Nonlinear_Dynamics_JL

Rewriting Fortran programs to Julia-lang.

fractalgasket

fractaltree

langford

$\begin{eqnarray} \left\{ \begin{array}{l} \frac{dx}{dt} = (z-u)x-wy \\ \frac{dy}{dt} = wx-(z-u)y \\ \frac{dz}{dt} = n+z-\frac{z^3}{3}-(x^2+y^2)(1+lz)+ezx^3 \end{array} \right. \nonumber \end{eqnarray}$

logistic

$x_{n+1}=rx_n(1-x_n)$

lorenz

$\begin{eqnarray} \left\{ \begin{array}{l} \frac{dx}{dt} = -px+py \\ \frac{dy}{dt} = -xz+rx-y \\ \frac{dz}{dt} = xy-bz \end{array} \right. \nonumber \end{eqnarray}$

mandelbrot

$\begin{eqnarray} z_{n+1}&=&z_n^2+c \nonumber \\ z_{n+1}&=&z_n^3+c \nonumber \\ z_{n+1}&=&z_n^4+c \nonumber \\ z_{n+1}&=&z_n^5+c \nonumber \\ z_{n+1}&=&\tan (z_n)+c \nonumber \\ z_{n+1}&=&\tan (z_n^4)+c \nonumber \\ z_{n+1}&=&\tan (z_n^27)+c \nonumber \\ z_{n+1}&=&\tan (z_n^256)+c \nonumber \\ z_{n+1}&=&\tan (z_n^3125)+c \nonumber \end{eqnarray}$

randomwalk

SIR

$\begin{eqnarray} \left\{ \begin{array}{l} \frac{dS}{dt} = -\beta SI \\ \frac{dI}{dt} = \beta SI - \gamma I \\ \frac{dR}{dt} = \gamma I \end{array} \right. \nonumber \end{eqnarray}$

💪😀 : S (Susceptible)
🦠🤧 : I (Infectious)
💉😷 : R (Removed/Recovered)

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