Dynamical Analysis and Big Bang Bifurcations of 1D and 2D Gompertz's Growth Functions
| Autor: | Danièle Fournier-Prunaret, J. Leonel Rocha, Abdel-Kaddous Taha |
|---|---|
| Přispěvatelé: | Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA), Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT) |
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Big Bang
Population dynamics Gompertz function Type (model theory) 01 natural sciences 010305 fluids & plasmas Gompertz’s growth functions Fractal Big bang bifurcations 0103 physical sciences Applied mathematics [NLIN]Nonlinear Sciences [physics] Logistic function 010301 acoustics Engineering (miscellaneous) Bifurcation Mathematics Applied Mathematics Mathematical analysis Fold and flip bifurcations Modeling and Simulation [NLIN.NLIN-CD]Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD] Embedding Diffeomorphism Difeomorfismo |
| Zdroj: | International journal of bifurcation and chaos in applied sciences and engineering International journal of bifurcation and chaos in applied sciences and engineering, World Scientific Publishing, 2016, 26 (11), ⟨10.1142/S0218127416300305⟩ International journal of bifurcation and chaos in applied sciences and engineering, 2016, 26 (11), ⟨10.1142/S0218127416300305⟩ Repositório Científico de Acesso Aberto de Portugal Repositório Científico de Acesso Aberto de Portugal (RCAAP) instacron:RCAAP |
| ISSN: | 0218-1274 1793-6551 |
| DOI: | 10.1142/S0218127416300305⟩ |
| Popis: | International audience; 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. |
| Databáze: | OpenAIRE |
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