论文标题
HOPF分叉延迟微分方程的伪谱近似
Pseudospectral approximation of Hopf bifurcation for delay differential equations
论文作者
论文摘要
伪型近似将DDE（延迟微分方程）降低为ODE（普通微分方程）。接下来可以使用ODE工具执行数值分叉分析。以示例为例，我们表明，这将产生一种有效且可靠的方法来定性以及定量分析某些DDE。为了证实该方法，我们接下来表明近似ODE的结构让人联想到沿DDE溶液的转换发生器的结构。然后，我们专注于HOPF分叉，然后利用这种相似性来揭示DDE和ODE分叉系数之间的联系，并证明当尺寸接近Infinity时，后者与前者的收敛性。
Pseudospectral approximation reduces DDE (delay differential equations) to ODE (ordinary differential equations). Next one can use ODE tools to perform a numerical bifurcation analysis. By way of an example we show that this yields an efficient and reliable method to qualitatively as well as quantitatively analyse certain DDE. To substantiate the method, we next show that the structure of the approximating ODE is reminiscent of the structure of the generator of translation along solutions of the DDE. Concentrating on the Hopf bifurcation, we then exploit this similarity to reveal the connection between DDE and ODE bifurcation coefficients and to prove the convergence of the latter to the former when the dimension approaches infinity.
