Dynamics of a Two-Dimensional Slow-Fast Belousov-Zhabotinsky Model

被引：0

作者：

Xu, Ruihan ^{[1
]}

Sun, Ming ^{[1
]}

Zhang, Xiang ^{[2
,3
]}

机构：

[1] Shanghai Jiao Tong Univ, Sch Math Sci, Shanghai 200240, Peoples R China

[2] Shanghai Jiao Tong Univ, Sch Math Sci, MOE LSC, Shanghai 200240, Peoples R China

[3] Shanghai Jiao Tong Univ, CMA Shanghai, Shanghai 200240, Peoples R China

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2024年 / 23卷 / SUPPL 1期

关键词：

Belousov-Zhabotinsky differential systems; Slow-fast systems; Global stability; Relaxation oscillation; Canard explosion; SINGULAR PERTURBATION-THEORY; CANARD; OSCILLATIONS;

D O I：

10.1007/s12346-024-01139-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For the reduced two-dimensional Belousov-Zhabotinsky slow-fast differential system, the known results are the existence of one limit cycle and its stability for particular values of the parameters. Here, we characterize all dynamics of this system except one degenerate case. The results include global stability of the positive equilibrium, supercritical and subcritical Hopf bifurcations, the existence of a canard explosion and relaxation oscillation, and the coexistence of one nest of two limit cycles with the outer one originating from the supercritical Hopf bifurcation at one canard point and the inner one from the subcritical Hopf bifurcation at another canard point. This last one is a new dynamical phenomenon.

引用

页数：19

共 50 条

[31] On the slow-fast dynamics of a tri-trophic food chain model with fear and Allee effects [J].

Salman, Sanaa Moussa ;

Shchepakina, Elena .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2024, 47 (11) :8985-9003

[32] Perturbation on dynamics of ferroin-catalyzed Belousov-Zhabotinsky reaction by monomer N-isopropylacrylamide and poly(N-isopropylacrylamide) [J].

Lateef, Shafia ;

Ganaie, Nadeem Bashir ;

Peerzada, Ghulam Mustafa .

POLYMER BULLETIN, 2022, 79 (05) :2777-2798

[33] REDUCTION OF SLOW-FAST PERIODIC SYSTEMS WITH APPLICATIONS TO POPULATION DYNAMICS MODELS [J].

Marva, M. ;

Poggiale, J. -C. ;

Bravo De La Parra, R. .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2012, 22 (10)

[34] SMOOTH TO DISCONTINUOUS SYSTEMS: A GEOMETRIC AND NUMERICAL METHOD FOR SLOW-FAST DYNAMICS [J].

Dieci, Luca ;

Elia, Cinzia .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2018, 23 (07) :2935-2950

[35] Slow-fast dynamics of a time-delayed electro-optic oscillator [J].

Weicker, Lionel ;

Erneux, Thomas ;

D'Huys, Otti ;

Danckaert, Jan ;

Jacquot, Maxime ;

Chembo, Yanne ;

Larger, Laurent .

PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2013, 371 (1999)

[36] Slow-fast oscillatory dynamics and phantom attractors in stochastic modeling of biochemical reactions [J].

Bashkirtseva, Irina ;

Ryashko, Lev .

CHAOS, 2022, 32 (03)

[37] Geometric Desingularization in Slow-Fast Systems with Application to the Glycolytic Oscillations Model [J].

Kosiuk, Ilona ;

Szmolyan, Peter .

NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS I-III, 2010, 1281 :235-+

[38] CANARD CYCLE IN A SLOW-FAST BITROPHIC FOOD CHAIN MODEL IN CHEMOSTAT [J].

Li, Jun .

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2024, 14 (03) :1360-1373

[39] Bursting during intermittency route to thermoacoustic instability: Effects of slow-fast dynamics [J].

Tandon, Shruti ;

Pawar, Samadhan A. ;

Banerjee, Subham ;

Varghese, Alan J. ;

Durairaj, Premraj ;

Sujith, R. I. .

CHAOS, 2020, 30 (10)

[40] On analysis of inputs triggering large nonlinear neural responses Slow-fast dynamics in the Wendling neural mass model [J].

Hebbink, Jurgen ;

van Gils, Stephan A. ;

Meijer, Hil G. E. .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2020, 83

← 1 2 3 4 5 →