Stabilization of synchronous equilibria in regular dynamical networks with delayed coupling

被引：3

作者：

Maia, Daniel ^{[1
]}

Kurths, Juergen ^{[2
,3
]}

Yanchuk, Serhiy ^{[3
,4
]}

机构：

[1] Univ Fed Rural Pernambuco, Acad Unity Belo Jardim, BR-166 Belo Jardim, PE, Brazil

[2] Humboldt Univ, Dept Phys, D-12489 Berlin, Germany

[3] Potsdam Inst Climate Impact Res, D-14473 Potsdam, Germany

[4] Humboldt Univ, Inst Math, D-12489 Berlin, Germany

来源：

NONLINEAR DYNAMICS | 2023年 / 111卷 / 08期

关键词：

Oscillation death; Delayed systems; Stability; Synchronous equilibria; DIFFERENTIAL EQUATIONS; SYNCHRONIZATION; STABILITY; STATES; SPECTRUM; CHAOS;

D O I：

10.1007/s11071-022-08220-w

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

We consider the synchronization problem of dynamical networks with delayed interactions. More specifically, we focus on the stabilization of synchronous equilibria in regular networks where the degrees of all nodes are equal. By studying such control near a Hopf bifurcation, we obtain necessary and sufficient conditions for stabilization. It is shown that the stabilization domains in the parameter space reappear periodically with time-delay. We find that the frequency of reappearance of the control domains is linearly proportional to the number of cycle multipartitions of the network.

引用

页码：7377 / 7390

页数：14

共 71 条

[1] Synchronization in complex networks [J].

Arenas, Alex ;

Diaz-Guilera, Albert ;

Kurths, Jurgen ;

Moreno, Yamir ;

Zhou, Changsong .

PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 2008, 469 (03) :93-153

[2] Stability and bifurcations in neural fields with finite propagation speed and general connectivity [J].

Atay, FM ;

Hutt, A .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2005, 65 (02) :644-666

[3] Delay master stability of inertial oscillator networks [J].

Boerner, Reyk ;

Schultz, Paul ;

Uenzelmann, Benjamin ;

Wang, Deli ;

Hellmann, Frank ;

Kurths, Jurgen .

PHYSICAL REVIEW RESEARCH, 2020, 2 (02)

[4] Synchronization properties of network motifs: Influence of coupling delay and symmetry [J].

D'Huys, O. ;

Vicente, R. ;

Erneux, T. ;

Danckaert, J. ;

Fischer, I. .

CHAOS, 2008, 18 (03)

[5] Role of delay for the symmetry in the dynamics of networks [J].

D'Huys, O. ;

Fischer, I. ;

Danckaert, J. ;

Vicente, R. .

PHYSICAL REVIEW E, 2011, 83 (04)

[6] Cluster and group synchronization in delay-coupled networks [J].

Dahms, Thomas ;

Lehnert, Judith ;

Schoell, Eckehard .

PHYSICAL REVIEW E, 2012, 86 (01)

[7] Explosive synchronization enhanced by time-delayed coupling [J].

Dal'Maso Peron, Thomas Kaue ;

Rodrigues, Francisco A. .

PHYSICAL REVIEW E, 2012, 86 (01)

[8] Key role of coupling, delay, and noise in resting brain fluctuations [J].

Deco, Gustavo ;

Jirsa, Viktor ;

McIntosh, A. R. ;

Sporns, Olaf ;

Koetter, Rolf .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 2009, 106 (25) :10302-10307

[9] DYNAMIC STABILITY OF STEADY-STATES AND STATIC STABILIZATION IN UNBRANCHED METABOLIC PATHWAYS [J].

DIBROV, BF ;

ZHABOTINSKY, AM ;

KHOLODENKO, BN .

JOURNAL OF MATHEMATICAL BIOLOGY, 1982, 15 (01) :51-63

[10] Synchronizing Distant Nodes: A Universal Classification of Networks [J].

Flunkert, V. ;

Yanchuk, S. ;

Dahms, T. ;

Schoell, E. .

PHYSICAL REVIEW LETTERS, 2010, 105 (25)

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