An Algorithm for Approximate Solutions to Weakly Filtered Synchronous Control Systems and Nonlinear Renewal Processes

A multi-time perturbation algorithm is derived to study certain synchronous control systems and nonlinear renewal processes. The new methods presented here study singular perturbation problems for nonlinear Volterra integro-differential equations whose kernels are close to the Dirac delta function. The algorithm provides useful approximate solutions to weakly filtered phase-locked loop circuits and to nonlinear renewal equations describing certain population dynamics.