Fast Sampling of Evolving Systems with Periodic Trajectories

TL;DR

The paper introduces a fast, scalable method for evaluating periodic solutions of certain nonlinear ODE systems, leveraging integral representations and parallel computation to improve efficiency.

Contribution

It presents a novel approach to compute periodic solutions as sums of integrals, enabling faster evaluation for systems with nonlinear parametrization and state nonlinearities.

Findings

Method achieves significant speedup in evaluating periodic solutions.

Applicable to predator-prey and neuronal models.

Demonstrates scalability and practical utility.

Abstract

We propose a novel method for fast and scalable evaluation of periodic solutions of systems of ordinary differential equations for a given set of parameter values and initial conditions. The equations governing the system dynamics are supposed to be of a special class, albeit admitting nonlinear parametrization and state nonlinearities. The method enables to represent a given periodic solution as sums of computable integrals and functions that are explicitly dependent on parameters of interest and initial conditions. This allows invoking parallel computational streams in order to increase speed of calculations. Performance and practical implications of the method are illustrated with examples including classical predator-prey system and models of neuronal cells.