Mackey-Glass Discrete Equation¶
New in version 0.1.
Changed in version 0.2.
This function generates data according a discrete realization of Mackey-Glass equation as follows
\(x_{k+1} = c \cdot x_k + \frac{\large{a \cdot x_{k-d}}}{b + x^{e}_{k-d}}\)
The original Mackey-Glass equation [1] is the nonlinear time delay differential equation.
Example Usage¶
In this example is simulated 1000 samples with arguments that cause chaotic behaviour.
N = 1000
x = signalz.mackey_glass(N, a=0.2, b=0.8, c=0.9, d=23, e=10, initial=0.1)
The parameters a, b, c, d, e can be a scalar or a vector. In case of a vector, every item represents parameter for one sample.
Function Documentation¶
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signalz.generators.mackey_glass.mackey_glass(n, a=0.2, b=0.8, c=0.9, d=23, e=10, initial=0.1)[source]¶ Mackey-Glass discrete equation.
Args:
- n - length of the output data (int) - how many samples will be on output
Kwargs:
Parameters a, b, c, d, e can be a scalar or a vector. In case of a vector, every item represents parameter for one sample.
- a - parameter of the model (float, 1d array), default is 0.2
- b - parameter of the model (float, 1d array), default is 0.8
- c - parameter of the model (float, 1d array), default is 0.9
- d - time delay of the model (int, 1d array), default is 23
- e - parameter of the model (float, 1d array), default is 10
- initial - initial value (float), default is 0.1
Returns:
- x - output of Mackey-Glass equation