Bifurcation Solutions to the Templator Model in Chemical Self-Replication

IF 1.9 4区数学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

International Journal of Bifurcation and Chaos Pub Date : 2023-12-11 DOI:10.1142/s0218127423501742

Qian Cao, Xiongxiong Bao

引用次数: 0

Abstract

In this paper, we are concerned with a diffusive templator model in chemical self-replication, which describes the process of an individual molecule duplicating itself. Firstly, the stability of non-negative constant equilibrium solution is introduced. Then the existence of Hopf bifurcation is proved. Particularly, the stability and the direction of Hopf bifurcation for the spatially homogeneous model are discussed. Furthermore, by space decomposition and implicit function theorem, it is shown that the system may undergo a steady-state bifurcation with a two-dimensional kernel. Finally, several numerical simulations are completed to demonstrate the theoretical results.

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化学自我复制中模板模型的分岔解

本文关注化学自我复制中的扩散模板模型，该模型描述了单个分子自我复制的过程。首先，介绍了非负常数平衡解的稳定性。然后证明了霍普夫分岔的存在。特别是讨论了空间均质模型的稳定性和霍普夫分岔的方向。此外，通过空间分解和隐函数定理，证明了系统可能发生具有二维内核的稳态分岔。最后，完成了几个数值模拟来证明理论结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Bifurcation and Chaos 数学-数学跨学科应用

CiteScore

4.10

自引率

13.60%

发文量

237

审稿时长

2-4 weeks

期刊介绍： The International Journal of Bifurcation and Chaos is widely regarded as a leading journal in the exciting fields of chaos theory and nonlinear science. Represented by an international editorial board comprising top researchers from a wide variety of disciplines, it is setting high standards in scientific and production quality. The journal has been reputedly acclaimed by the scientific community around the world, and has featured many important papers by leading researchers from various areas of applied sciences and engineering. The discipline of chaos theory has created a universal paradigm, a scientific parlance, and a mathematical tool for grappling with complex dynamical phenomena. In every field of applied sciences (astronomy, atmospheric sciences, biology, chemistry, economics, geophysics, life and medical sciences, physics, social sciences, ecology, etc.) and engineering (aerospace, chemical, electronic, civil, computer, information, mechanical, software, telecommunication, etc.), the local and global manifestations of chaos and bifurcation have burst forth in an unprecedented universality, linking scientists heretofore unfamiliar with one another''s fields, and offering an opportunity to reshape our grasp of reality.