Hopf Bifurcation in a Delayed Equation with Diffusion Driven by Carrying Capacity

Yuanxian Hui, Yunfeng Liu and Zhong Zhao
Additional contact information
Yuanxian Hui: School of Mathematics and Statistics, Huanghuai University, Zhumadian 463000, China
Yunfeng Liu: Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, China
Zhong Zhao: School of Mathematics and Statistics, Huanghuai University, Zhumadian 463000, China

Mathematics, 2022, vol. 10, issue 14, 1-16

Abstract: In this paper, a delayed reaction–diffusion equation with carrying capacity-driven diffusion is investigated. The stability of the positive equilibrium solutions and the existence of the Hopf bifurcation of the equation are considered by studying the principal eigenvalue of an associated elliptic operator. The properties of the bifurcating periodic solutions are also obtained by using the normal form theory and the center manifold reduction. Furthermore, some representative numerical simulations are provided to illustrate the main theoretical results.

Keywords: Hopf bifurcation; time delay; reaction–diffusion equation; the ideal free distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/14/2382/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/14/2382/ (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:10:y:2022:i:14:p:2382-:d:857244

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 ().