• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Advances in Difference Equations >Andronov–Hopf and Neimark–Sacker bifurcations in time-delay differential equations and difference equations with applications to models for diseases and animal populations
【24h】

Andronov–Hopf and Neimark–Sacker bifurcations in time-delay differential equations and difference equations with applications to models for diseases and animal populations

机译：Andronov-hopf和Neimark-sacker在时间延迟微分方程中分叉和差分方程，应用于疾病和动物种群的模型

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

摘要

In many areas, researchers might think that a differential equation model is required, but one might be forced to use an approximate difference equation model if data is only available at discrete points in time. In this paper, a detailed comparison is given of the behavior of continuous and discrete models for two representative time-delay models, namely a model for HIV and an extended logistic growth model. For each model, there are seven different time-delay versions because there are seven different positions to include time delays. For the seven different time-delay versions of each model, proofs are given of necessary and sufficient conditions for the existence and stability of equilibrium points and for the existence of Andronov–Hopf bifurcations in the differential equations and Neimark–Sacker bifurcations in the difference equations. We show that only five of the seven time-delay versions have bifurcations and that all bifurcation versions have supercritical limit cycles with one having a repelling cycle and four having attracting cycles. Numerical simulations are used to illustrate the analytical results and to show that critical times for Neimark–Sacker bifurcations are less than critical times for Andronov–Hopf bifurcations but converge to them as the time step of the discretization tends to zero.
机译：在许多领域，研究人员可能认为需要差动方程模型，但如果数据仅在离散点处可用，则可能被迫使用近似差分等式模型。在本文中，给出了两个代表性时间延迟模型的连续和离散模型的行为，即艾滋病毒的模型和扩展逻辑生长模型。对于每个模型，有七种不同的时延版本，因为存在七个不同的位置来包括时间延迟。对于每个型号的七种不同的时滞版本，给出了均衡点的存在和稳定性的必要和充分条件，以及在差分方程中的微分方程和Neimark-Sacker分叉中存在的Andronov-Hopf分叉的存在。我们表明，只有七个时延版本中的五个具有分叉，并且所有分叉版本都具有超临界极限循环，其中一个具有排斥循环和吸引循环的四个。数值模拟用于说明分析结果，并表明Neimark-Sacker分叉的临界时间小于Andronov-Hopf分叉分叉的临界时间，而是随着离散化的时间步长而收敛到它们趋于零。

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