三种自组织规则的对称性破坏:复杂性起源的一般理论

IF 1.9 4区 数学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Wen-Hao Wu, Ze-Zheng Li, Wen-Xu Wang
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引用次数: 0

摘要

自然界中复杂的时空模式极大地挑战了以还原论为基础的现代科学。缺乏超越还原论的范式阻碍了我们对复杂性出现的理解。无数模式的多样性破坏了任何普遍机制的概念。然而,我们在这里证明,打破三个简单自组织规则的对称性,就会产生自然界中几乎所有的模式,如各种各样的图灵模式、分形、螺旋波、靶波和平面波,以及混沌模式。对称性破缺植根于基本物理量,如正负力、空间、时间和边界。除了再现复杂性的特征外,我们还发现了一些新现象,如图灵模式的突然渗透、分形与混沌之间的相变、行波中的混沌边缘等。我们的非对称自组织理论为所有领域的复杂性起源建立了一个简单而统一的框架,揭示了物理学第一原理与复杂世界之间的深刻关系。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Symmetry Breaking of Three Self-Organization Rules: A General Theory for the Origin of Complexity

Complex spatiotemporal patterns in nature significantly challenge reductionism-based modern science. The lack of a paradigm beyond reductionism hinders our understanding of the emergence of complexity. The diversity of countless patterns undermines any notion of universal mechanisms. Here, however, we show that breaking the symmetry of three simple and self-organization rules gives rise to nearly all patterns in nature, such as a wide variety of Turing patterns, fractals, spiral, target and plane waves, as well as chaotic patterns. The symmetry breaking is rooted in the basic physical quantities, such as positive and negative forces, space, time and bounds. Besides reproducing the hallmarks of complexity, we discover some novel phenomena, such as abrupt percolation of Turing patterns, phase transition between fractals and chaos, chaotic edge in traveling waves, etc. Our asymmetric self-organization theory established a simple and unified framework for the origin of complexity in all fields, and unveiled a deep relationship between the first principles of physics and the complex world.

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来源期刊
International Journal of Bifurcation and Chaos
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.
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