image thumbnail

Parameter Switching Algorithm

version 1.0.0 (1.76 KB) by Nikolay Kuznetsov
The Parameter Switching (PS) algorithm can be used to approximate the attractors of continuous-time chaotic systems like the Lorenz system

28 Downloads

Updated 15 Jan 2021

View License

The PS algorithm allows to approximate numerical attractors of chaotic dynamical systems depending on a single real control parameter $p\in R$, such as the Lorenz system, Rossler system, Chen system, Lotka-Volterras ystem, Rabinovich-Fabrikant system, Hindmarsh-Rose system, Lu system, classes of minimal networks and many others, which are modeled by the following Initial Value Problem (IVP):

\begin{equation}
\dot{x(t)}=f(x(t))+pAx(t), x(0)=x_0,

where $t\in[0,T]$, $T>0$, $x_0\in \mathbb{R}^n$, $A\in \mathbb{R}^{n\times n} is a constant matrix, and $f:\mathbb{R}^n\rightarrow \mathbb{R}^n$ is a continuous nonlinear function.

The code can be made via some convergent explicit fixed step-size $h$ numerical scheme, here the standard RK numerical scheme.
If every $h$ one switches $p$ within a chosen set of values, the obtained "switched" attractor $A^*$ approximates the "averaged" attractor $A^0$ obtained for $p$ replaced with the average value of the switched values.
Details on applications and algorithm convergence can be found on e.g.:

Marius-F. Danca, Convergence of a parameter switching algorithm for a class of nonlinear continuous systems and a generalization of Parrondo's paradox, Communications in Nonlinear Science and Numerical Simulation, 18(3), 500–510 (2013).

Marius-F. Danca, Michal Feckan, Nikolay Kuznetsov, Guanrong Chen, Attractor as a convex combination of a set of attractors, Communications in Nonlinear Science and Numerical Simulation, 2021, accepted

Marius-F. Danca, Random parameter-switching synthesis of a class of hyperbolic attractors, CHAOS, 18, 033111 (2008)

Cite As

Marius-F. Danca, Matlab code of the Parameter Switching algorithm

MATLAB Release Compatibility
Created with R2020b
Compatible with any release
Platform Compatibility
Windows macOS Linux

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!