Nonlinear-Systems-Chaos
Nonlinear-Systems-Chaos copied to clipboard
Non-Linear Dynamic Systems
Nonlinear System Dynamics
Nonlinear Dynamics Systems
1-Dimensional Systems
Logistic Map
![](https://github.com/yiqiangjizhang/Nonlinear-Systems-Chaos/raw/main/1-Logistic-Map/logistic_map_r_0_4.png)
Euler Method
![](https://github.com/yiqiangjizhang/Nonlinear-Systems-Chaos/raw/main/2-Euler-Method/euler_approx.png)
Fixed Points Stability
![](https://github.com/yiqiangjizhang/Nonlinear-Systems-Chaos/raw/main/3-Fixed-Points-Stability/numerical_plot_dt.png)
Pitchfork Bifurcation
![](https://github.com/yiqiangjizhang/Nonlinear-Systems-Chaos/raw/main/4-Pitchfork-Bifurcation/subcritical_bif_hysteresis.png)
Neuron Model
![](https://github.com/yiqiangjizhang/Nonlinear-Systems-Chaos/raw/main/5-Neuron-Model/neuron_model_I_0.png)
Laser
![](https://github.com/yiqiangjizhang/Nonlinear-Systems-Chaos/raw/main/6-Laser/laser_turn_on_v_linear.png)
Adler equation
![](https://github.com/yiqiangjizhang/Nonlinear-Systems-Chaos/raw/main/9-Adler_eq/adler_eq_theta_time_init_cond.png)
Delayed Logistic equation
![](https://github.com/yiqiangjizhang/Nonlinear-Systems-Chaos/raw/main/10-Delayed-Logistic-Equation/delayed_logistic_eq.png)
Stability Test
![](https://github.com/yiqiangjizhang/Nonlinear-Systems-Chaos/raw/main/11-Stability-test/stability_diagram.png)
2-Dimensional Systems
2D System Phase Portrait
![](https://github.com/yiqiangjizhang/Nonlinear-Systems-Chaos/raw/main/Pons/2D-Systems/exercise2_1_2DLinearSystem_xy.png)
Direction Field
![](https://github.com/yiqiangjizhang/Nonlinear-Systems-Chaos/raw/main/Pons/2D-Systems/direction_field.png)
Chaotic Systems - Lorenz System
Let us consider the Lorenz system:
![](https://github.com/yiqiangjizhang/Nonlinear-Systems-Chaos/raw/main/Pons/Chaos/lorenz_system_rho_21_xz.png)
![](https://github.com/yiqiangjizhang/Nonlinear-Systems-Chaos/raw/main/Pons/Chaos/lorenz_system_rho_2415_xz.png)
![](https://github.com/yiqiangjizhang/Nonlinear-Systems-Chaos/raw/main/Pons/Chaos/lorenz_system_rho_30_xz.png)
Maximum Lyapunov Exponent
![](https://github.com/yiqiangjizhang/Nonlinear-Systems-Chaos/raw/main/Pons/Chaos/MLE_rho_21_x.png)
![](https://github.com/yiqiangjizhang/Nonlinear-Systems-Chaos/raw/main/Pons/Chaos/MLE_rho_2415_x.png)
Henon Map
![](https://github.com/yiqiangjizhang/Nonlinear-Systems-Chaos/raw/main/Pons/Chaos/henon_map.png)
Rossler System
![](https://github.com/yiqiangjizhang/Nonlinear-Systems-Chaos/raw/main/Pons/Chaos/rossler_system_xyz.png)
![](https://github.com/yiqiangjizhang/Nonlinear-Systems-Chaos/raw/main/Pons/Chaos/rossler_system_3D.png)
![](https://github.com/yiqiangjizhang/Nonlinear-Systems-Chaos/raw/main/Pons/Chaos/rossler_system_3D_all.png)