Dynamics towards the steady state applied for the Smith-Slatkin mapping. (March 2018)

• Record Type: Journal Article
• Authors: de Oliveira, Juliano A.; N. Ramos, Larissa C.; Leonel, Edson D.
• Is Part Of: Chaos, solitons and fractals. Volume 108(2018)
• Page Start: 119
• Page End: 122
• Publication Date: 2018-03
• Subjects: Smith–Slatkin mapping -- Critical exponents -- Scaling invariance; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2017.12.024
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: We derived explicit forms for the convergence to the steady state for a 1-D Smith–Slatkin mapping at and near at bifurcations. We used a phenomenological description with a set of scaling hypothesis leading to a homogeneous function giving a scaling law. The procedure is supported by numerical simulations and confirmed by a theoretical description. At the bifurcation we used an approximation transforming the difference equation into a differential one whose solution remount all scaling features. Near the bifurcation an investigation of fixed point stability leads to the decay for the stationary state. Simulations are made in the pitchfork, transcritical and period doubling bifurcations.