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...