Finite Cascades of Pitchfork Bifurcations and Multistability in Generalized Lorenz-96 Models
In this paper, we study a family of dynamical systems with circulant symmetry, which are obtained from the Lorenz-96 model by modifying its nonlinear terms. For each member of this family, the dimension <i>n</i> can be arbitrarily chosen and a forcing parameter <i>F</i> acts...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2020-12-01
|
| Series: | Mathematical and Computational Applications |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2297-8747/25/4/78 |
| _version_ | 1797545150744887296 |
|---|---|
| author | Anouk F. G. Pelzer Alef E. Sterk |
| author_facet | Anouk F. G. Pelzer Alef E. Sterk |
| author_sort | Anouk F. G. Pelzer |
| collection | DOAJ |
| description | In this paper, we study a family of dynamical systems with circulant symmetry, which are obtained from the Lorenz-96 model by modifying its nonlinear terms. For each member of this family, the dimension <i>n</i> can be arbitrarily chosen and a forcing parameter <i>F</i> acts as a bifurcation parameter. The primary focus in this paper is on the occurrence of finite cascades of pitchfork bifurcations, where the length of such a cascade depends on the divisibility properties of the dimension <i>n</i>. A particularly intriguing aspect of this phenomenon is that the parameter values <i>F</i> of the pitchfork bifurcations seem to satisfy the Feigenbaum scaling law. Further bifurcations can lead to the coexistence of periodic or chaotic attractors. We also describe scenarios in which the number of coexisting attractors can be reduced through collisions with an equilibrium. |
| first_indexed | 2024-03-10T14:11:23Z |
| format | Article |
| id | doaj.art-197625cd4c9a45b794729385eb73d97e |
| institution | Directory Open Access Journal |
| issn | 1300-686X 2297-8747 |
| language | English |
| last_indexed | 2024-03-10T14:11:23Z |
| publishDate | 2020-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematical and Computational Applications |
| spelling | doaj.art-197625cd4c9a45b794729385eb73d97e2023-11-21T00:05:11ZengMDPI AGMathematical and Computational Applications1300-686X2297-87472020-12-012547810.3390/mca25040078Finite Cascades of Pitchfork Bifurcations and Multistability in Generalized Lorenz-96 ModelsAnouk F. G. Pelzer0Alef E. Sterk1Bernoulli Institute for Mathematics, Computer Science, and Artificial Intelligence, University of Groningen, P.O. Box 407, 9700 AK Groningen, The NetherlandsBernoulli Institute for Mathematics, Computer Science, and Artificial Intelligence, University of Groningen, P.O. Box 407, 9700 AK Groningen, The NetherlandsIn this paper, we study a family of dynamical systems with circulant symmetry, which are obtained from the Lorenz-96 model by modifying its nonlinear terms. For each member of this family, the dimension <i>n</i> can be arbitrarily chosen and a forcing parameter <i>F</i> acts as a bifurcation parameter. The primary focus in this paper is on the occurrence of finite cascades of pitchfork bifurcations, where the length of such a cascade depends on the divisibility properties of the dimension <i>n</i>. A particularly intriguing aspect of this phenomenon is that the parameter values <i>F</i> of the pitchfork bifurcations seem to satisfy the Feigenbaum scaling law. Further bifurcations can lead to the coexistence of periodic or chaotic attractors. We also describe scenarios in which the number of coexisting attractors can be reduced through collisions with an equilibrium.https://www.mdpi.com/2297-8747/25/4/78Lorenz-96 modelcirculant symmetrypitchfork bifurcationsFeigenbaum scalingmultistability |
| spellingShingle | Anouk F. G. Pelzer Alef E. Sterk Finite Cascades of Pitchfork Bifurcations and Multistability in Generalized Lorenz-96 Models Mathematical and Computational Applications Lorenz-96 model circulant symmetry pitchfork bifurcations Feigenbaum scaling multistability |
| title | Finite Cascades of Pitchfork Bifurcations and Multistability in Generalized Lorenz-96 Models |
| title_full | Finite Cascades of Pitchfork Bifurcations and Multistability in Generalized Lorenz-96 Models |
| title_fullStr | Finite Cascades of Pitchfork Bifurcations and Multistability in Generalized Lorenz-96 Models |
| title_full_unstemmed | Finite Cascades of Pitchfork Bifurcations and Multistability in Generalized Lorenz-96 Models |
| title_short | Finite Cascades of Pitchfork Bifurcations and Multistability in Generalized Lorenz-96 Models |
| title_sort | finite cascades of pitchfork bifurcations and multistability in generalized lorenz 96 models |
| topic | Lorenz-96 model circulant symmetry pitchfork bifurcations Feigenbaum scaling multistability |
| url | https://www.mdpi.com/2297-8747/25/4/78 |
| work_keys_str_mv | AT anoukfgpelzer finitecascadesofpitchforkbifurcationsandmultistabilityingeneralizedlorenz96models AT alefesterk finitecascadesofpitchforkbifurcationsandmultistabilityingeneralizedlorenz96models |