def compute_phase_diagram(hunting_rate_x, hunting_rate_y, duration, start_x, start_y):
'''
Compute multiple simulations with parameters taken from the arguments.
Create graph that shows the simulation results one after the other.
ARGUMENTS
---------
hunting_rate_x: hunting rate for species 1 (small fish)
hunting_rate_y: hunting rate for species 2 (predatory fish)
duration: list of duration for each simulation
start_x: list of start values for species 1
start_y list of start values for species 2
'''
model = EnhancedModel() #create a simulation object instance
figure() #create new figure window
#max_i = len(duration)-1
xmax, ymax = -1e100, -1e100
xmin, ymin = 1e100, 1e100
#do simulations with the different parameter values,
#plot results into phase plane
for i in range(len(duration)):
model.init_hunting(hunting_rate_x, hunting_rate_y,
start_x[i], start_y[i], duration[i])
model.simulateDynamic() #solve ODE
res = model.getResults() #get results as a storage.DictStore object
#color_tuple = cm.jet(i/max_i)
plot(res['x'], res['y'], color='black', linestyle='-')
#find maximum figure dimensions for quiver plot
xmax = max(xmax, amax(res['x']))
ymax = max(ymax, amax(res['y']))
xmin = min(xmin, amin(res['x']))
ymin = min(ymin, amin(res['y']))
#Sample differentials at different points in phase plane,
#plot field of arrows
X, Y = mgrid[xmin:xmax:20j,ymin:ymax:20j]
U, V = zeros(X.shape), zeros(X.shape)
for i in range(X.shape[0]):
for j in range(X.shape[1]):
s_dt = model.dynamic(0, [X[i,j], Y[i,j]])
U[i,j],V[i,j] = s_dt[0], s_dt[1]
#The axes don't have the same scale, therefore scale the arrows
#TODO: this is a bad hack; future keyword 'angles' should do the trick
scale_xy = (ymin-ymax)/(xmin-xmax) * 1.3
quiver(X, Y, scale_xy*U, V, pivot='center', units='inches', color='red',zorder=0)
#finishing touches on plot
xlabel('x - prey')
ylabel('y - predators')
legend()
title('Predator prey with hunting - hx = %g, hy = %g' % (hunting_rate_x, hunting_rate_y))
def compute_scenario(hunting_rate_x, hunting_rate_y, duration):
'''
Compute multiple simulations with parameters taken from the arguments.
Create graph that shows the simulation results one after the other.
ARGUMENTS
---------
hunting_rate_x: list of hunting rates for species 1 (small fish)
hunting_rate_y: list of hunting rates for species 2 (predatory fish)
duration: list of duration for each simulation
'''
model = EnhancedModel() #create a simulation object instance
figure() #create new figure window
max_i = len(duration)-1
x, y = 1, 0.1
cum_duration = 0
#do simulations with the different parameter values, plot results
for i in range(len(duration)):
model.init_hunting(hunting_rate_x[i], hunting_rate_y[i], x, y, duration[i])
model.simulateDynamic() #solve ODE
res = model.getResults() #get results as a storage.DictStore object
color_tuple = cm.jet(i/max_i)
#label_str = 'r1=%g' % r1 #create descriptive string
label_str = 'hx: %g, hy: %g' % (hunting_rate_x[i], hunting_rate_y[i])
plot(res['time'] + cum_duration, res['x'],
label='x: '+label_str, color=color_tuple, linestyle=':')
plot(res['time'] + cum_duration, res['y'],
label='y: ', color=color_tuple, linestyle='--')
plot(res['time'] + cum_duration, res['hunting_yield'],
label='yield: ', color=color_tuple, linestyle='-')
#start next simulation with state values from previous simulation
x = res['x'][-1]
y = res['y'][-1]
#cumulative duration to put the simulation's plots after each other
cum_duration += duration[i]
#finishing touches on plot
xlabel('time')
ylabel('x: prey, y: predators')
legend()
title('Predator prey with hunting')