Stability mosaics in a forced Brusselator

Freire, Joana G.; Gallas, Márcia Russman; Gallas, Jason A. C.

doi:10.1140/epjst/e2017-70020-x

Cited by 7 publications

(4 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We find the low-frequency limit of the Duffing oscillator to display unexpectedly regular mosaics in the control parameter space, corresponding to stable periodic oscillations of increasingly complex waveforms. Although we focus here on the Duffing oscillator, similar chaos-free zones were also found in other driven systems and will be discussed elsewhere [15].…”

mentioning

confidence: 57%

Chaos-free oscillations

Freire¹,

Gallas²,

Gallas³

2017

EPL

Self Cite

View full text Add to dashboard Cite

Oscillators have widespread applications in micro-and nanomechanical devices, in lasers of various types, in chemical and biochemical models, among others. However, applications are normally marred by the presence of chaos, requiring expensive control techniques to bypass it. Here, we show that the low-frequency limit of driven systems, a poorly explored region, is a wide chaos-free zone. Specifically, for a popular model of micro-and nanomechanical devices and for the Brusselator, we report the discovery of an unexpectedly wide mosaic of phases resulting from stable periodic oscillations of increasing complexity but totally free from chaos.

show abstract

mentioning

confidence: 57%

Chaos-free oscillations

Freire¹,

Gallas²,

Gallas³

2017

EPL

Self Cite

View full text Add to dashboard Cite

show abstract

“…4 below), which are standard ingredients for bifurcation diagrams; furthermore, the maximum bubble radius and the maximum absolute value of the bubble wall velocity, which are important for applications; finally, the period, the Lyapunov exponent and the winding number of the attractors found, quantities that are essential for a detailed analysis of bifurcation structures. A strategy to represent the results of parametric studies involving high-dimensional parameter spaces consists in creating high-resolution bi-parametric plots, a rapidly spreading technique in the investigation of nonlinear systems with a high-dimensional parameter space [39][40][41][42][43][44][45][46][47][48][49]. The system studied here, a bubble in water with dual-frequency acoustic excitation, has a four-dimensional driving parameter space (P A1 , P A2 , ω R1 , ω R2 ).…”

Section: Numerical Implementation and Parameter Choicementioning

confidence: 99%

Non-feedback technique to directly control multistability in nonlinear oscillators by dual-frequency driving

et al. 2018

View full text Add to dashboard Cite

A novel method to control multistability of nonlinear oscillators by applying dual-frequency driving is presented. The test model is the Keller-Miksis equation describing the oscillation of a bubble in a liquid. It is solved by an in-house initial-value problem solver capable to exploit the high computational resources of professional graphics cards. Dur-Electronic supplementary material The online version of this article (

show abstract

“…( 3) and ( 4), the equilibrium point (EQP) is given by (x, y) = (0, 0). Bifurcation analysis of the stability of the Brusselator model has generated much interest in the selforganization of non-equilibrium chemical systems, i.e., dynamic phenomena in reacting systems far from equilibrium (e.g., [Nicolis, & Prigogine, 1977;Ma, & Hu, 2014;Freire et al, 2017;Zhao, & Ma, 2019]). Given the importance of stability under non-equilibrium conditions, the degree to which non-equilibrium affects stability must be considered.…”

Section: Introductionmentioning

confidence: 99%

Kosambi–Cartan–Chern Stability in the Intermediate Nonequilibrium Region of the Brusselator Model

Yamasaki

Yajima

2022

Int. J. Bifurcation Chaos

View full text Add to dashboard Cite

This study applies the Kosambi–Cartan–Chern (KCC) theory to the Brusselator model to derive differential geometric quantities related to bifurcation phenomena. Based on these geometric quantities, the KCC stability of the Brusselator model is analyzed in linear and nonlinear cases to determine the extent to which nonequilibrium affects bifurcation and stability. The geometric quantities of the Brusselator model have a constant value in the linear case, and are functions of spatial variables with parameter dependence in the nonlinear case. Therefore, the KCC stability of the nonlinear case shows various distribution patterns, depending on the distance from the equilibrium point (EQP), as follows: in the regions near or far enough from the EQP, the distribution of KCC stability is uniform and regular; and in the intermediate nonequilibrium region, the distribution varies and shows complex patterns with parameter dependence. These results indicate that stability in the intermediate nonequilibrium region plays an important role in the dynamic complex patterns in the Brusselator model.

show abstract

Stability mosaics in a forced Brusselator

Cited by 7 publications

References 28 publications

Chaos-free oscillations

Chaos-free oscillations

Non-feedback technique to directly control multistability in nonlinear oscillators by dual-frequency driving

Kosambi–Cartan–Chern Stability in the Intermediate Nonequilibrium Region of the Brusselator Model

Contact Info

Product

Resources

About