Application Backstepping Method for Stabilizing and Solving Delayed Lotaka-Volterra with A Dynamical Graph
Article Sidebar
Main Article Content
Abstract
The primary goal of this work is to introduce dynamic graphs. Specifically, it will demonstrate that the matrix is the basic matrix of interconnections (adjacency). It functions to explain a particular graph D's nominal structure based on the presumption that graph D's lines' functional dependence that is, the matrix E's elements (edges) are arranged so, that equation. It can be obtained by two scalar equations and described the evolution of the dynamic matrix E over time.
To transform nonlinear differential equations derived from delay differential equations (DDEs) to linear differential equations, the purpose of using a dynamical graph. With this method, we applied on the biological problem of Lotaka-Volterra delay to studying stability by the backstepping method to delay differential equation (DDE) system to investigate stability on the impact of unsure interconnections between subsystems and solve it.
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
Tikrit Journal of Pure Science is licensed under the Creative Commons Attribution 4.0 International License, which allows users to copy, create extracts, abstracts, and new works from the article, alter and revise the article, and make commercial use of the article (including reuse and/or resale of the article by commercial entities), provided the user gives appropriate credit (with a link to the formal publication through the relevant DOI), provides a link to the license, indicates if changes were made, and the licensor is not represented as endorsing the use made of the work. The authors hold the copyright for their published work on the Tikrit J. Pure Sci. website, while Tikrit J. Pure Sci. is responsible for appreciate citation of their work, which is released under CC-BY-4.0, enabling the unrestricted use, distribution, and reproduction of an article in any medium, provided that the original work is properly cited.
References
1. Ruan S. On nonlinear dynamics of predator-prey models with discrete delay. Mathematical Modelling of Natural Phenomena. 2009;4(2):140-88. . https://doi.org/10.1051/mmnp/20094207
2. MOHAMMEDALI KH. METHODS FOR APPROXIMATING AND STABILIZING THE SOLUTION OF NONLINEAR RICCATI MATRIX DELAY DIFFERENTIAL EQUATION: SAINS MALAYSIA; 2018.
3. Zhou J, Wen C, Zhou J, Wen C. Adaptive control of time-varying nonlinear systems. Adaptive Backstepping Control of Uncertain Systems: Nonsmooth Nonlinearities, Interactions or Time-Variations. 2008:33-50.
4. Faeq IR, Abdalrahman SO. The Stability and Catastrophic Behavior of Finite Periodic Solutions in Non-Linear Differential Equations. Tikrit Journal of Pure Science. 2023;28(6):146-52. https://doi.org/10.25130/tjps.v28i6.1382
5. Adil HM, Tawfik IM. On Some Types of Matrices for Fan Plane Graph and Their Dual. Tikrit Journal of Pure Science. 2023;28(2):104-7. https://doi.org/10.25130/tjps.v28i2.1341
6. Al-Shumam AA. On the Domination Numbers of Certain Prism Graphs. Tik J of Pure Sci. 2022;27(1):90-8. https://doi.org/10.25130/tjps.v27i1.85
7. Šiljak D. Dynamic graphs. Nonlinear Analysis: Hybrid Systems. 2008;2(2):544-67.
8. Poleszczuk J, editor Delayed differential equations in description of biochemical reactions channels. XXI Congress of Differential Equations and Applications XI Congress of Applied Mathematics Ciudad Real; 2009.
9. Yskak T. Stability of Solutions of Delay Differential Equations. Siberian Advances in Mathematics. 2023;33(3):253-60.