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Cobweb

class phaseportrait.Cobweb(dF, initial_position, xrange, *, dF_args={None}, yrange=[], max_steps=100, n_points=100, **kargs)

A class used to represent a Cobweb plot and a time series to study the convergence of a 1D map x(t+1) = f(x).

Parameters

  • dF : callable

    A dF type funcion.

  • initial_position : float

    Initial x of the iteration.

  • xrange : list

    Range of the x axis in the main plot.

Key Arguments

  • dF_args : dict

    If necesary, must contain the kargs for the dF funcion.

  • yrange : list

    Range of the y axis in the main plot

  • max_steps : int, default=100

    Maximum number of points to be represented.

  • n_points : int, default=10000

    Number of points in the bisector.

  • Title : str, default='Cobweb plot'

    Title of the plot.

  • xlabel : str, default=r'$X_{n}$'

    x label of the plot.

  • ylabel : str, default=r'$X_{n+1}$'

    y label of the plot.

Methods

Cobweb.plot

Cobweb.plot(*args, **kargs)

Creates two figures, one containing the Cobweb plot and other with the time series.

Returns

  • tuple(matplotlib Figure (Cobweb plot), matplotlib Axis (Cobweb plot), matplotlib Figure (Time series), matplotlib Axis (Time series))

Cobweb.add_slider

Cobweb.add_slider(param_name, *, valinit=None, valstep=0.1, valinterval=10)

Adds a slider which can change the value of a parameter in execution time.

Parameters

  • param_name : str The string key of the variable. Must be the same as the key in the dF function.

Key Arguments

  • valinit : float, default=None

    Initial value of the parameter.

  • valinterval : Union[float, list], default=0.1

    The range of values the slider of the parameter will cover.

  • valstep : float, default=10

    Precision in the slider.

Returns

  • None

Cobweb.initial_position_slider

Cobweb.initial_position_slider(*, valinit=None, valstep=0.05, valinterval=None)

Adds a slider for changing initial value on a cobweb plot.

Key Arguments

  • valinit : float

    Initial position. Default value is the same as initial position given when initializing Cobweb object.

  • valinterval : Union[float, list]

    The range of values the slider of the parameter will cover.

  • valstep : float

    Precision in the slider.

Returns

  • None

Examples

Logistic map cobweb plot and time series, defining the logistic map as a 1D dF function. 

from phaseportrait import Cobweb

def Logistic(x, *, r=1.5):
    return r*x*(1-x)

# Cobweb plot and time series.
LogisticCobweb = Cobweb(Logistic, 0.2, [0,1], dF_args={'r':1.5}, yrange=[0,1])
LogisticCobweb.add_slider('r', valinit=1.5, valinterval=[0,4])
LogisticCobweb.initial_position_slider(valstep=0.01)
LogisticCobweb.plot()

This will output the following plots:

image