Equivalence of MTS and CMR methods on the normal form of Turing–Hopf bifurcation in delayed reaction–diffusion equations

Yuting Ding and Pei Yu

Chaos, Solitons & Fractals, 2026, vol. 202, issue P1

Abstract: In the study of dynamics and bifurcations of delay differential systems, computing the normal form associated with a singular point is both unavoidable and often technically challenging. Developing efficient computational methods or algorithms for such systems is therefore of great importance for the analysis of real-world problems. The multiple time scales (MTS) method is frequently applied in physics and engineering, but it lacks mathematical rigorousness. In contrast, the center manifold reduction (CMR) method is founded on rigorous mathematical theory, yet it is difficult to apply to practical problems. In this paper, we establish the third-order equivalence of the MTS and CMR methods in computing the normal form of Turing–Hopf bifurcation in general delayed reaction–diffusion equations with advection-diffusion and nonlocal effects. This result provides a rigorous mathematical foundation for applying the simpler MTS method to bifurcation problems in delayed reaction–diffusion systems. An illustrative example is presented, comparing the normal forms obtained by the two approaches and verifying the theoretical results.

Keywords: Reaction–diffusion equation; Advection diffusion; Nonlocal effect; MTS; CMR; Turing–Hopf bifurcation; Normal form (search for similar items in EconPapers)
Date: 2026
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077925014985
Full text for ScienceDirect subscribers only

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:eee:chsofr:v:202:y:2026:i:p1:s0960077925014985

DOI: 10.1016/j.chaos.2025.117485

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().