1. Theory of nonlinear dynamic systems Practice 7
Juhász János
Szélig Ádám
Goda Márton

2. Project homework www.demonstrations.wolfram.com
Choose a Wolfram project from the list in the Wiki page of the class

3. Project homework
Choose a Wolfram project from the list in the Wiki page of the class, and fill the form (Wiki)
Implement the Wolfram project in Matlab, with GUI
Compare the results of your solution with the original one
Examine the model and write around 5 pages about it (background, simulation, mathematical properties, applications,…)
Hand in:
1. your code the instructors via
2. the written document to the lecturer in paper
The updates about the homework will be on the Wiki page of the class

4. Project homework Some requirements: For the written part:
references about the background,
figures about typical behaviors of the model
For the Matlab part:
Comments in the code
Input error check and handle (do not divide with zero, check if the input is numeric or not,…)
Automatic initial condition and plotting
Synchronization between the connected fields (e.g.: slider and edit text box)
Separate the GUI and the actual model if it is needed (structured program)
Avoid error messages

5. GUI Creating a GUI with GUIDE Drag&drop Proper Naming Convention
Event handling
Google is your Friend 

6. Lorenz system
The nonlinear and chaotic dynamics of a shallow fluid layer are investigated numerically using large-scale parallel numerical simulations
Very simplified model of flows or atmospheric circulation
Under certain parameter settings behave chaotically (rho>24.74)
We assume that the parameters are positive.

7. Lorenz system Gobally attracting attractor
The chaos is within the attractor
This chaos is permanent
Lorenz peak map: simple demonstration of the order in the chaos

8. Pendulum with excitation and attenuation
Different kind of chaos
After the transient the system reach a stable orbit
Transient chaos

9. GUI++
Global parameters
Automatic update
Dynamic Event Management

10. Error Handling Type checking of formal parameters Easy to operate
Parameter settings (default values)

11. Object-oriented programming / structuring
Why?
At the short of codes may seem difficult
At development it is essential
After clarification of input parameters =>
It is possible to sub-divide tasks
Can separately test!

12. Tank you for your attention!

13. Matlab® supplement
[X,Y] = meshgrid(x,y) replicates the grid vectors x and y to produce a full grid.
[y(2); y(1)]; [1. equ of the system; 2. equ of the system]
[t,y]=ode45(equation, [t0,tmax][Xinit,Yinit]); there are other solvers as well, first we try this
figure creates figure graphics objects. Figure objects are the individual windows on the screen in which the MATLAB software displays graphical output.
plot(x,y,how…) drawing, has many options
subplot(m,n,p) (divide the figure m*n parts, draws in the p th region)
contour(X,Y,Z), contour(X,Y,Z,n), and contour(X,Y,Z,v) draw contour plots of Z using X and Y to determine the x- and y-axis limits.