Effect of Discrete Time Delays On The Stability of
A Dynamical System

I. C. Eli; E. N. Ekaka-a

doi:https://doi.org/10.14445/22315373/IJMTT-V67I8P505

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 67 | Issue 8 | Year 2021 | Article Id. IJMTT-V67I8P505 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I8P505

Effect of Discrete Time Delays On The Stability of A Dynamical System

I. C. Eli, E. N. Ekaka-a

Citation :

I. C. Eli, E. N. Ekaka-a, "Effect of Discrete Time Delays On The Stability of A Dynamical System," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 8, pp. 45-49, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I8P505

Abstract

In this study, the effect of discrete time delays on the stability of a dynamical system was considered. On the implementation of the computational techniques called ODE15s, it is shown that the dynamical system is dominantly unstable. It is also observed from the results that as the discrete time delays is increased then the yeast species 2 (Candida Parapsilosis) dominates yeast species 1 (Candida Albican) which implies thatyeast species 2will drive yeast species 1into extinction.

Keywords

Time delays, stability, dynamical system and ODE15s.

References

[1] Burden, R. L and Faires, J. D., Numerical Analysis, ninth edition, Canada., (2011).
[2] Patrice, N., Contribution to the control theory of some partial functional integrodifferential equations in Banach spaces. A Ph.D thesis presented to the Department of Pure and Applied Mathematics (PAM), African University of Science and Technology, Abuja. Nigeria., (2016).
[3] George, I, Atsu, J. U. and Ekaka-a, E. N., Deterministic Stabilization of a Dynamical System using a computational approach. International Journal of Advanced Engineering, Management and Science (IJAEMS), 4(1) (2018) 2454 – 1311.
[4] Glendenning, P., Stability, Instability and Chaos; an introduction to the theory of nonlinear differential equations, Cambridge, (1994) 25 – 36.
[5] Hwang, C. and Cheng, Y. C., A note on the use of the Lambert W. function in the stability analysis of time-delay systems. Automatic, 41(11) (2005) 1979 – 1985.
[6] Wang, Z. H., Numerical Stability test of neutral delay differential equations. Mathematical problems in Engineering, article Id 698043., (2008).
[7] Akpodee, R. E. and Ekaka-a, E. N., Deterministic stability analysis using a numerical simulation approach, 300k of proceedings – Academic Conference Publications and Research International on Sub-Sahara African Potentials in the new millennium, 3(1) (2015).
[8] Shukla J. B; Agarwal, A. Dubey, B and Sinha, P., Existence and Survival of two competing species in a polluted environment: a mathematical model, Journal of Biological Systems, 9(2) (2001) 89 – 103.
[9] Shukla J.B; Sharma S., Dubey B. and Sinha P., Modelling the survival of a resource dependent population: Effects of toxicants (pollutants) emitted from external sources as well as formed by its precursors, Nonlinear Analysis: Real World Application, (2009) 54 – 70.
[10] Ekaka-a, E. N. and Nafo, N. M., Stabilizing a mathematical model of stock market population system, Scientia Africa, 11(1) (2012) 92 – 97.
[11] Yan Y. and Ekaka-a, E. N., Stability of a mathematical model of population system. Journal of the Franklin institute. 348(10) (2011) 2744 – 2758.
[12] Abrams, P. A. and Wilson, W. G., Coexistence of competitors in meta communities due to spatial variation in resource growth rates, does R* predict the outcome of competition? American Naturalist, 7 (2004) 929 – 940.