2025/09/17 by Lucas MacQuarrie, Pei Yu, MacQuarrie, Lucas +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Differential Equations and Numerical Methods #Gene Regulatory Network Analysis #Mathematical theory #Oscillation (cell signaling) #Perturbation (astronomy) #Perturbation theory (quantum mechanics) #Relaxation (psychology) #Simple (philosophy) #Singular perturbation #stochastic dynamics and bifurcation
paper · pdf · doi:10.1142/s021812742630020x
published in International Journal of Bifurcation and Chaos 36(09) (World Scientific)
openalex created_date 2025/10/10 · openalex publication_date 2026/04/04 · openalex updated_date 2026/08/05
Simple conditions have been developed in [Zhang, W., Wahl, L. & Yu, P. [2014] “Viral blips may not need a trigger: How transient viremia can arise in deterministic in-host models,” SIAM Rev. 56, 127–155; Yu, P. & Wang, X. [2019] “Analysis on recurrence behavior in oscillating networks of biologically relevant organic reactions,” Math. Biosci. Eng. 16, 5263–5286], which are used to identify the existence of slow–fast relaxation oscillations that appear in differential systems, where the geometric singular perturbation theory is not applicable. In this study, we present seven models which fail to satisfy these conditions, yet still show recurrence phenomena, that motivate us to generalize these conditions to establish new simple hypothetical conditions for identifying slow–fast relaxation oscillations and providing arguments toward the development of a mathematical theory.