2003/03/21 by Hugo L. D. de S. Cavalcante, Cavalcante, Hugo L. D. de S., J. R. Rios Leite +1
Physics and Astronomy · #Chaos control and synchronization #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #nlin.CD
paper · pdf · doi:10.48550/arxiv.nlin/0303049
5 pages, 7 figures, published. Journal ref: Physical Review E, 66, 026210 (2002)
arxiv created 2003/03/21 · openalex publication_date 2003/03/21 · arxiv updated 2016/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The natural measure in a map with type-III intermittent chaos is used to define critical exponents for the average of a variable from a dynamical system near bifurcation. Numerical experiments were done with maps and verify the analytical predictions. Physical experiments to test the usefulness of such exponents to characterize the nonlinearity at bifurcations were done in a driven electronic circuit with diode as nonlinear element. Two critical exponents were measured: ν= 0.55 for the critical exponent of the average of the voltage across the diode and β= 0.62 for the exponent of the average length of the laminar phases. Both values are consistent with the predictions of a type-III intermittency of cubic nonlinearity. The averages of variables in intermittent chaotic systems is a technique complementary to the measurements of laminar phase histograms, to identify the nonlinear mechanisms. The averages exponents may have a broad application in ultrafast chaotic phenomena.