Synchronization of slow-fast systems

被引：16

作者：

Omelchenko, I. ^{[1
]}

Rosenblum, M. ^{[1
]}

Pikovsky, A. ^{[1
]}

机构：

[1] Univ Potsdam, Dept Phys & Astron, D-14476 Potsdam, Germany

来源：

EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS | 2010年 / 191卷 / 01期

关键词：

RELAXATION OSCILLATIONS; DYNAMICS; NEURONS; MODEL;

D O I：

10.1140/epjst/e2010-01338-4

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We describe different patterns of synchronization of two systems, each possessing oscillations on two very different time scales. Synchronization of slow and fast oscillations are characterized separately, leading to a possibility to observe partially synchronized states where, e. g., the slow motions are synchronous while the fast are desynchronized. As a first example we study two diffusively coupled Hindmarsh-Rose oscillators in the regime of regular or chaotic bursting and describe different synchronous states like phase synchronization of slow variables, burst and spike synchronization of fast variables, and complete synchronization. Next, we study two coupled four-dimensional model systems with chaotic slow dynamics and find phase synchronization of slow motion, complete and partially complete synchrony.

引用

页码：3 / 14

页数：12

共 50 条

[41] Reliability and robustness of oscillations in some slow-fast chaotic systems
Jaquette, Jonathan
Kedia, Sonal
Sander, Evelyn
Touboul, Jonathan D.
[J]. CHAOS, 2023, 33 (10)
[42] The Bifurcation of a Slow-Fast Separatrix Loop in a Family of Singular Systems
Kaleda, P. I.
[J]. DOKLADY MATHEMATICS, 2010, 82 (02) : 716 - 718
[43] Interaction of the folded Whitney umbrella and swallowtail in slow-fast systems
I. A. Bogaevsky
[J]. Proceedings of the Steklov Institute of Mathematics, 2012, 278 : 22 - 26
[44] Large Deviations and Importance Sampling for Systems of Slow-Fast Motion
Spiliopoulos, Konstantinos
[J]. APPLIED MATHEMATICS AND OPTIMIZATION, 2013, 67 (01): : 123 - 161
[45] On the global structure of normal forms for slow-fast Hamiltonian systems
M. Avendaño Camacho
Yu. Vorobiev
[J]. Russian Journal of Mathematical Physics, 2013, 20 : 138 - 148
[46] Large deviations for stochastic nonlinear systems of slow-fast diffusions with
Yuan, Shenglan
Schilling, Rene
Duan, Jinqiao
[J]. INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 2023, 148
[47] Linear singularly perturbed systems without slow-fast split
Artstein, Zvi
[J]. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2023, 86 (03) : 871 - 884
[48] Rate and Bifurcation Induced Transitions in Asymptotically Slow-Fast Systems
Jelbart, Samuel
[J]. SIAM Journal on Applied Dynamical Systems, 2024, 23 (03): : 1836 - 1869
[49] On the accuracy of conservation of adiabatic invariants in slow-fast Hamiltonian systems
Su, Tan
[J]. REGULAR & CHAOTIC DYNAMICS, 2012, 17 (01): : 54 - 62
[50] The bifurcation of a slow-fast separatrix loop in a family of singular systems
P. I. Kaleda
[J]. Doklady Mathematics, 2010, 82 : 716 - 718

← 1 2 3 4 5 →