2017/01/20 by Dominique Delcourt, Delcourt, Dominique
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Chaos control and synchronization #Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation
paper · pdf · doi:10.48550/arxiv.1701.05796
openalex publication_date 2017/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the well known logistic map, the parameter of interest is weighted by a coefficient that decreases linearly when this parameter increases. Since such a linear decrease forms a specific case, we consider the more general case where this coefficient decreases nonlinearly as in a hyperbolic tangent relaxation of a system toward equilibrium. We show that, in this latter case, the asymptotic values obtained via iteration of the logistic map are considerably modified. We demonstrate that both the steepness of the nonlinear decrease as well as its upper and lower boundaries significantly alter the bifurcation diagram. New period doubling features and transitions to chaos appear, possibly leading to regimes with small periods. Computations with a variety of parameter values show that the logistic map can be significantly reordered in the case of a nonlinear growth rate.