python - 我正在尝试通过绘制捕食者与猎物的图表来可视化我的 Predator-Prey 模型的解决方案（使用 Runge-kutta 3）。但它不会情节

Question

我试图通过在 python 中绘制捕食者与猎物数量的图表来可视化我的代码的解决方案，并使用黑色圆圈标记当前状态。我的代码运行正常，除了我无法让图表的绘图部分打印图表上的图表。

这是我当前的python代码：

import matplotlib.pyplot as plt
import numpy as np
from trajectoryplotsupport import *

def ExactTrajectory(dt, ntimesteps):
    tt = np.linspace(0, dt*ntimesteps, ntimesteps+1)
    x = np.cos(2*np.pi*tt)
    y = np.sin(2*np.pi*tt)
    return x,y

def GetVelocity(pos, tn):
    u =-2.0*np.pi * pos[1]
    v = 2.0*np.pi * pos[0]
    vel = np.array([u,v])
    return vel

def RK3(p, t):
    vel = GetVelocity(p, t) # stage 1 velocity
    pt = p + 0.5*dt*vel # stage 1 provisional position
    vel = GetVelocity(pt, t+dt) # stage 2 velocity
    pt = 0.25 * p + 0.75*( pt + dt*vel ) # stage 2 provisional position
    vel = GetVelocity(pt, t+0.5*dt) # stage 3 velocity
    p = ( p + 2.0*(pt + dt*vel) )/3.0 # stage 3 provisional position
    return p

def PreyPred(p, t):
    b = 0.5    # prey birth rate
    m = 0.2    # predator mortality
    a = 0.04   # effect of predator abundance on prey
    r = 0.01   # effect of prey abundance on predator
    h, w = p[0], p[1]    # initial densities of prey and predator are h(0) = 4.0 and w(0) = 8.0
    dht = h*(b - a*w)
    dwt = w*(-m + r*h)
    return np.array([dht, dwt])

#################MAIN CODE#############
p = np.array([4.0, 8.0])    # initial position
ntimesteps = 120            # number of time steps
finalTime = 480             # final time
dt = 1                      # time step

xe,ye = ExactTrajectory(dt, ntimesteps)  # call exact trajectory

# Check on computations. Create 2 array to track the positions and initialize
pos = np.zeros(2)                     # create current position array
pos[0] = xe[0]; pos[1]=ye[0]          # initialize current position

fig, lastPosition = InitialPlot(p, xe,ye)

for it in range(finalTime):  # time loop
    t = it*dt    # set current time
    p = RK3(p, t)
    print(t, p)
    UpdatePlot(fig,lastPosition,p,t)  # update the plot

ttpoints = np.arange(0, 480, dt)         #edited
hpoints, wpoints  = [], []
p = np.array([0, 0], float)
for tt in ttpoints:
        hpoints.append(p[0])          
        wpoints.append(p[1])          
        p += RK3(p, tt)             
        
plt.plot(ttpoints, hpoints)
plt.plot(ttpoints, wpoints)
plt.xlabel("Prey")
plt.ylabel("Predator")
plt.plot(hpoints, wpoints)
plt.show()

标签： pythonnumpymatplotlibrunge-kutta