Temporal variability in a system of coupled mitotic timers

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

doi:10.1007/bf00198921

Cited by 19 publications

(8 citation statements)

References 23 publications

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“…Since the work of Van der Pol and Van der Mark [1], the studies of coupled nonchaotic oscillators have provided a rich source of ideas and insights regarding the role of different coupling types, as well as the dependence on the oscillator structure in the generation of new dynamical regimes [2][3][4]. It has been shown that even ensembles consisting of identical oscillators may generate a variety of rhythms that differ in their period and phase relations based on the coupling organization [5][6][7][8]. Apart from such rhythmogenic activity, coupling can even suppress oscillations in a network by different mechanisms.…”

mentioning

confidence: 99%

Transition from Amplitude to Oscillation Death via Turing Bifurcation

2013

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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.

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confidence: 99%

Transition from Amplitude to Oscillation Death via Turing Bifurcation

2013

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“…alternates between periodic, quasiperiodic and even chaotic behavior, reflecting the complex temporal variability observed in real biological systems [22,23].…”

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confidence: 99%

Diverse routes to oscillation death in a coupled-oscillator system

et al. 2009

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We study oscillation death (OD) in a well-known coupled-oscillator system that has been used to model cardiovascular phenomena. We derive exact analytic conditions that allow the prediction of OD through the two known bifurcation routes, in the same model, and for different numbers of coupled oscillators. Our exact analytic results enable us to generalize OD as a multiparametersensitive phenomenon. It can be induced, not only by changes in couplings, but also by changes in the oscillator frequencies or amplitudes. We observe synchronization transitions as a function of coupling and confirm the robustness of the phenomena in the presence of noise. Numerical and analogue simulations are in good agreement with the theory.Coupled oscillator systems exhibit a variety of phenomena relevant to physics, biology, and other branches of science and technology. Here, we study oscillation death (OD) [1], a form of synchronization [2] in which the oscillators interact in such a way as to quench each other's oscillations [3][4][5][6]. This intriguing phenomenon was noted in the 19th century by Rayleigh [2], who found that adjacent organ pipes of the same pitch can reduce each other to silence. Since then, OD has been studied in diverse applications including oceanography [7], chemical engineering [8], solid-state lasers [9] and a variety of other experimental systems [4,[10][11][12]. OD is known to occur via two distinct bifurcation mechanisms: (i) Hopf bifurcation, where the coupling induces stability at the origin of the phase space, thus collapsing the orbits to zero, which can happen only if the oscillators are sufficiently different [5,[13][14][15][16] (or for identical oscillators if there are delays [17,18] in the coupling); or (ii) for non-identical oscillators, saddle-node bifurcation [4] in which new fixed points appear on/near the coupled limit cycles, annihilating the periodic orbits. Recently, Karnatak et al. [19] were able to produce OD in two identical coupled oscillators through the saddlenode route, using dissimilar non-delayed coupling.In this Letter, we show that a coupled-oscillator system, which has been used extensively in modeling coupled rhythmic processes in mathematics, physics and biology [26] can undergo OD via both bifurcation routes. We obtain exact analytic conditions for OD, and compare the theory with numerical simulations and analogue electronic experiments. We thus generalize OD as a phenomenon that occurs, not only through coupling-increased dissipativity [2], but also when a measure of dispersion among the parameters of the coupled system is exceeded [21]. We also show that, near the onset of death, the coupled system PACS 82.40.Bj -Oscillations, chaos, and bifurcations PACS 05.45.Xt -Synchronization; coupled oscillators PACS 05.45.-a -Nonlinear dynamics and chaos

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“…After proliferation, the daughter cells are in a similar phase as the mother, which decreases the time to form stable clusters significantly. Normally, stronger coupling lengthens the period of coupled systems, 29,80 but the situation is different in the present case because Q controls the re-influx of AI and a higher internal AI concentration shortens the repressilator cycle. Compared to the coupling strength Q, the system size N and the cluster composition have a minor influence on the period.…”

Section: Clustering Due To Regular Oscillations In Cell Coloniesmentioning

confidence: 72%

Complex and unexpected dynamics in simple genetic regulatory networks

Borg

Ullner

Alagha

et al. 2014

Int. J. Mod. Phys. B

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One aim of synthetic biology is to construct increasingly complex genetic networks from interconnected simpler ones to address challenges in medicine and biotechnology. However, as systems increase in size and complexity, emergent properties lead to unexpected and complex dynamics due to nonlinear and nonequilibrium properties from component interactions. We focus on four different studies of biological systems which exhibit complex and unexpected dynamics. Using simple synthetic genetic networks, small and large populations of phase-coupled quorum sensing repressilators, Goodwin oscillators, and bistable switches, we review how coupled and stochastic components can result in clustering, chaos, noise-induced coherence and speed-dependent decision making. A system of repressilators exhibits oscillations, limit cycles, steady states or chaos depending on the nature and strength of the coupling mechanism. In large repressilator networks, rich dynamics can also be exhibited, such as clustering and chaos. In populations of Goodwin oscillators, noise can induce coherent oscillations. In bistable systems, the speed with which incoming external signals reach steady state can bias the network towards particular attractors. These studies showcase the range of dynamical behavior that simple synthetic genetic networks can exhibit. In addition, they demonstrate the ability of mathematical modeling to analyze nonlinearity and inhomogeneity within these systems.

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Temporal variability in a system of coupled mitotic timers

Cited by 19 publications

References 23 publications

Transition from Amplitude to Oscillation Death via Turing Bifurcation

Transition from Amplitude to Oscillation Death via Turing Bifurcation

Diverse routes to oscillation death in a coupled-oscillator system

Complex and unexpected dynamics in simple genetic regulatory networks

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