IJPAM: Volume 93, No. 4 (2014)

CRITICAL SLOWING DOWN IN
BIOLOGICAL BISTABLE MODELS

R.A. Alharbey$^1$, L.A.M. Nejad$^2$, S. Lynch$^2$, S.S. Hassan$^{2,3}$
$^1$Mathematics Department
Faculty of Science
King Abdul-Aziz University
P.O. Box 42696, Jeddah, 21551, KINGDOM OF SAUDI ARABIA
$^2$School of Computing, Maths. & Digital Technology
Manchester Metropolitan University
Manchester M1 5GD, UK
$^3$Department of Mathematics
College of Science
University of Bahrain
P.O. Box 32038, KINGDOM OF BAHRAIN


Abstract. We investigate both analytically and computationally, the bistable behaviour in some biological mathematical models, namely: spruce budworm infestations, the Thomas reaction model and the activator-inhibitor model of Gierer-Meinhardt.

Bistable behaviour is achieved by treating some of the concentration, supply, degradation and reaction rates as control parameters. Critical slowing down in the switching time response due to perturbed control parameters is examined at the critical points of the bistable curves. Switching between stable states may occur sharply, monotonically, non-monotonically or via oscillations, depending on the nonlinear feedback process. The scaling for the switching delay time fits the inverse square root law $\beta^{-\frac{1}{2}}$ for the three models ($\beta$ is the perturbation of the control parameter).

Received: March 26, 2014

AMS Subject Classification:

Key Words and Phrases: bistable behaviour, critical slowing down, mathematical models in biology

Download paper from here.




DOI: 10.12732/ijpam.v93i4.8 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 93
Issue: 4
Pages: 581 - 602

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).