Impulsive stabilization and stability analysis for Gilpin–Ayala competition model involved in harmful species via LMI approach and variational methods

Ruofeng Rao, Xinsong Yang, Rongqiang Tang, Yulin Zhang, Xinggui Li and Lei Shi

Mathematics and Computers in Simulation (MATCOM), 2021, vol. 188, issue C, 571-590

Abstract: Firstly, a dynamic analysis for reaction–diffusion Gilpin–Ayala competition model involved in harmful species is considered under Dirichlet boundary value condition. Existence of multiple stationary solutions is verified by way of Mountain Pass lemma, and the local stability result of the null solution is obtained by employing linear approximation principle. Secondly, the authors utilize variational methods and linear matrix inequality (LMI) technique to deduce the LMI-based global exponential stability criterion on the null solution which becomes the unique stationary solution of a Markovian jumping ecosystem with delayed feedback under a reasonable boundedness assumption on population densities. Particularly, LMI criterion is involved in free weight coefficient matrix, which reduces the conservatism of the algorithm. In addition, a new impulse control stabilization criterion is also derived, in which no differentiable assumptions on time-delayed functions are proposed. Finally, three numerical examples show the effectiveness of the proposed methods. It is worth mentioning that the obtained stability criteria of null solution presented some useful hints on how to eliminate pests and bacteria.

Keywords: Gilpin–Ayala competition model; Linear matrix inequality (LMI); Mountain Pass lemma; Variational methods; Markovian jumping; Impulse control on stabilization (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:188:y:2021:i:c:p:571-590

DOI: 10.1016/j.matcom.2021.04.025

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