Multiparameter bifurcations and mixed-mode oscillations in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Q</mml:mi></mml:math>-switched<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>CO</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>lasers

Doedel, Eusebius J.; Lambruschini, Carlos L. Pando

doi:10.1103/physreve.89.052904

Cited by 21 publications

(11 citation statements)

References 79 publications

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“…The bifurcation analysis of periodic orbits in the circuit was carried out with use of parameter continuation package AUTO-07p [46]. Specifically, we set up Eqs.…”

Section: Numerical Computationmentioning

confidence: 99%

Qualitative and quantitative stability analysis of penta-rhythmic circuits

2016

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Inhibitory circuits of relaxation oscillators are often-used models for the dynamics of biological networks. We present a qualitative and quantitative stability analysis of such a circuit constituted by three reciprocally coupled oscillators of a Fitzhugh-Nagumo type as nodes. Depending on inhibitory strengths, and parameters of individual oscillators, the circuit exhibits polyrhythmicity of up to five simultaneously stable rhythms. With methods of bifurcation analysis and phase reduction, we investigate qualitative changes in stability of these circuit rhythms for a wide range of parameters. Furthermore, we quantify how robustly rhythms are maintained under random perturbations by monitoring phase diffusion in the circuit. Our findings allow us to describe how circuit dynamics relate to dynamics of individual nodes. We also find that quantitative and qualitative stability of polyrhythmicity do not always align.arXiv:1509.04514v1 [nlin.CD] 15 Sep 2015

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“…The bifurcation analysis of periodic orbits in the circuit was carried out with use of parameter continuation package AUTO-07p [46]. Specifically, we set up Eqs.…”

Section: Numerical Computationmentioning

confidence: 99%

Qualitative and quantitative stability analysis of penta-rhythmic circuits

2016

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“…First, the most familiar adding transitions are the ones mediated by windows of chaos, as frequently observed in mixed-mode oscillations. 21,22 Second, there are mixed-mode oscillations where windows of chaos are totally absent 19,35 (see the previous paragraph). Third, there are the transitions involving concatenated periodic oscillations and nested progressions as described in Figs.…”

Section: Types Of Nested Progressionsmentioning

confidence: 98%

“…19 MMOs are very common patterns found in wide classes of nonlinear oscillators, as described by several authors in a focus issue of Chaos dedicated to MMOs 21 and, more recently, e.g., in CO 2 lasers. 22 The BFSO model is governed by ten equations (nine of them independent) and 14 rate constants and is computationally quite demanding to investigate. Thus, we were motivated to look for a simpler model that could provide useful insight with much less burden.…”

Section: Introductionmentioning

confidence: 99%

Nested arithmetic progressions of oscillatory phases in Olsen's enzyme reaction model

Gallas

2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We report some regular organizations of stability phases discovered among self-sustained oscillations of a biochemical oscillator. The signature of such organizations is a nested arithmetic progression in the number of spikes of consecutive windows of periodic oscillations. In one of them, there is a main progression of windows whose consecutive number of spikes differs by one unit. Such windows are separated by a secondary progression of smaller windows whose number of spikes differs by two units. Another more complex progression involves a fan-like nested alternation of stability phases whose number of spikes seems to grow indefinitely and to accumulate methodically in cycles. Arithmetic progressions exist abundantly in several control parameter planes and can be observed by tuning just one among several possible rate constants governing the enzyme reaction.

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“…equation (2.8)). In order to understand the differences between these two branches, the characteristics of continuation of the obtained solutions over the lattice spacing h (using the computer software AUTO [17,18]) are displayed in Fig. 3 and the top row of Fig.…”

Section: The Lattice Skyrme Modelmentioning

confidence: 99%

Lattice three-dimensional skyrmions revisited

Charalampidis¹,

Ioannidou²,

Kevrekidis³

2015

Phys. Scr.

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In the continuum a skyrmion is a topological nontrivial map between Riemannian manifolds, and a stationary point of a particular energy functional. This paper describes lattice analogues of the aforementioned skyrmions, namely a natural way of using the topological properties of the three-dimensional continuum Skyrme model to achieve topological stability on the lattice. In particular, using fixed point iterations, numerically exact lattice skyrmions are constructed; and their stability under small perturbations is explored by means of linear stability analysis. While stable branches of such solutions are identified, it is also shown that they possess a particularly delicate bifurcation structure, especially so in the vicinity of the continuum limit. The corresponding bifurcation diagram is elucidated and a prescription for selecting the branch asymptoting to the well-known continuum limit is given. Finally, the robustness of the spectrally stable solutions is corroborated by virtue of direct numerical simulations . *

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Multiparameter bifurcations and mixed-mode oscillations inQ-switchedCO2lasers

Cited by 21 publications

References 79 publications

Qualitative and quantitative stability analysis of penta-rhythmic circuits

Qualitative and quantitative stability analysis of penta-rhythmic circuits

Nested arithmetic progressions of oscillatory phases in Olsen's enzyme reaction model

Lattice three-dimensional skyrmions revisited

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