...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Chaos >Scalings of mixed-mode regimes in a simple polynomial three-variable model of nonlinear dynamical systems
【24h】

Scalings of mixed-mode regimes in a simple polynomial three-variable model of nonlinear dynamical systems

机译：非线性动力系统的简单多项式三变量模型中混合模态的标度

获取原文
获取原文并翻译 | 示例
   

获取外文期刊封面封底 >>

       
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

We describe scaling laws for a control parameter for various sequences of bifurcations of the LS_n mixed-mode regimes consisting of single large amplitude maximum followed by n small amplitude peaks. These regimes are obtained in a normalized version of a simple three-variable polynomial model that contains only one nonlinear cubic term. The period adding bifurcations for LS_n patterns scales as 1 at low n and as 1~2 at sufficiently large values of n. Similar scaling laws 1/k at low k and 1/k~2 at sufficiently high values of k describe the period adding bifurcations for complex k(LS_n)(LS_(n+1)) patterns. A finite number of basic LS_n patterns and infinite sequences of complex k(LS_n)(LS_(n+1)) patterns exist in the model. Each periodic pattern loses its stability by the period doubling bifurcations scaled by the Feigenbaum law. Also an infinite number of the broken Farey trees exists between complex periodic orbits. A family of 1D return maps constructed from appropriate Poincare sections is a very fruitful tool in studies of the dynamical system. Analysis of this family of maps supports the scaling laws found using the numerical integration of the model.
机译：我们描述了LS_n混合模式方案的各种分叉序列的控制参数的缩放定律，其中LS_n混合模式方案由单个大振幅最大值和n个小振幅峰组成。这些形式是在仅包含一个非线性三次项的简单三变量多项式模型的归一化版本中获得的。对于LS_n模式，增加分叉的周期在低n时缩放为1 / n，在足够大的n值时缩放为1 / n〜2。在低k处类似的缩放定律1 / k和在k足够高的情况下有1 / k〜2描述了为复杂k（LS_n）（LS_（n + 1））模式添加分叉的周期。模型中存在有限数量的基本LS_n模式和无限个复杂的k（LS_n）（LS_（n + 1））模式序列。每个周期模式都会因费根鲍姆定律所缩放的周期翻倍而失去稳定性。在复杂的周期性轨道之间还存在无限数量的破碎的Farey树。从适当的Poincare部分构造的一维一维返回图家族是研究动力学系统的非常有用的工具。对这一系列地图的分析支持使用模型的数值积分找到的缩放定律。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号