The Lorenz Attractor Simulink Model

The Lorenz System designed in Simulink. Two models included and a file to get the rottating 3d plot.

This is a design of the lorenz non-linear model, known as the Lorenz Attractor, defined by:

x'=σ*(y-x)

y'=x*(ρ-z)-y

z'=β*z+x*y

Where x=x(t), y=y(t), z=z(t) and t=[0,100].

For initial conditions:

x(0)=y(0)=z(0)=5 (defined inside the integrator blocks)

And system parameters:

σ=10,ρ=30,β=-3

In the first model, the refine factor has been changed to 4 for a smoother simulation and the states are saved in the workspace.

In the second model, the stepping options have been set to 5 so one can step forward the simulation every 5 seconds and observe the change in the 3 plots.

One can easily change the initial values and the system parameters and explore the different results.

After you run the system in Simulink, you can run the .m file to get the 3d plot being produced gradually in time.

This is included in [1].

https://www.youtube.com/watch?v=8kKkq2mk7gA

Video about the Lorenz system

https://www.youtube.com/watch?v=OXTS-d9HdB4

References:

[1] An introduction to Control Theory Applications Using Matlab, https://www.researchgate.net/publication/281374146_An_Introduction_to_Control_Theory_Applications_with_Matlab

[2] DIFFERENTIAL EQUATIONS,DYNAMICAL SYSTEMS, AND AN INTRODUCTION TO CHAOS, Hirsch, Smale, Devaney. Elsevier Academic Press.

Channel: https://www.youtube.com/@lazaros_moysis