{"title":"竞争性无序动态系统中的完备性-稳定性关系。","authors":"Onofrio Mazzarisi, Matteo Smerlak","doi":"10.1103/PhysRevE.110.054403","DOIUrl":null,"url":null,"abstract":"<p><p>Robert May famously used random matrix theory to predict that large, complex systems cannot admit stable fixed points. However, this general conclusion is not always supported by empirical observation: from cells to biomes, biological systems are large, complex, and often stable. In this paper, we revisit May's argument in light of recent developments in both ecology and random matrix theory. We focus on competitive systems, and, using a nonlinear generalization of the competitive Lotka-Volterra model, we show that there are, in fact, two kinds of complexity-stability relationships in disordered dynamical systems: if self-interactions grow faster with density than cross-interactions, complexity is destabilizing; but if cross-interactions grow faster than self-interactions, complexity is stabilizing.</p>","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"110 5-1","pages":"054403"},"PeriodicalIF":2.4000,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Complexity-stability relationships in competitive disordered dynamical systems.\",\"authors\":\"Onofrio Mazzarisi, Matteo Smerlak\",\"doi\":\"10.1103/PhysRevE.110.054403\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>Robert May famously used random matrix theory to predict that large, complex systems cannot admit stable fixed points. However, this general conclusion is not always supported by empirical observation: from cells to biomes, biological systems are large, complex, and often stable. In this paper, we revisit May's argument in light of recent developments in both ecology and random matrix theory. We focus on competitive systems, and, using a nonlinear generalization of the competitive Lotka-Volterra model, we show that there are, in fact, two kinds of complexity-stability relationships in disordered dynamical systems: if self-interactions grow faster with density than cross-interactions, complexity is destabilizing; but if cross-interactions grow faster than self-interactions, complexity is stabilizing.</p>\",\"PeriodicalId\":20085,\"journal\":{\"name\":\"Physical review. E\",\"volume\":\"110 5-1\",\"pages\":\"054403\"},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2024-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physical review. E\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1103/PhysRevE.110.054403\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical review. E","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/PhysRevE.110.054403","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
Complexity-stability relationships in competitive disordered dynamical systems.
Robert May famously used random matrix theory to predict that large, complex systems cannot admit stable fixed points. However, this general conclusion is not always supported by empirical observation: from cells to biomes, biological systems are large, complex, and often stable. In this paper, we revisit May's argument in light of recent developments in both ecology and random matrix theory. We focus on competitive systems, and, using a nonlinear generalization of the competitive Lotka-Volterra model, we show that there are, in fact, two kinds of complexity-stability relationships in disordered dynamical systems: if self-interactions grow faster with density than cross-interactions, complexity is destabilizing; but if cross-interactions grow faster than self-interactions, complexity is stabilizing.
期刊介绍:
Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.