Dynamics towards the steady state applied for the Smith-Slatkin mapping

Imagem de Miniatura
de Oliveira, Juliano A. [UNESP]
N. Ramos, Larissa C. [UNESP]
Leonel, Edson D. [UNESP]
Título da Revista
ISSN da Revista
Título de Volume
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.
Critical exponents, Scaling invariance, Smith–Slatkin mapping
Como citar
Chaos, Solitons and Fractals, v. 108, p. 119-122.