Birhythmicity in a system of two coupled identical oscillators

Volkov, E.I.; Stolyarov, Maksim N.

doi:10.1016/0375-9601(91)90162-2

Cited by 32 publications

(9 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Many biophysical systems display certain properties found here. Stabilization of the anti-phase solution is consistent with other publications [29,[31][32][33][34][35][36]. The birhythmicity of the in-phase and the anti-phase oscillations is found in models of pancreatic β cells [37], yeast glycolysis [38], and coupled neural oscillators [31].…”

Section: Discussionsupporting

confidence: 90%

Dynamics of coupled repressilators: The role of mRNA kinetics and transcription cooperativity

2011

View full text Add to dashboard Cite

Oscillatory regulatory networks have been discovered in many cellular pathways. An especially challenging area is studying dynamics of cellular oscillators interacting with one another in a population. Synchronization is only one of and the simplest outcome of such interaction. It is suggested that the outcome depends on the structure of the network. Phase-attractive (synchronizing) and phase-repulsive coupling structures were distinguished for regulatory oscillators. In this paper, we question this separation. We study an example of two interacting repressilators (artificial regulatory oscillators based on cyclic repression). We show that changing the cooperativity of transcription repression (Hill coefficient) and reaction timescales dramatically alter synchronization properties. The network becomes birhythmic-it chooses between the in-phase and antiphase synchronization. Thus, the type of synchronization is not characteristic for the network structure. However, we conclude that the specific scenario of emergence and stabilization of synchronous solutions is much more characteristic.

show abstract

Section: Discussionsupporting

confidence: 90%

Dynamics of coupled repressilators: The role of mRNA kinetics and transcription cooperativity

2011

View full text Add to dashboard Cite

show abstract

“…It is still not clear why phase-repulsive coupling permits the formation of APLC/IPLC switching. Intuitively it may be due to the increase in repressilator "stiffness" for large values of n. Similar frequency trigger covering a wide range of parameters was observed in the system of two FitzHugh-Nagumo oscillators coupled via the recovery variable if their stiffness was large [37].…”

Section: Discussionmentioning

confidence: 61%

Flexible dynamics of two quorum-sensing coupled repressilators

Hellen

Volkov

2017

Phys. Rev. E

View full text Add to dashboard Cite

Genetic oscillators play important roles in cell life regulation. The regulatory efficiency usually depends strongly on the emergence of stable collective dynamic modes, which requires designing the interactions between genetic networks. We investigate the dynamics of two identical synthetic genetic repressilators coupled by an additional plasmid which implements quorum sensing (QS) in each network thereby supporting global coupling. In a basic genetic ring oscillator network in which three genes inhibit each other in unidirectional manner, QS stimulates the transcriptional activity of chosen genes providing for competition between inhibitory and stimulatory activities localized in those genes. The "promoter strength", the Hill cooperativity coefficient of transcription repression, and the coupling strength, i.e., parameters controlling the basic rates of genetic reactions, were chosen for extensive bifurcation analysis. The results are presented as a map of dynamic regimes. We found that the remarkable multistability of the antiphase limit cycle and stable homogeneous and inhomogeneous steady states exists over broad ranges of control parameters. We studied the antiphase limit cycle stability and the evolution of irregular oscillatory regimes in the parameter areas where the antiphase cycle loses stability. In these regions we observed developing complex oscillations, collective chaos, and multistability between regular limit cycles and complex oscillations over uncommonly large intervals of coupling strength. QS coupling stimulates the appearance of intrachaotic periodic windows with spatially symmetric and asymmetric partial limit cycles which, in turn, change the type of chaos from a simple antiphase character into chaos composed of pieces of the trajectories having alternating polarity. The very rich dynamics discovered in the system of two identical simple ring oscillators may serve as a possible background for biological phenotypic diversification, as well as a stimulator to search for similar coupling in oscillator arrays in other areas of nature, e.g., in neurobiology, ecology, climatology, etc.

show abstract

“…The idea of the broken symmetry steady state pioneered by Turing [17] for stationary media received its mathematical formulation by Prigogine and Lefever [18] for two identical oscillating elements-Brusselators, coupled in a diffusionlike manner. Furthermore, it has been shown theoretically that OD is model independent, persisting for large parametric regions in several models of diffusively coupled chemical [19] or biological oscillators [7,[20][21][22][23][24]. Experimentally, the extinction of oscillations in chemical reactors coupled by mutual mass exchange was initially reported by Dolnik and Marek [25].…”

mentioning

confidence: 97%

Transition from Amplitude to Oscillation Death via Turing Bifurcation

2013

View full text Add to dashboard Cite

Coupled oscillators are shown to experience two structurally different oscillation quenching types: amplitude death (AD) and oscillation death (OD). We demonstrate that both AD and OD can occur in one system and find that the transition between them underlies a classical, Turing-type bifurcation, providing a clear classification of these significantly different dynamical regimes. The implications of obtaining a homogeneous (AD) or inhomogeneous (OD) steady state, as well as their significance for physical and biological applications and control studies, are also pointed out.

show abstract

Birhythmicity in a system of two coupled identical oscillators

Cited by 32 publications

References 8 publications

Dynamics of coupled repressilators: The role of mRNA kinetics and transcription cooperativity

Dynamics of coupled repressilators: The role of mRNA kinetics and transcription cooperativity

Flexible dynamics of two quorum-sensing coupled repressilators

Transition from Amplitude to Oscillation Death via Turing Bifurcation

Contact Info

Product

Resources

About