The folder contains a basic analysis for the main examples of Dynamical systems (discrete and continuos), as
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Logistic Map: one-dimensional discrete map
$x_{n+1} = r x_n (1-x_n)$ . -
Henon Map: two-dimensional discrete map
$x_{n+1}= 1 + y_n - a^2 x_n$ ,$y_{n+1} = b x_n$ . -
Lotka-Volterra Model: two-dimensional continuos model, describing predator-prey dynamics,
$\dot{x} = K_x x (1-y)$ ,$\dot{y} = -K_y y (1 - x)$ . -
Lorenz Model: three-dimensional continuos model
$\dot{x} = \sigma(y-x)$ ,$\dot{y} = rx - y - xz$ ,$\dot{z} = xy - bz$ . - In Other Dynamical Systems could be found others model, i.e. Standard Map.m.
Additionally, in the folder are some examples of Synchronization phenomena for coupled chaotic maps:
- Synchronization of coupled map in (1+1)-dimension lattice.
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Spatio-Temporal synchronization of coupled maps in (2+1)-dimension lattice.
Typical chaotic maps used are Bernoulli map
$f(x) = 2x \ \text{mod}(1)$ and Tend map ($f(x) = ax$ if$x \in [0,1/2]$ or$f(x) = a(1-x)$ if$x\in(1/2,1]$ ).