 Numerical approximations on the transient analysis of bioelectric phenomena at long time scales via the Mittag-Leffler functionEnrique Hernández-Balaguera Chaos, Solitons & Fractals, 2021, vol. 145, issue C Abstract: This paper discusses the complexity of distributed relaxation processes in biological systems, particularly with regard to the slowest timescale phenomena that influence the modeling of physiological events. Specifically, our main interest is to determine the optimal excitation time at which the transient response, described in terms of relatively slow decays and memory effects, can be considered negligible. We estimate the time scale required for the Mittag-Leffler function to reach and stay within a range about the final value (dc “pseudo-steady state”). From numerical computations, we consider the problem of approximating holding times with common and rational (Padé-type) asymptotic approximations for comparative purposes. It is important to understand the physiological processes and to explore new mathematical models, based on efficient approximations, in order to design safe, controllable, and effective protocols for the electrical stimulation of excitable cells and the characterization of biological tissues. Keywords: Fractional calculus; Mittag-Leffler function; Bioelectricity; Cell membrane; Biological tissue; Constant phase element (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:145:y:2021:i:c:s096007792100120x DOI: 10.1016/j.chaos.2021.110768 Access Statistics for this article Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros More articles in Chaos, Solitons & Fractals from Elsevier |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.