CoCalc -- Code for Final Project.sagews

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#Simulation as well as Frequency Model for Iext. By using interaction can test the change in parameters of the FitzHugh-Nagumo model of a neuron in order to see how the model interacts. This simulates the model using desolve_odeint rather than Eulers.
@interact
def Iext(I=(0.01,0.05,0.1,0.2,0.201,0.208,0.209,0.21,0.25,0.3,0.5,0.7,0.9,1,1.5,2.0),m=(0.001,0.01,0.1,0.5,1,5),b=(0.001,0.01,0.1,0.5,1,5)):
    var("V","w")
    t=srange(0,1000,0.1)
    sol=desolve_odeint([(V*(1-V)*(V-0.2))-w+I,0.01*(V-(0.5*w))], ics=[m,b], dvars=[V,w], times=t)
    p=list_plot(zip(t,sol[:,0]), plotjoined=True)+list_plot(zip(t,sol[:,1]), plotjoined=True, color="purple")
    show(p)

Interact: please open in CoCalc

#Model Simulation 
Iext=[0.25,0.3,0.5,0.7,0.9]
Frequency=[0.008,0.01,0.013,0.015,0.02]
list_plot(zip(Frequency,Iext),axes_lables=["Frequency (Hz), Iext"])

verbose 0 (163: primitive.py, options) WARNING: Ignoring option 'axes_lables'=['Frequency (Hz), Iext']
verbose 0 (163: primitive.py, options) 
The allowed options for Point set defined by 5 point(s) are:
    alpha          How transparent the point is.                               
    faceted        If True color the edge of the point. (only for 2D plots)    
    hue            The color given as a hue.                                   
    legend_color   The color of the legend text                                
    legend_label   The label for this item in the legend.                      
    marker         the marker symbol for 2D plots only (see documentation of plot() for details)
    markeredgecolorthe color of the marker edge (only for 2D plots)            
    rgbcolor       The color as an RGB tuple.                                  
    size           How big the point is (i.e., area in points^2=(1/72 inch)^2).
    zorder         The layer level in which to draw                            

verbose 0 (163: primitive.py, options) WARNING: Ignoring option 'axes_lables'=['Frequency (Hz), Iext']
verbose 0 (163: primitive.py, options) 
The allowed options for Point set defined by 5 point(s) are:
    alpha          How transparent the point is.                               
    faceted        If True color the edge of the point. (only for 2D plots)    
    hue            The color given as a hue.                                   
    legend_color   The color of the legend text                                
    legend_label   The label for this item in the legend.                      
    marker         the marker symbol for 2D plots only (see documentation of plot() for details)
    markeredgecolorthe color of the marker edge (only for 2D plots)            
    rgbcolor       The color as an RGB tuple.                                  
    size           How big the point is (i.e., area in points^2=(1/72 inch)^2).
    zorder         The layer level in which to draw                            

verbose 0 (163: primitive.py, options) WARNING: Ignoring option 'axes_lables'=['Frequency (Hz), Iext']
verbose 0 (163: primitive.py, options) 
The allowed options for Point set defined by 5 point(s) are:
    alpha          How transparent the point is.                               
    faceted        If True color the edge of the point. (only for 2D plots)    
    hue            The color given as a hue.                                   
    legend_color   The color of the legend text                                
    legend_label   The label for this item in the legend.                      
    marker         the marker symbol for 2D plots only (see documentation of plot() for details)
    markeredgecolorthe color of the marker edge (only for 2D plots)            
    rgbcolor       The color as an RGB tuple.                                  
    size           How big the point is (i.e., area in points^2=(1/72 inch)^2).
    zorder         The layer level in which to draw                            


var("V")
var("w")

V
w

f(V)=V*(1-V)*(V-0.2)

Vprime(V)=f(V)-w+0.1

Wprime(w)=0.01*(V-(0.5*w))

plot_vector_field((Vprime(V), Wprime(w)), (V,-2,2), (w,-2,2))

testpoints=[(1,1), (2,2), (1,-1), (2,-2), (-1,-1), (-2,-2),(-1,1),(-2,2)]

#Vector Field with Trajecotries and Equilibirum point(0,0). Subthreshold
t=srange(0, 1000, 0.1)
vf=plot_vector_field((Vprime(V),Wprime(w)),(V,-2,2),(w,-2,2))+ point([0,0], color="blue", size=40)
for i in srange (0,len(testpoints),1):
    sol=desolve_odeint([f(V)-w+0.1,0.01*(V-(0.5*w)) ], ics=testpoints[i], dvars=[V,w], times=t)
    p=list_plot(zip(sol[:,0], sol[:,1]), color="red", plotjoined=True)+vf
    show(p, ymin= -2, ymax=2, xmin=-2, xmax=2)

#redefining V prime for new test with changed Iext value
Vprime2(V)=f(V)-w+0.208

#Vector Field with Trajecotries and Equilibirum point(0,0). Threshold
t=srange(0, 1000, 0.1)
vf=plot_vector_field((Vprime2(V),Wprime(w)),(V,-2,2),(w,-2,2))+ point([0,0], color="blue", size=40) 
for i in srange (0,len(testpoints),1):
    sol=desolve_odeint([f(V)-w+0.208,0.01*(V-(0.5*w)) ], ics=testpoints[i], dvars=[V,w], times=t)
    p=list_plot(zip(sol[:,0], sol[:,1]), color="red", plotjoined=True)+vf
    show(p, ymin= -2, ymax=2, xmin=-2, xmax=2)

#redefining V prime for new test with changed Iext value
Vprime3(V)=f(V)-w+0.5

#Vector Field with Trajecotries and Equilibirum point(0,0). Supra-threshold
t=srange(0, 1000, 0.1)
vf=plot_vector_field((Vprime3(V),Wprime(w)),(V,-2,2),(w,-2,2))+ point([0,0], color="blue", size=40) 
for i in srange (0,len(testpoints),1):
    sol=desolve_odeint([f(V)-w+0.5,0.01*(V-(0.5*w)) ], ics=testpoints[i], dvars=[V,w], times=t)
    p=list_plot(zip(sol[:,0], sol[:,1]), color="red", plotjoined=True)+vf
    show(p, ymin= -2, ymax=2, xmin=-2, xmax=2)

#Sub-Threshold State Space Code
t=srange(0,100,0.1)
sol4=desolve_odeint((f(V)-w+0.1, 0.01*(V-(0.5*w))), ics=[0.1,0.1], dvars=[V,w], times=t)
list_plot(sol4, axes_labels=["V", "w"])
plotjoined=True

#Threshold State Space Code
t=srange(0,100,0.1)
sol5=desolve_odeint((f(V)-w+0.208, 0.01*(V-(0.5*w))), ics=[0.1,0.1], dvars=[V,w], times=t)
list_plot(sol5, axes_labels=["V", "w"])
plotjoined=True

#SupraThreshold State Space Code
t=srange(0,100,0.1)
sol6=desolve_odeint((f(V)-w+0.5, 0.01*(V-(0.5*w))), ics=[0.1,0.1], dvars=[V,w], times=t)
list_plot(sol6, axes_labels=["V", "w"])
plotjoined=True

#sub-Threshold State Space Code with nullclines
t=srange(0,100,0.1)
sol4=desolve_odeint((f(V)-w+0.1, 0.01*(V-(0.5*w))), ics=[0.1,0.1], dvars=[V,w], times=t)
list_plot(sol4, axes_labels=["V", "w"])+plot(2*V,color="red")+plot((1+V)+0.1,color="red")+plot(V-0.2+0.1,color="red")
plotjoined=True

#Threshold State Space Code with nullclines
t=srange(0,100,0.1)
sol5=desolve_odeint((f(V)-w+0.208, 0.01*(V-(0.5*w))), ics=[0.1,0.1], dvars=[V,w], times=t)
list_plot(sol5, axes_labels=["V", "w"])+plot(2*V,color="red")+plot((1+V)+0.1,color="red")+plot(V-0.2+0.1,color="red")
plotjoined=True

#SupraThreshold State Space Code with nullclines
t=srange(0,100,0.1)
sol6=desolve_odeint((f(V)-w+0.5, 0.01*(V-(0.5*w))), ics=[0.1,0.1], dvars=[V,w], times=t)
list_plot(sol6, axes_labels=["V", "w"])+ plot(2*V,color="red")+plot((1+V)+0.1,color="red")+plot(V-0.2+0.1,color="red")
plotjoined=True

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