A mathematical definition of complex adaptive system as interaction space
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914855804469248 |
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| author | Giordano, Paolo |
| author_facet | Giordano, Paolo |
| contents | We define a mathematical notion of complex adaptive system by following the original intuition of G.K. Zipf about the principle of least effort, an intuitive idea which is nowadays informally widespread in complex systems modeling. We call generalized evolution principle this mathematical notion of interaction spaces theory. Formalizing and generalizing Mandelbrot's ideas, we also prove that a large class of these systems satisfy a power law. We finally illustrate the notion of complex adaptive system with theorems describing a Von Thünen-like model. The latter can be easily generalized to other complex systems and describes the appearance of emergent patterns. Every notion is introduced both using an intuitive description with lots of examples, and using a modern mathematical language. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_02181 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A mathematical definition of complex adaptive system as interaction space Giordano, Paolo Mathematical Physics Adaptation and Self-Organizing Systems Cellular Automata and Lattice Gases Pattern Formation and Solitons We define a mathematical notion of complex adaptive system by following the original intuition of G.K. Zipf about the principle of least effort, an intuitive idea which is nowadays informally widespread in complex systems modeling. We call generalized evolution principle this mathematical notion of interaction spaces theory. Formalizing and generalizing Mandelbrot's ideas, we also prove that a large class of these systems satisfy a power law. We finally illustrate the notion of complex adaptive system with theorems describing a Von Thünen-like model. The latter can be easily generalized to other complex systems and describes the appearance of emergent patterns. Every notion is introduced both using an intuitive description with lots of examples, and using a modern mathematical language. |
| title | A mathematical definition of complex adaptive system as interaction space |
| topic | Mathematical Physics Adaptation and Self-Organizing Systems Cellular Automata and Lattice Gases Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2407.02181 |