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6.6 chaosys - integrate dynamical system given by a set of ordinary differential equations

chaosys gives the user the possibility to compute time series data for a couple of dynamical systems, among which are Lorenz, Chua, Roessler etc. This routine is not meant as a replacement for Matlab's suite of functions for solving ODEs, but as a fast way to generate some data sets to evaluate the processing capabilities of TSTOOL. The integration is done by an ODE solver using an Adams Pece scheme with local extrapolation [151]. It is at least faster than Matlab's native ODE solver. However, it is not possible to extend the set of systems without recompiling chaosys.

Syntax:

Input arguments:

Output arguments:

Example:

 
x = chaosys(20000, 0.025, [0.1 -0.1 0.02], 0);
plot(x(:,1));
Definitions of the ODEs:
The parameters of the odes are a vector of [a,b,...].
Lorenz:

$\displaystyle \frac{{\rm d}y_1}{{\rm d}t}$ $\displaystyle = a(y_1 - y_2)$    
$\displaystyle \frac{{\rm d}y_2}{{\rm d}t}$ $\displaystyle = by_1 - y_2 - y_1 y_3$    
$\displaystyle \frac{{\rm d}y_3}{{\rm d}t}$ $\displaystyle = y_1 y_2 + cy_3$    

Generalized Chua:

$\displaystyle \frac{{\rm d}y_1}{{\rm d}t}$ $\displaystyle = a(y_1 - by_2)$    
$\displaystyle \frac{{\rm d}y_2}{{\rm d}t}$ $\displaystyle = by_1 - y_2 + y_3$    
$\displaystyle \frac{{\rm d}y_3}{{\rm d}t}$ $\displaystyle = -cy_2$    

Duffing:

$\displaystyle \frac{{\rm d}y_1}{{\rm d}t}$ $\displaystyle = y_2$    
$\displaystyle \frac{{\rm d}y_2}{{\rm d}t}$ $\displaystyle = -y_1 - y_1^3 - by_2 + a\cos y_3$    
$\displaystyle \frac{{\rm d}y_3}{{\rm d}t}$ $\displaystyle = c$    

Rössler:

$\displaystyle \frac{{\rm d}y_1}{{\rm d}t}$ $\displaystyle = -y_2 - y_3$    
$\displaystyle \frac{{\rm d}y_2}{{\rm d}t}$ $\displaystyle = -y_1 + ay_2$    
$\displaystyle \frac{{\rm d}y_3}{{\rm d}t}$ $\displaystyle = b + y_3(y_1 - c)$    

Toda oscillator:

$\displaystyle \frac{{\rm d}y_1}{{\rm d}t}$ $\displaystyle = 1 + a\sin (bt) - by_2 - \exp y_1$    
$\displaystyle \frac{{\rm d}y_2}{{\rm d}t}$ $\displaystyle = y_1$    

van der Pol oscillator:

$\displaystyle \frac{{\rm d}y_1}{{\rm d}t}$ $\displaystyle = a\sin (bt) - c(by_2^2 - 1) - d^2y_1$    
$\displaystyle \frac{{\rm d}y_2}{{\rm d}t}$ $\displaystyle = y_1$    

pendulum:

$\displaystyle \frac{{\rm d}y_1}{{\rm d}t}$ $\displaystyle = a\sin (bt) - cby_2 - d\sin y_1$    
$\displaystyle \frac{{\rm d}y_2}{{\rm d}t}$ $\displaystyle = y_1$    


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Next: 6.7 corrsum - Computation Up: 6. Mex-Function Reference Previous: 6.5 cao - Determine   Contents
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