Phase Portrait Three Dimensional Rossler Systemrestart:
with(plots):with(DEtools):Define the differential equation using parameters:a := 0.1; b := 0.1; c := 14;RosslerDE := [diff(x(t),t) = -y(t) - z(t),
diff(y(t),t) = x(t) + a*y(t),
diff(z(t),t) = b + z(t)*(x(t) -c)];The initial conditions are given in the first line and can be changed.IC:=[[x(0)= 5,y(0)=0, z(0)=0],[x(0)= 16,y(0)=0, z(0)=0]];Plot x versus zDEplot(RosslerDE, [x(t),y(t),z(t)], t=0..50,
IC,linecolour=BLUE, x=-30..30, y=-30..30,z=-1..40, stepsize=0.01,
arrows=NONE, method=classical[rk4],scene=[x,z]);Plot y versus zDEplot(RosslerDE, [x(t),y(t),z(t)], t=0..50,
IC,linecolour=BLUE, x=-30..30, y=-30..30,z=-1..40, stepsize=0.01,
arrows=NONE, method=classical[rk4],scene=[y,z]);Plot x versus yDEplot(RosslerDE, [x(t),y(t),z(t)], t=0..50,
IC,linecolour=BLUE, x=-30..30, y=-30..30,z=-1..40, stepsize=0.01,
arrows=NONE, method=classical[rk4],scene=[x,y]);3 Dimensional plot which can be rotated:IC3d:=[[x(0)= 16,y(0)=0, z(0)=0]];
DEplot3d(RosslerDE, [x(t),y(t),z(t)], t=0..70,thickness=1,
IC3d,linecolour=BLUE, x=-30..30, y=-30..30,z=0..45,
stepsize=0.01,
arrows=NONE, method=classical[rk4],scene=[x,y,z]);Plot t versus xICt:=[[x(0)= 16,y(0)=0, z(0)=0]];
DEplot(RosslerDE, [x(t),y(t),z(t)], t=0..100,
ICt,linecolour=BLUE,thickness=1, x=-30..30, y=-30..30,z=0..50, stepsize=0.01,
arrows=NONE, method=classical[rk4],scene=[t,x]);