4
votes
1answer
108 views

Poincaré maps and interpretation

What are Poincaré maps and how to understand them? Wikipedia says: In mathematics, particularly in dynamical systems, a first recurrence map or Poincaré map, named after Henri Poincaré, is ...
1
vote
0answers
59 views

Phase space volume and correlation dimension

This may seem trivial but I will appreciate help in determining the functional form of the probability density function (pdf) for the following case. Will highly appreciate some guidelines on how to ...
0
votes
0answers
27 views

Pick marginal circles in phase plot of a non-linear dynamic system

Context: I'm studying non-linear dynamics with Mathematica. Part of the problem: Given the following system: $\ddot{x} = x - x^3 - 0.2 \dot{x} + g(\sin(t) + \cos(2t))$, find two values of $g$ that ...
1
vote
1answer
111 views

Doubts regarding dimension of a system:Definitions and algorithms

I need to do phase reconstruction from time series data. In doing so, I encountered Takens' embedding theorem and Cao's minimum embedding dimension $d$ by nearest neighbor method. In paper "Optimal ...
2
votes
2answers
245 views

Phase volume contraction in dissipative systems

I am confused about phase-volume contraction in dissipative systems. Please help me catch the flaw in my understanding. From a macroscopic point of view I understand that a dynamic system tends to go ...