Math. Model. Nat. Phenom.
Volume 11, Number 4, 2016Ecology, Epidemiology and Evolution
|Page(s)||73 - 88|
|Published online||19 July 2016|
Fast Sampling of Evolving Systems with Periodic Trajectories
University of Leicester, Department of Mathematics, United Kingdom
2 Saint-Petersburg State Electrotechnical University, Department of Automation and Control Processes, Russia
* Corresponding author. E-mail: I.Tyukin@le.ac.uk
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 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.
Mathematics Subject Classification: 93B30 / 34A05 / 92B99 / 93B15
Key words: parameter estimation / nonlinear parametrization / parallel computation / integral representations
© EDP Sciences, 2016
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