[[1,2],[1,2]], # plot arguments
)
add_system_params(sim,N,
k=[8.0,40.0],
m=[1,1.5],
L=[0.5,1],
b=[0.8,0.5],
x_1=0,
x_N=0,
k_N=0,
L_N=0,
)
print sim.equations()
sim.run(0,10)
# <codecell>
N=3
sim=Simulation()
add_system(sim,N,"x[i]''=(-b[i] * x[i]' - k[i] * (x[i] -x[i-1] -L[i]) + k[i+1] * (x[i+1] - x[i] - L[i+1])) / m[i]",
[[0.5,0.0],[2.25,0.0],[4.0,0.0]], # initial conditions
[[1,2],[1,2],[1,2]], # plot arguments
)
add_system_params(sim,N,
k=[8.0,40.0,10.0],
m=[1,1.5,1.0],
L=[0.5,1,2.0],
# In[8]:
sim=Simulation()
sim.figsize=(20,5)
sim.add("deer' = r*deer*(1-deer/K)-c*deer*wolf",
initial_value=350,
plot=True)
sim.add("wolf' = -Wd*wolf+D*deer*wolf",
initial_value=50,
plot=True)
sim.params(r=0.25,D=0.001,c=0.005,Wd=0.3,K=1e500)
print(sim.equations())
sim.run(0,500)
# fig=sim.figures[0]
# fig.savefig('predprey_dynamics1.pdf')
# fig.savefig('predprey_dynamics1.png')
# fig=sim.figures[1]
# fig.savefig('predprey_dynamics2.pdf')
# fig.savefig('predprey_dynamics2.png')
# In[9]:
from pyndamics import phase_plot
phase_plot(sim,'deer','wolf')
)
add_system_params(
sim,
N,
k=[8.0, 40.0],
m=[1, 1.5],
L=[0.5, 1],
b=[0.8, 0.5],
x_1=0,
x_N=0,
k_N=0,
L_N=0,
)
print sim.equations()
sim.run(0, 10)
# <codecell>
N = 3
sim = Simulation()
add_system(
sim,
N,
"x[i]''=(-b[i] * x[i]' - k[i] * (x[i] -x[i-1] -L[i]) + k[i+1] * (x[i+1] - x[i] - L[i+1])) / m[i]",
[[0.5, 0.0], [2.25, 0.0], [4.0, 0.0]], # initial conditions
[[1, 2], [1, 2], [1, 2]], # plot arguments
)
add_system_params(
ylabel('Number of Mice')
# ## Predator-Prey Dynamics
# In[8]:
sim = Simulation()
sim.figsize = (20, 5)
sim.add("deer' = r*deer*(1-deer/K)-c*deer*wolf", initial_value=350, plot=True)
sim.add("wolf' = -Wd*wolf+D*deer*wolf", initial_value=50, plot=True)
sim.params(r=0.25, D=0.001, c=0.005, Wd=0.3, K=1e500)
print(sim.equations())
sim.run(0, 500)
# fig=sim.figures[0]
# fig.savefig('predprey_dynamics1.pdf')
# fig.savefig('predprey_dynamics1.png')
# fig=sim.figures[1]
# fig.savefig('predprey_dynamics2.pdf')
# fig.savefig('predprey_dynamics2.png')
# In[9]:
from pyndamics import phase_plot
phase_plot(sim, 'deer', 'wolf')
