Intrinsic electronic noise strength significantly alters a period doubling cascade to chaos

Abstract

For universality in the approach, it is customary to appropriately rescale problems to a single or a set of dimensionless equations with dimensionless quantities involved or to rescale the experimental setup to a suitable size for the laboratory conditions. Theoretical results and/or experimental findings are supposed to be valid for both the original and the rescaled problems. Here, however, we show in an analog computer model nonlinear system how the experimental results depend on the scale factor. This is because the intrinsic noise in the experimental setup remains constant as it is not affected by the scale factor. The particular case considered here offers a genuine noise-level effect in significantly altering a period-doubling cascade to chaos besides producing an expected truncated cascade. By monitoring with increasing value a significant parameter in the dynamics of the problem when searching for its solution, the system alien to the noise (or better said with a negligible noise level) follows a period-doubling cascade from period one to period two to period four to period eight and, eventually, chaos. However, if the intrinsic noise strength significantly enters the evolution, there appears a parallel sequence of period doublings different from the one found in the previous case.