Research on Stability and Bifurcation for Two-Dimensional Two-Parameter Squared Discrete Dynamical Systems

Limei Liu () and Xitong Zhong
Additional contact information
Limei Liu: College of Applied Mathematics, Jilin University of Finance and Economics, Changchun 130117, China
Xitong Zhong: College of Applied Mathematics, Jilin University of Finance and Economics, Changchun 130117, China

Mathematics, 2024, vol. 12, issue 15, 1-15

Abstract: This study investigates a class of two-dimensional, two-parameter squared discrete dynamical systems. It determines the conditions for local stability at the fixed points for these proposed systems. Theoretical and numerical analyses are conducted to examine the bifurcation behavior of the proposed systems. Conditions for the existence of Naimark–Sacker bifurcation, transcritical bifurcation, and flip bifurcation are derived using center manifold theorem and bifurcation theory. Results of the theoretical analyses are validated by numerical simulation studies. Numerical simulations also reveal the complex bifurcation behaviors exhibited by the proposed systems and their advantage in image encryption.

Keywords: two-dimensional two-parameter squared discrete dynamical systems; Naimark–Sacker bifurcation; transcritical bifurcation; flip bifurcation; stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/15/2423/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/15/2423/ (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:12:y:2024:i:15:p:2423-:d:1449695

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 ().