分数阶稳定化学反应系统的分岔反控制策略

IF 2.9 2区 化学 Q2 CHEMISTRY, MULTIDISCIPLINARY
Zuozhi Liu
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引用次数: 0

摘要

建立合适的微分动力学模型来描述真实的自然现象已成为当今社会的热门话题。在本研究中,我们处理一个分数级化学反应体系。利用不动点定理,证明了分数阶化学反应体系的存在唯一性。利用不等式技巧,证明了分数阶化学反应体系的非负性。应用一个合适的函数,证明了分数阶化学反应体系解的一致有界性。利用包含状态反馈和参数摄动的混合控制器,讨论了分数阶稳定化学反应系统的Hopf分岔反控制问题。建立了保证分数阶稳定化学反应系统稳定性和Hopf分岔发生的一种新的时滞无关条件。研究表明,对于分数阶稳定化学反应系统,混合控制器中的时滞对于系统的稳定和控制Hopf分岔的发生起着至关重要的作用。为了验证得出的关键结论,进行了MATLAB仿真,并给出了分岔图。所得结果对控制化学成分具有重要的理论指导价值。这种探索思想也可用于研究许多其他学科的分数阶微分系统的分岔控制和分岔反控制问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Bifurcation Anti-Control Tactics of a Fractional-Order Stable Chemical Reaction System
Establishing suitable differential dynamical models to describe the real natural phenomenon in chemistry and physics has become a very hot topic in nowadays society. In this present research, we deal with a fractional-order chemical reaction system. Taking advantage of the fixed point theorem, we prove the existence and uniqueness of the fractional-order chemical reaction system. Using the inequality skill, we prove the non-negativeness of the fractional-order chemical reaction system. By applying a suitable function, we prove the uniform boundedness of the solution to the fractional-order chemical reaction system. With the aid of a hybrid controller including state feedback and parameter perturbation, we discuss the Hopf bifurcation anti-control issue of the fractional-order stable chemical reaction system. A novel delay-independent condition ensuring the stability and the onset of Hopf bifurcation of the involved fractional-order stable chemical reaction system is set up. The study manifests that the delay in the hybrid controller plays a vital role in stabilizing the system and controlling the occurrence of Hopf bifurcation of the fractional-order stable chemical reaction system. In order to validate the derived key conclusions, MATLAB simulations are executed and bifurcation plots are given. The obtained results of this article have momentous theoretical guiding value in controlling the chemical compositions. The exploration idea can also be utilized to investigate the bifurcation control and bifurcation anti-control problems in lots of other fractional-order differential systems in numerous disciplines.
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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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