We propose a method for computing the Lyapunov exponents of renewal equations (delay equations of Volterra type) and of coupled systems of renewal and delay differential equations. The method consists in the reformulation of the delay equation as an abstract differential equation, the reduction of the latter to a system of ordinary differential equations via pseudospectral collocation, and the application of the standard discrete QR method. The effectiveness of the method is shown experimentally and a MATLAB implementation is provided.

翻译：本文提出了一种计算更新方程（沃尔泰拉型延迟方程）以及更新方程与延迟微分方程耦合系统李雅普诺夫指数的方法。该方法将延迟方程重新表述为抽象微分方程，通过伪谱配置法将其简化为常微分方程组，并应用标准离散QR方法。通过实验验证了该方法的有效性，并提供了MATLAB实现。