Sage: dynamics of planar systems

 

## Chapter 6 - exercise 29 
##	attach("nonl-u29.py")


var('x y')

F = y
G = x - x*x 

[x0,x1]=[-1,2] 
[y0,y1]=[-1,1] 

## prime integral
v1 = y*y/2  + x**3/3 - x**2/2 

## plot levelset {v1=0} (homoclinic orbit)
V = implicit_plot( v1 , (x,x0,x1), (y,y0,y1), color='blue' , 
				linewidth = 1 ) 


S = streamline_plot( (F,G) , (x,x0,x1), (y,y0,y1), color='black',
			density=2 , linewidth=0.3 )

P = S + V 

P.show(axes=1,aspect_ratio=1,figsize=10)

#P.save("uloha29.png",axes=1)