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Questions tagged [chaotic-systems]

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Calculating Lyapunov exponent for 3D system

I am trying to calculate the Lyapunov spectrum of a Lorenz model, \begin{align} \begin{split} \frac{dx}{dt} =& \sigma(y - x), \\ \frac{dy}{dt} =& x(\rho - z) - y, \\ \frac{dz}{dt} =& xy - \...
SHR's user avatar
  • 11
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1 answer
282 views

computing Lyapunov exponents numerically

I am trying to compute numerically the Lyapunov exponents of an ODE. I follow the method described in Parker, Chua "Practical Numerical Algorithms for Chaotic systems" There is also relevant ...
0x11111's user avatar
  • 101
4 votes
0 answers
193 views

SINDy Vs standard methods for system identification

I have been trying to understand the recently proposed Sparse Identification of Nonlinear Dynamics SINDy. Despite several attempts, I seem to fail to understand the difference between SINDy and the ...
Chenna K's user avatar
  • 944
2 votes
2 answers
450 views

Calculating Lyapunov exponent (LE) for pendulum using ellipsoid growth - code yields negative LEs

I was redirected here from physics stack exchange where hopefully my question is more appropriate. Per my advisor, I have read the textbook Chaos, an introduction to dynamical systems by Alligood, ...
t-osu's user avatar
  • 31
7 votes
2 answers
150 views

What good are hard-sphere event-driven molecular dynamics simulations in the face of chaos?

Simple hard-sphere dynamical systems can exhibit chaotic dynamics. Due to finite-precision arithmetic when implemented on a computer, the presence of chaos implies that for a given set of initial data,...
joshphysics's user avatar
1 vote
0 answers
222 views

How to implement chaotic sender and receiver with ordinary differential equations?

I am referring this paper, and trying to implement chaotic sender and receiver, to decode message, as given in section $V^{th}$ Chaotic signal masking. The process that I want to implement is figure ...
Userhanu's user avatar
  • 151
2 votes
0 answers
68 views

How to classify chaotic systems from a stability perspective

I am wondering what chaotic systems are from the perspective of numerical analysis. I am talking about 'deterministic chaos' such as for instance the 'logistic map' exhibits it. That is, the solution ...
highsciguy's user avatar
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0 votes
2 answers
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The "standard map" and Jupiter's red spot [closed]

Has there been an attempt to "explain" Jupiter's Red Spot via what is known as the standard map in chaos theory? I cannot be the first to notice the visual similarities...       &...
Joseph O'Rourke's user avatar