CoCalc Public Filesgraded-Lab 8 / Lab8-turnin.sagewsOpen with one click!
Author: Madison Parsons
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# Lab 1: # Name: # I worked on this code with: # Please do all of your work for this week's lab in this worksheet. If # you wish to create other worksheets for scratch work, you can, but # this is the one that will be graded. You do not need to do anything # to turn in your lab. It will be collected by your TA at the beginning # of (or right before) next week’s lab. # Be sure to clearly label which question you are answering as you go and to # use enough comments that you and the grader can understand your code.1
# 1 #The equilibrium points are when R and J are both equal to zero # R is equal to zero when it is equals to (bJ)/a # J is equal to zero when it is equals to (-cR)/d
#2 var("a") var("b") var("c") var("d") var("R") var("J")
a b c d R J
#3 ListRJ=[(1,1),(2,4),(-2,3),(-4,5),(-5,-6),(-2,-8),(4,-6),(3,-9)]
#4 a=4 d=4 b=.5 R_prime(R,V)=a*R J_prime(R,V)=d*J fig1= plot_vector_field((R_prime,J_prime),(R,-10,10),(J,-10,10),axes_labels=['R','J']) show(fig1) #this equilibrium is unstable
#5 a=-4 d=-4 b=.5 R_prime(R,J)=a*R J_prime(R,J)=d*J fig1= plot_vector_field((R_prime,J_prime),(R,-10,10),(J,-10,10),axes_labels=['R','J']) show(fig1) #this equilibrium is stable
#6 #The first one is when they both have feelings and the second one is when neither of tehm have feelings
#7 a=4 d=-4 b=.5 R_prime(R,V)=a*R J_prime(R,V)=d*J fig1= plot_vector_field((R_prime,J_prime),(R,-10,10),(J,-10,10),axes_labels=['R','J']) show(fig1) #this saddle point equilibrium is unstable
#8 a=4 d=4 b=.5 R_prime(R,V)=a*R J_prime(R,V)=d*J fig1= plot_vector_field((R_prime,J_prime),(R,-10,10),(J,-10,10),axes_labels=['R','J']) point((0,0),color="red",size=1000)+fig1
#9 #This is a saddle point and therefore is unstable
#10 a=3 d=4 var("R", "J") t1 = srange(0,10,0.1) sol=desolve_odeint([a*R], ics=[100], dvars=[R], times=t) t2 = srange(0,10,.1) sol2=desolve_odeint([d*J],ics=[100], times=t, dvars=[J]) list_plot(zip(t,sol), axes_labels=["R","J "],color="red")+list_plot(zip(t2,sol2), axes_labels=["R","J"])
(R, J)
#11 b=4 c=4 R_prime(R,J)=b*J J_prime(R,J)=c*R fig1= plot_vector_field((R_prime,J_prime),(R,-10,10),(J,-10,10),axes_labels=['R','J']) show(fig1) #this shows an unstable saddle equilibrium point
#12 b=-4 c=-4 R_prime(R,J)=b*J J_prime(R,J)=c*R fig1= plot_vector_field((R_prime,J_prime),(R,-10,10),(J,-10,10),axes_labels=['R','J']) show(fig1)
#The equilibrium is still an unstable saddle point just going in the opposite direction
#13 b=4 c=-4 R_prime(R,J)=b*J J_prime(R,J)=c*R fig1= plot_vector_field((R_prime,J_prime),(R,-10,10),(J,-10,10),axes_labels=['R','J']) show(fig1) #this equilibrium point shows a stable spiral
#14 b=4 c=-4 R_prime(R,J)=b*J J_prime(R,J)=c*R fig1= plot_vector_field((R_prime,J_prime),(R,-10,10),(J,-10,10),axes_labels=['R','J']) point((0,0),color="red",size=1000)+fig1
#15 #the equilibrium is stable becuase the trajectory is spiraling around the equilibrium point, getting closer and closer to the point
#16 b=3 c=4 var("R", "J") t1 = srange(0,10,0.1) sol=desolve_odeint([b*J], ics=[100], dvars=[J], times=t) t2 = srange(0,10,.1) sol2=desolve_odeint([c*R],ics=[100], times=t, dvars=[R]) list_plot(zip(t,sol), axes_labels=["R","J "],color="red")+list_plot(zip(t2,sol2), axes_labels=["R","J"])
(R, J)
b=3 c=4 var("R", "J") t1 = srange(0,10,0.1) sol=desolve_odeint([b*J], ics=[10], dvars=[J], times=t) t2 = srange(0,10,.1) sol2=desolve_odeint([c*R],ics=[100], times=t, dvars=[R]) list_plot(zip(t,sol), axes_labels=["R","J "],color="red")+list_plot(zip(t2,sol2), axes_labels=["R","J"])
(R, J)
#10 part two a=3 d=4 var("R", "J") t1 = srange(0,10,0.1) sol=desolve_odeint([a*R], ics=[5], dvars=[R], times=t) t2 = srange(0,10,.1) sol2=desolve_odeint([d*J],ics=[100], times=t, dvars=[J]) list_plot(zip(t,sol), axes_labels=["R","J "],color="red")+list_plot(zip(t2,sol2), axes_labels=["R","J"])
(R, J)
#17 b=4 c=-4 R_prime(R,J)=b*J J_prime(R,J)=c*R fig1= plot_vector_field((R_prime,J_prime),(R,-10,10),(J,-10,10),axes_labels=['R','J']) t1 = srange(0,10,0.1) sol=desolve_odeint([b*J], ics=[5], dvars=[R], times=t) t2 = srange(0,10,.1) sol2=desolve_odeint([c*R],ics=[100], times=t, dvars=[J]) list_plot(zip(t,sol), axes_labels=["R","J "],color="red")+list_plot(zip(t2,sol2), axes_labels=["R","J"]) show (fig1+list_plot)
#18 b=4 c=-4 R_prime(R,J)=J J_prime(R,J)=-R+.05J fig1= plot_vector_field((R_prime,J_prime),(R,-10,10),(J,-10,10),axes_labels=['R','J']) t1 = srange(0,10,0.1) sol=desolve_odeint([b*J], ics=[5], dvars=[R], times=t) t2 = srange(0,10,.1) sol2=desolve_odeint([c*R],ics=[100], times=t, dvars=[J]) list_plot(zip(t,sol), axes_labels=["R","J "],color="red")+list_plot(zip(t2,sol2), axes_labels=["R","J"]) list_plot+fig1
#in this tiem series plot as one individuals love begins to increase the others love will decrease.
#19 This term is appropriately because the values are getting closer and closer to the quilibrium point, as a resultt, it is a stable spiral.
#20 b=4 c=-4 R_prime(R,J)= J J_prime(R,J)=-R+.05*J fig1= plot_vector_field((R_prime,J_prime),(R,-10,10),(J,-10,10),axes_labels=['R','J']) var("R", "J") t1 = srange(0,10,0.1) sol=desolve_odeint([b*J], ics=[10], dvars=[J], times=t) t2 = srange(0,10,.1) sol2=desolve_odeint([c*R],ics=[100], times=t, dvars=[R]) list_plot(zip(t,sol), axes_labels=["R","J "],color="red")+list_plot(zip(t2,sol2), axes_labels=["R","J"]) show(fig1)+show(list_plot)
(R, J)
<function list_plot at 0x7f56474212a8>
Error in lines 12-12 Traceback (most recent call last): File "/cocalc/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 1191, in execute flags=compile_flags), namespace, locals) File "", line 1, in <module> TypeError: unsupported operand type(s) for +: 'NoneType' and 'NoneType'
#21 b=4 c=-4 R_prime(R,J)=J J_prime(R,J)=-R+.05*J fig1= plot_vector_field((R_prime,J_prime),(R,-10,10),(J,-10,10),axes_labels=['R','J']) t1 = srange(0,10,0.1) sol=desolve_odeint([b*J], ics=[5], dvars=[R], times=t) t2 = srange(0,10,.1) sol2=desolve_odeint([c*R],ics=[100], times=t, dvars=[J]) list_plot(zip(t,sol), axes_labels=["R","J "],color="red")+list_plot(zip(t2,sol2), axes_labels=["R","J"]) list_plot+fig1 #in this tiem series plot as one individuals love begins to increase the others love will decrease.
#This is a semi stable equilibrium because the value first head towards the equilibrium point and then away from it #4.2.1 var("H") var("P") var("G") k1=.2 k2=.2 k3=.2 n=2 t=srange(0,100,.1) Pprime=(H-(k2*P)) Gprime=(P-(k3*G)) Hprime=((1/(1+G^n)))-k1*H sol=desolve_odeint([Hprime,Pprime,Gprime],ics=[1,1,1],dvars=[H,P,G],times=t) list_plot(zip(t,sol[:,0]), plotjoined=True)+list_plot(zip(t,sol[:,1]), plotjoined=True,color="pink")+list_plot(zip(t,sol[:,2]),plotjoined=True,color="red")
H P G
var("H") var("P") var("G") k1=.2 k2=.2 k3=.2 n=50 t=srange(0,100,.1) Pprime=(H-(k2*P)) Gprime=(P-(k3*G)) Hprime=((1/(1+G^n)))-k1*H sol=desolve_odeint([Hprime,Pprime,Gprime],ics=[1,1,1],dvars=[H,P,G],times=t) list_plot(zip(t,sol[:,0]), plotjoined=True)+list_plot(zip(t,sol[:,1]), plotjoined=True,color="pink")+list_plot(zip(t,sol[:,2]),plotjoined=True,color="red")
H P G
#4.2.2 n=15 t=srange(0,100,.1) Pprime=(H-(k2*P)) Gprime=(P-(k3*G)) Hprime=((1/(1+G^n)))-k1*H sol=desolve_odeint([Hprime,Pprime,Gprime],ics=[1,5,7],dvars=[H,P,G],times=t) sol=desolve_odeint([Hprime,Pprime,Gprime],ics=[1,1,1],dvars=[H,P,G],times=t) list_plot(zip(t,sol[:,0]), plotjoined=True)+list_plot(zip(t,sol[:,1]), plotjoined=True,color="pink")+list_plot(zip(t,sol[:,2]),plotjoined=True,color="red")
Error in lines 3-3 Traceback (most recent call last): File "/cocalc/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 1234, in execute flags=compile_flags), namespace, locals) File "", line 1, in <module> NameError: name 'H' is not defined
#4.2.3 var("H") var("G") k1=.2 k2=.2 k3=.2 n=5 t=srange(0,100,.1) Gprime=P-(k3*G) Hprime=((1/(1+(G^n)))-k1*H) sol=desolve_odeint([Hprime,Gprime],ics=[1,1],dvars=[H,G],times=t) list_plot(zip(t,sol[:,0]), plotjoined=True)+list_plot(zip(t,sol[:,1]), plotjoined=True,color="pink")
H G