Finite Cascades of Pitchfork Bifurcations and Multistability in Generalized Lorenz-96 Models

被引：0

作者：

Fetzer, Anouk F. G. ^{[1
]}

Sterk, Alef E. ^{[1
]}

机构：

[1] Univ Groningen, Bernoulli Inst Math Comp Sci & Artificial Intelli, POB 407, NL-9700 AK Groningen, Netherlands

来源：

MATHEMATICAL AND COMPUTATIONAL APPLICATIONS | 2020年 / 25卷 / 04期

关键词：

Lorenz-96; model; circulant symmetry; pitchfork bifurcations; Feigenbaum scaling; multistability; KALMAN FILTER; ERROR; PREDICTABILITY; UNIVERSALITY; DYNAMICS; PROOF;

D O I：

10.3390/mca25040078

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 n can be arbitrarily chosen and a forcing parameter F 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 n. A particularly intriguing aspect of this phenomenon is that the parameter values F 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.

引用

页数：19