Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL
Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL
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DOI：
10.1145/513001.513002
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发表时间：
2002-03-01
影响因子：
2.7
通讯作者：
Roose, D
中科院分区：
文献类型：
--
作者：
Engelborghs, K;Luzyanina, T;Roose, D
我们描述了DDE-BIFTOOL，一个Matlab软件包的数值分歧分析系统的延迟微分方程与几个固定的，离散的延迟。该软件包实现了稳态解和周期解的连续性及其稳定性分析。它还计算和继续稳定状态的折叠和霍普夫分叉，从后者，它可以切换到周期解的发出分支。我们描述的数值方法，该软件包的基础上，并说明其使用和功能，通过分析三个例子：两个模型的耦合神经元延迟反馈和模型的两个振荡器耦合延迟。
We describe DDE-BIFTOOL, a Matlab package for numerical bifurcation analysis of systems of delay differential equations with several fixed, discrete delays. The package implements continuation of steady state solutions and periodic solutions and their stability analysis. It also computes and continues steady state fold and Hopf bifurcations and, from the latter, it can switch to the emanating branch of periodic solutions. We describe the numerical methods upon which the package is based and illustrate its usage and capabilities through analysing three examples: two models of coupled neurons with delayed feedback and a model of two oscillators coupled with delay.