Lectures:

In this page we'll post useful information about the lectures: source codes, data, references, etc...

• Introduction
• One-dimensional flows
• Bifurcations
• Two-dimensional flows
• Chaos
• Synchronization
• Bottom of page

Software/Goodies:

• A practical introduction to Matlab (HTML [PDF])
• Matlab Help
• Maple Workshop notes
• Matlab GUI for differential equations: dfield and pplane.
• XXP/AUTO: webpage/dowload, tutorial, sample ode files.

Lab:
GMCS-422 computer lab

Intro:

• Fractal: basin of attraction for an oscillating magnet: [ more info ]
  
  
  

• Fractal: the Mandelbrot set: self similarity (click on image)
  

• Sensitive dependence to intial conditions: the butterfly effect.
  • Lorenz attractor demo
  
  
  
  • The Lorenz attractor: lorenzmio.m, threeplot.m
    
  
  
  • The Rossler attractor: Rossler.m, threeplot.m
    
  
  
  • Sensitive dependence to ICs: sensitive.m
    

One-dimensional flows:

• Matlab example of ode45.m: the Lorenz system: lorenz_ode45.m
  
• Matlab GUI for differential equations: dfield and pplane.

Bifurcations:

• Transcritical bifurcation over a bifurcation curve (Ex 3.2.1): TC_bif.mws
  
• Subcritical Pitchfork bifurcation: pitchfork.mws
  
• insect Outbreak: outbreak.m, plotisosurface.m
  

Two-dimensional flows:

• Approximating the manifolds of a fixed point: manifold_approx.mws
  

Chaos:

• Lorenz attractor demo



• The Lorenz attractor: lorenzmio.m, threeplot.m
  


• Sensitive dependence to ICs: sensitive.m
  

• lorenz map: lorenz_map.m
  


• Extensible pendulum [For more details please read: 'Regular and Chaotic Behaviour in an Extensible Pendulum'. R. Carretero-González, H.N. Núñez-Yépez and A.L. Salas-Brito. Eur. J. Phys. 15, 3 (1994) 139-148. Abstract, PDF.]
  
  • Poincare sections:
    
  • Phase space deformation:
    
  • Chaos in the extensible pendulum: driver.m, ext_pend_potential.m, ext_pend_ODEs.m, pendulum_shot.m, ext_pend.mws,
    
  
  
• Transition to chaos in the magnetic pendulum: MagPend.ppt