Abstract
Two-parameter diagrams obtained through the 0-1 test of chaos for nonlinear oscillatory continuous systems are presented in this paper. The diagrams are the results of a parallel approach to tackle enormous memory and computational time requirements due to the known oversampling problem associated with the use of the 0-1 test for chaos in continuous systems. Our rectangular diagrams with black-and-white shades of gray levels correspond to the numbers between 0 and 1 obtained as the result of the 0-1 test for chaos. A comparison between the two-parameter diagrams for the 0-1 test with the color bifurcation diagrams for oscillatory systems obtained from another method (period-n identification) is also considered. Illustrative examples are based on both the well-known Lorenz model and a model describing two equivalent electric arc circuits.
Highlights
The 0–1 test for chaos is a computational tool to analyze nonlinear dynamical systems based on their time series responses [1]–[5]
Parallel computations of two-parameter bifurcation diagrams for the 0–1 test for chaos were presented in this paper
Effectiveness of parallel computation has been analyzed from the point of view of the size N × N of the computed diagrams and the value of P, the number of threads
Summary
The 0–1 test for chaos is a computational tool to analyze nonlinear dynamical systems based on their time series responses [1]–[5]. THE 0–1 TEST FOR CHAOS WITH TWO VARYING PARAMETERS The nonlinear circuits shown in Fig. have been recently analyzed in [14] where their 1D and color 2D bifurcation diagrams were obtained through the identification of the number of local maximum values in one period of oscillation. For the circuits in Fig. we identify periodic oscillations with the value of n from 1 to as high as 64 Another novelty of this paper is an analysis of parallel computation of the two-parameter diagrams for the 0–1 test as we provide the values of the parallel efficiency coefficients and parallel computing times in comparison to the sequential (single processor) computations. Notice the difference between the coefficients E(P, 600) and the close values of tpar (360, 600) and tpar (720, 600)) above
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call