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Advisor(s)
Abstract(s)
In this paper, we study the dynamics and bifurcation properties of a three-parameter family
of 1D Gompertz’s growth functions, which are defined by the population size functions of the
Gompertz logistic growth equation. The dynamical behavior is complex leading to a diversified
bifurcation structure, leading to the big bang bifurcations of the so-called “box-within-a-box”
fractal type. We provide and discuss sufficient conditions for the existence of these bifurcation
cascades for 1D Gompertz’s growth functions. Moreover, this work concerns the description
of some bifurcation properties of a Hénon’s map type embedding: a “continuous” embedding
of 1D Gompertz’s growth functions into a 2D diffeomorphism. More particularly, properties
that characterize the big bang bifurcations are considered in relation with this coupling of two
population size functions, varying the embedding parameter. The existence of communication
areas of crossroad area type or swallowtails are identified for this 2D diffeomorphism.
Description
Keywords
Gompertz’s growth functions Population dynamics Big bang bifurcations Fold and flip bifurcations Embedding Difeomorfismo
Citation
ROCHA, J. Leonel; TAHA, Abdel-Kaddous; FOURNIER-PRUNARET,D. - Dynamical Analysis and Big Bang Bifurcations of 1D and 2D Gompertz’s Growth Functions. International Journal of Bifurcation and Chaos. ISSN 0218-1274. Vol. 26, N. º11, (2016), pp. 1-22
Publisher
World Scientific Publishing