In [1]:

import numpy as np

from example_models import get_phase_plane
from modelbase2 import plot
from modelbase2.simulator import Simulator
from modelbase2.types import unwrap

import numpy as np from example_models import get_phase_plane from modelbase2 import plot from modelbase2.simulator import Simulator from modelbase2.types import unwrap

Stability analysis¶

modelbase2 offers routines to easily visualise the stability of the model over a wide range of parameters.

plot.trajectories2d shows the vector field depending on the values of two variables as a quiver plot.

In [2]:

_ = plot.trajectories_2d(
    get_phase_plane(),
    x1=("s1", np.linspace(0, 2, 20)),
    x2=("s2", np.linspace(0, 2, 20)),
)

_ = plot.trajectories_2d( get_phase_plane(), x1=("s1", np.linspace(0, 2, 20)), x2=("s2", np.linspace(0, 2, 20)), )

As always, plot.trajectories_2d returns matplotlib Figure and Axes objects, so you can further customise the plot.
Below we visualise example trajectories for different initial conditions of the model.

In [3]:

fig, ax = plot.trajectories_2d(
    get_phase_plane(),
    x1=("s1", np.linspace(0, 2, 20)),
    x2=("s2", np.linspace(0, 2, 20)),
)

for s1 in np.linspace(0, 1, 4):
    for s2 in np.linspace(0, 2, 4):
        c = unwrap(
            Simulator(get_phase_plane(), y0={"s1": s1, "s2": s2})
            .simulate(1.5)
            .get_result()
        ).variables
        ax.plot(c["s1"], c["s2"])

fig, ax = plot.trajectories_2d( get_phase_plane(), x1=("s1", np.linspace(0, 2, 20)), x2=("s2", np.linspace(0, 2, 20)), ) for s1 in np.linspace(0, 1, 4): for s2 in np.linspace(0, 2, 4): c = unwrap( Simulator(get_phase_plane(), y0={"s1": s1, "s2": s2}) .simulate(1.5) .get_result() ).variables ax.plot(c["s1"], c["s2"])