Averages and critical exponents in type-III intermittent chaos

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 a nonlinear element. Two critical exponents were determined at the same bifurcation: one from the fitting of the average voltage across the diode and the other one from the average length of the laminar phase events. 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 average exponents may have a broad application in ultrafast chaotic phenomena.