Convergence to the stationary point in a discrete one-dimensional mapping
Hans Muller J. de Mendonça1; Edson Denis Leonel1; Juliano Antonio de Oliveira2
1 Universidade Estadual Paulista (UNESP), Instituto de Geociências e Ciências Exatas; 2 Universidade Estadual Paulista (UNESP), Câmpus de São João da Boa Vista
Resumo
Convergence to asymptotic steady state in several one dimensional maps as logistic, cubic and Hassell maps are characterized by considering a phenomenological description supported by numerical simulations and confirmed by a theoretical description. We aim study the Hassell map and as the control parameter is varied, bifurcations in the stationary points appear. At transcritical bifurcation the convergence to the fixed point is characterized by a decay exponent $\beta$ and near the bifurcation, the decay to the fixed point is exponential with a relaxation time given by a power law, which the slope is independent of the nonlinearity. The formalism is general and can be extended to other dissipative mappings.
Palavras-chave: Hassell mapping; Transcritical bifurcation; Lyapunov exponents; Fixed points ; Relaxations