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$x$ is the population density of preys (e.g. rabbits). -
$y$ is the population density of predators (e.g. foxes)
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$\alpha = 1.0$ : prey growth rate -
$\beta = 0.1$ : prey death rate because of predators -
$\gamma = 0.75$ : predators death rate -
$\delta = 0.075$ : predators growth rate because of preys -
$\Delta t = 0.001$ : time step
$x(t+\Delta t) = x(t) + (\alpha x(t) - \beta x(t) y(t)) \Delta t$ $y(t+\Delta t) = y(t) + (-\gamma y(t) + \delta x(t) y(t)) \Delta t$
- Fork this repository on GitHub and clone it on your laptop.
- Use Python to implement the Lotka-Volterra model and run it over 30000 time steps. Save the results into NumPy arrays.
- Plot the results for each prognostic variable with Matplotlib.
- Save your code and results on GitHub.
Source article: Lorenz, E. N., 1963: Deterministic Nonperiodic Flow. J. Atmos. Sci., 20, 130–141
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$x$ is proportional to the intensity of the convection (the rate of fluid flow). -
$y$ is proportional to the temperature difference between the rising and falling air currents. -
$z$ is proportional to the distortion of the vertical temperature profile from a linear one.
$\rho = 28$ $\sigma = 10$ $\beta = 8/3$ -
$\Delta t = 0.01$ : time step
$x(t+\Delta t) = x(t) + \sigma (y(t) - x(t)) \Delta t$ $y(t+\Delta t) = y(t) + (\rho x(t) - y(t) - x(t) z(t)) \Delta t$ $z(t+\Delta t) = z(t) + (x(t) y(t) - \beta z(t)) \Delta t$
- Fork this repository on GitHub and clone it on your laptop.
- Use Python to implement the Lorenz 63 model and run it over 10000 time steps. Save the results into NumPy arrays.
- Plot the results for each prognostic variable with Matplotlib.
- Plot the results in 3D, make a movie.
- Save your code and results on GitHub.
- Try to increase or decrease the time step.
- Try to restart the model after 5000 steps.
- Try to restart the model after 5000 steps, but truncating the result of the 5000th step.