s=var('R,J')
t=srange(0,20,0.05)
ic1=[.5,.6]
ic2=[.5,-.2]
ic3=[-.9,.6]
ic4=[-.5,-.7]
@interact
def Romeo_Juliet(a=slider(-2,2,0.5,default=-1),
                 b=slider(-2,2,0.5,default=0),
                 c=slider(-2,2,0.5,default=0),
                 d=slider(-2,2,0.5,default=-1)):
    titleeq= ("$R'= "+'%2.1f'%(a)+" R "+"%+2.1f"%(b)+" J$\n"
              +"$J' = "+'%2.1f'%(c)+" R "+"%+2.1f"%(d)+" J$")
    vector_field=[a*R+b*J,c*R+d*J]
    pv=plot_vector_field(vector_field,(R,-1,1),(J,-1,1),plot_points=11,axes_labels=["R","J"])
    sol1=desolve_odeint(vector_field,times=t,ics=ic1,dvars=[R,J])
    ps1=list_plot(sol1,plotjoined=True,color='blue')+disk(ic1,.03,(0,2*pi),color='blue')
    sol2=desolve_odeint(vector_field,times=t,ics=ic2,dvars=[R,J])
    ps2=list_plot(sol2,plotjoined=True,color='red')+disk(ic2,.03,(0,2*pi),color='red')
    sol3=desolve_odeint(vector_field,times=t,ics=ic3,dvars=[R,J])
    ps3=list_plot(sol3,plotjoined=True,color='green')+disk(ic3,.03,(0,2*pi),color='green')
    sol4=desolve_odeint(vector_field,times=t,ics=ic4,dvars=[R,J])
    ps4=list_plot(sol4,plotjoined=True,color='purple')+disk(ic4,.03,(0,2*pi),color='purple')
    show(pv+ps1+ps2+ps3+ps4,xmin=-1,xmax=1,ymin=-1,ymax=1,aspect_ratio=1,
         title=titleeq,figsize=8,fontsize=20)

vs=var("D,M")
t=srange(0,50,0.05)
Dmax=3.1
Mmax=2.5
@interact
def Deer_Moose(r_D=slider(0,5,0.5,default=3,label="$r_D$"),
               r_M=slider(0,5,0.5,default=2,label="$r_M$"),
               alpha=slider(0,2,0.5,default=0.5,label="$\\alpha$"),
               D0=slider(0,Dmax,0.1,default=1,label="$D_0$"),
               M0=slider(0,Mmax,0.1,default=1,label="$M_0$")):
    titleeq=("$D'= " + '%2.1f'%(r_D) + " D - M D - D^2$\n " + "$M’= " + '%2.1f'%(r_M) + " M - " + '%2.1f'%(alpha) + " M D - M^2$")
    vector_field=[r_D*D-M*D-D^2,r_M*M-alpha*M*D-M^2]
    initial_value=[D0,M0]
    pv=plot_vector_field(vector_field,(D,0,Dmax),(M,0,Mmax), plot_points=11,axes_labels=["D","M"])
    sol1=desolve_odeint(vector_field,times=t,ics=initial_value,dvars=[D,M])
    ps1=list_plot(sol1,plotjoined=True,color='green',thickness=2)
    d1=disk(initial_value,.035,(0,2*pi),color='green')
    nullclines=( plot(r_D-D,(D,0,r_D),color="red",thickness=3)+plot(r_M-alpha*D,(D,0,r_M/alpha),color="blue",thickness=3))

    show(pv+ps1+d1+nullclines,xmin=0,xmax=Dmax,ymin=0,ymax=Mmax,aspect_ratio=1,title=titleeq,figsize=8,fontsize=20,svg=False)
    
def Scale_vf(xy):
    scale=sqrt(5+xy[0]^2+xy[1]^2)
    return [xy[0]/scale,xy[1]/scale]
vs=var("D,M")
t=srange(0,50,0.05)
Dmax=4.0
Mmax=3.5
@interact
def Deer_Moose_norm(r_D=slider(0,5,0.5,default=3,label="$r_D$")
                    r_M=slider(0,5,0.5,default=2,label="$r_M$"),
                    alpha=slider(0,2,0.5,default=0.5,label="$\\alpha$"),
                    D0=slider(0,Dmax,0.1,default=1,label="$D_0$"),
                    M0=slider(0,Mmax,0.1,default=1,label="$M_0$")):
    titleeq=("$D'= " + ''%2.1f'%(r_D) + " D - M D - D^2$\n " +"$M'= " + ''%2.1f'%(r_M) + " M - " + ''%2.1f’%(alpha) + " M D - M^2$")
    vector_field=[r_D*D-M*D-D^2,r_M*M-alpha*M*D-M^2]
    initial_value=[D0,M0]
    pv=plot_vector_field(Scale_vf(vector_field),(D,0,Dmax),(M,0,Mmax),plot_points=11,axes_labels=["D","M"])
    sol1=desolve_odeint(vector_field,times=t,ics=initial_value,dvars=[D,M])
    ps1=list_plot(sol1,plotjoined=True,color='green',thickness=2)
    d1=disk(initial_value,.035,(0,2*pi),color='green')
    nullclines=(plot(r_D-D,(D,0,r_D),color="red",thickness=3)
    +plot(r_M-alpha*D,(D,0,r_M/alpha),color="blue",thickness=3))
    show(pv+ps1+d1+nullclines,xmin=0,xmax=Dmax,ymin=0,ymax=Mmax,

    aspect_ratio=1,title=titleeq,figsize=8,fontsize=20,svg=False)