset, x1 = -3 .. 3, y1 = -3 .. 3, stepsize = .1, color = green, numpoints = 600, thickness = 2, linecolor = black, title = "second de");```

Unfortunately, I don`t know how to combine it in Maple...

 Page 1 of 1
﻿