Attractors of convex maps with positive Schwarzian derivative in the presence of noise
A two-parameter family of the functions \[ f_{r,b}(x)=a_{r,b}x(1- x)(1+bx(1-3x+2(2-x)x^ 2)) \] where \(a_{r,b}=4r/(1+b/8)\) and \(x\in [0,1]\), is studied numerically. The \(f_{r,0}\) is the known logistic system. The authors obtain, by varying parameter b, two coexisting attractors. The role of positive Schwarzian derivative is discussed and the influence of noise on these bifurcation phenomena is mentioned as well.
scientific article; zbMATH DE number 3971820
scientific article