Theory of nonlinear dynamic systems Practice 7 Juhász János juhasz.janos@.itk.ppke.hu Szélig Ádám szelig.adam.gyorgy@itk.ppke.hu Goda Márton goda.marton.aron@itk.ppke.hu 2018.06.19.

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

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 email 2. the written document to the lecturer in paper The updates about the homework will be on the Wiki page of the class

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

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

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.

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

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

GUI++ Global parameters Automatic update Dynamic Event Management

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

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!

Tank you for your attention!

Matlab® supplement [X,Y] = meshgrid(x,y) replicates the grid vectors x and y to produce a full grid. equation= @(t,y) [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.