Bifurcation Behavior and Hybrid Controller Design of a 2D Lotka–Volterra Commensal Symbiosis System Accompanying Delay

Qingyi Cui, Changjin Xu (), Wei Ou, Yicheng Pang, Zixin Liu, Peiluan Li and Lingyun Yao
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Qingyi Cui: School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China
Changjin Xu: Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang 550025, China
Wei Ou: School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China
Yicheng Pang: School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China
Zixin Liu: School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China
Peiluan Li: School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China
Lingyun Yao: Library, Guizhou University of Finance and Economics, Guiyang 550025, China

Mathematics, 2023, vol. 11, issue 23, 1-23

Abstract: All the time, differential dynamical models with delay has witness a tremendous application value in characterizing the internal law among diverse biological populations in biology. In the current article, on the basis of the previous publications, we formulate a new Lotka–Volterra commensal symbiosis system accompanying delay. Utilizing fixed point theorem, inequality tactics and an appropriate function, we gain the sufficient criteria on existence and uniqueness, non-negativeness and boundedness of the solution to the formulated delayed Lotka–Volterra commensal symbiosis system. Making use of stability and bifurcation theory of delayed differential equation, we focus on the emergence of bifurcation behavior and stability nature of the formulated delayed Lotka–Volterra commensal symbiosis system. A new delay-independent stability and bifurcation conditions on the model are presented. By constructing a positive definite function, we explore the global stability. By constructing two diverse hybrid delayed feedback controllers, we can adjusted the domain of stability and time of appearance of Hopf bifurcation of the delayed Lotka–Volterra commensal symbiosis system. The effect of time delay on the domain of stability and time of appearance of Hopf bifurcation of the model is given. Matlab experiment diagrams are provided to sustain the acquired key outcomes.

Keywords: Lotka–Volterra commensal symbiosis system; peculiarity of solution; Hopf bifurcation; stability; hybrid controller (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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