Utilize este identificador para referenciar este registo: http://hdl.handle.net/10400.21/5137
Título: Scaling law in Saddle-node bifurcations for one-dimensional maps: A complex variable approach
Autor: Duarte, Jorge
Januário, Cristina
Martins, Nuno
Sardanyés, Josep
Palavras-chave: Scaling Law
Saddle-Node Bifurcations
One-Dimensional Maps
Complex Variable
Critical slowing-down
Intermittency
Cooperation
Transitions
Hypercycles
Extinctions
Models
Ghosts
Data: Jan-2012
Editora: Springer
Citação: DUARTE, J.; [et al] – Scaling law in Saddle-node bifurcations for one-dimensional maps: A complex variable approach. Nonlinear Dynamics. ISSN: 0924-090X. Vol. 67, nr. 1 (2012), pp. 541-547
Resumo: The study of transient dynamical phenomena near bifurcation thresholds has attracted the interest of many researchers due to the relevance of bifurcations in different physical or biological systems. In the context of saddle-node bifurcations, where two or more fixed points collide annihilating each other, it is known that the dynamics can suffer the so-called delayed transition. This phenomenon emerges when the system spends a lot of time before reaching the remaining stable equilibrium, found after the bifurcation, because of the presence of a saddle-remnant in phase space. Some works have analytically tackled this phenomenon, especially in time-continuous dynamical systems, showing that the time delay, tau, scales according to an inverse square-root power law, tau similar to (mu-mu (c) )(-1/2), as the bifurcation parameter mu, is driven further away from its critical value, mu (c) . In this work, we first characterize analytically this scaling law using complex variable techniques for a family of one-dimensional maps, called the normal form for the saddle-node bifurcation. We then apply our general analytic results to a single-species ecological model with harvesting given by a unimodal map, characterizing the delayed transition and the scaling law arising due to the constant of harvesting. For both analyzed systems, we show that the numerical results are in perfect agreement with the analytical solutions we are providing. The procedure presented in this work can be used to characterize the scaling laws of one-dimensional discrete dynamical systems with saddle-node bifurcations.
Peer review: yes
URI: http://hdl.handle.net/10400.21/5137
ISSN: 0924-090X
Aparece nas colecções:ISEL - Matemática - Artigos



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