New Criteria for Analyzing the Permanence, Periodic Solution, and Global Attractiveness of the Competition and Cooperation Model of Two Enterprises with Feedback Controls and Delays

Ahmadjan Muhammadhaji () and Yimamu Maimaiti
Additional contact information
Ahmadjan Muhammadhaji: College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China
Yimamu Maimaiti: College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China

Mathematics, 2023, vol. 11, issue 21, 1-18

Abstract: This paper studies a class of the non-autonomous competition and cooperation model of two enterprises involving discrete time delays and feedback controls. The paper proposes new criteria for analyzing the permanence, periodic solution, and global attractiveness of the model. The common mathematical techniques of the Lyapunov method, the continuation theorem, and the comparison principle are used in this paper. By means of the comparison principle and inequality techniques, the concept of permanence is investigated, which refers to the long-term survival of the enterprises within the competitive and cooperative framework. Meanwhile, using the continuation theorem, we establish conditions under which the system exhibits periodic behavior. Additionally, the global attractiveness of the system is derived by constructing multiple Lyapunov functionals. Finally, an example is presented to illustrate the applicability and validity of the proposed criteria in this paper. This example serves as a demonstration that showcases the main results derived from the analysis.

Keywords: competition and cooperation model; feedback control; permanence; global attractivity; discrete delay (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/21/4442/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/21/4442/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:21:p:4442-:d:1268196

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().