一类改进Brusselator模型的Hopf分岔与自组织模式

IF 2.9 2区 化学 Q2 CHEMISTRY, MULTIDISCIPLINARY
Mengxin Chen
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引用次数: 0

摘要

本文报道了一个改进的Brusselator模型的Hopf分岔和自组织模式。该模型是一个非标准的Brusselator模型,涉及到非线性约束项。对于非扩散模型,我们给出了唯一正平衡的类型。发现唯一正平衡可以是焦点、节点或中心,并分别建立了它们的稳定性。特别是当平衡点为中心时,存在空间齐次Hopf分岔。应用第一李雅普诺夫数技术求解空间齐次Hopf分岔的方向。其次,给出了扩散模型的图灵不稳定性和空间非齐次Hopf分岔的发生条件。此外,我们还利用范式理论证明了Hopf分岔是超临界或亚临界的。最后,通过数值模拟,展示了由图灵不稳定性和Hopf分岔引起的周期解引起的自组织模式。我们的理论预测和数值结果表明,改进的Brusselator模型分别由于Hopf分岔和Turing不稳定性而具有时间周期振荡和空间振荡。这些结果可以帮助我们了解这种改进的Brusselator模型的时空动态。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Hopf Bifurcation and Self-Organization Pattern of a Modified Brusselator Model
This paper reports the Hopf bifurcation and self-organization pattern of a modified Brusselator model. The model is a non-standard Brusselator model, it involves the nonlinear restraint term. For the non-diffusive model, we give the types of unique positive equilibrium. It is found that the unique positive equilibrium may be focus, node, or center and we establish their stability, respectively. Especially, there exists the spatial homogeneous Hopf bifurcation when the equilibrium is a center. The first Lyapunov number technique is applied to perform the direction of the spatial homogeneous Hopf bifurcation. In the sequel, the occurrence conditions of the Turing instability and the spatial inhomogeneous Hopf bifurcation are given for the diffusive model. Moreover, by using the normal form theory, we show that the Hopf bifurcation is supercritical or subcritical. Finally, the self-organization patterns induced by the Turing instability and periodic solutions resulting from the Hopf bifurcation are displayed by employing numerical simulations. Our theoretical predictions and numerical results reveal that the modified Brusselator model enjoys the temporal period oscillation and spatial oscillation due to the Hopf bifurcation and Turing instability, respectively. These results may help us to figure out the spatio-temporal dynamics of such modified Brusselator model.
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来源期刊
CiteScore
4.40
自引率
26.90%
发文量
71
审稿时长
2 months
期刊介绍: MATCH Communications in Mathematical and in Computer Chemistry publishes papers of original research as well as reviews on chemically important mathematical results and non-routine applications of mathematical techniques to chemical problems. A paper acceptable for publication must contain non-trivial mathematics or communicate non-routine computer-based procedures AND have a clear connection to chemistry. Papers are published without any processing or publication charge.
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