Chaotic intermittency with non-differentiable M(x) function

Abstract

One-dimensional maps showing chaotic intermittency with discontinuous reinjection probability density functions are studied. For these maps, the reinjection mechanism possesses two different processes. The M function methodology is applied to analyze the complete reinjection mechanism and to determine the discontinuous reinjection probability density function. In these maps, the function M(x) is continuous and non-differentiable. Theoretical equations are found for the function M(x) and for the reinjection probability density function. Finally, the theoretical results are compared with numerical data finding high accuracy.

Review of Chaotic Intermittency

“…Two new methodologies together with their theoretical background to obtain the RPD function were introduced in recent years. One of them is the M function methodology [56][57][58][59][60][61][62][63][64]. This methodology introduces a generalized power law for the RPD.…”