论文标题
通过伪近似的续签方程的数值分叉分析
Numerical bifurcation analysis of renewal equations via pseudospectral approximation
论文作者
论文摘要
我们通过普通微分方程提出了非线性更新方程的近似值。我们认为综合状态绝对是连续的，并且满足延迟微分方程。通过将伪谱方法应用于微分方程的抽象公式，我们获得了普通微分方程的近似系统。我们提出了平衡和相关特征根的收敛证明，并使用生态学和流行病学中的一些模型来说明对均衡和周期性解决方案进行数值分叉分析的方法的好处。数值模拟表明，新近似系统的实现效率是[Breda等人，Siam杂志在应用动力学系统上的最初提出的效率，2016年]，因为它避免了代数方程的数值反转。
We propose an approximation of nonlinear renewal equations by means of ordinary differential equations. We consider the integrated state, which is absolutely continuous and satisfies a delay differential equation. By applying the pseudospectral approach to the abstract formulation of the differential equation, we obtain an approximating system of ordinary differential equations. We present convergence proofs for equilibria and the associated characteristic roots, and we use some models from ecology and epidemiology to illustrate the benefits of the approach to perform numerical bifurcation analyses of equilibria and periodic solutions. The numerical simulations show that the implementation of the new approximating system is ten times more efficient than the one originally proposed in [Breda et al, SIAM Journal on Applied Dynamical Systems, 2016], as it avoids the numerical inversion of an algebraic equation.
