Chaos-Aware Metrics for Self-Organizing and Swarm-Based Engineering Systems: A Systematic Review

Chaos-Aware Metrics for Self-Organizing and Swarm-Based Engineering Systems: A Systematic Review | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Chaos-Aware Metrics for Self-Organizing and Swarm-Based Engineering Systems: A Systematic Review Nikitas Gerolimos, Vasileios Alevizos, George A. Papakostas, Georgios Priniotakis This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7775297/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The utilization of self-organization and swarm intelligence has become increasingly prevalent in resilient and adaptive engineered systems. However, the evaluation process continues to be task-centric, with studies reporting on latency, coverage, or energy, while neglecting to provide comprehensive specifications regarding organizational quality, stability under perturbations, and recoverability. The present survey reviews chaos- and complexity-aware metrics, including largest Lyapunov exponents, entropy families, algebraic connectivity, clustering/modularity, and order parameters. The survey then maps the use of these metrics across swarm algorithms and distributed infrastructures. The theoretical underpinnings of this approach draw from the fields of nonlinear dynamics and network science, while the algorithmic lens encompasses both classic controllers and those enhanced by chaos. The range of applications extends from smart fabrics to underwater swarms and energy/supply networks. The present study introduces the Chaos-Aware Design Index (CADI), a reporting template that complements standard KPIs with indicators of stability, order, cohesion, and emergence. The present argument is that metrics should function as design levers as opposed to serving as after-the-fact diagnostics. The employment of a vocabulary that is both chaos- and network-aware has been demonstrated to facilitate reproducibility, the establishment of comparable benchmarks, and the transfer of knowledge across diverse domains, ranging from materials science to robotic swarms and infrastructure engineering. Swarm intelligence Self-organization Chaos theory Entropy Lyapunov exponents Biomimicry Smart fabrics AUV swarms PRISMA Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7775297","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":535039792,"identity":"dafc1eab-ee49-4585-a9f0-e76fc8d7f6e7","order_by":0,"name":"Nikitas Gerolimos","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzElEQVRIiWNgGAWjYNCCAgkgwXyAgcGAaC0GIC1sCSRpARE8RKo351987MMHA4tofv4z36QLCg7LM/CvfYBXi+WMZ8kzZxhI5M6ckbtNeobBYcMGief4rTO4ccaYmQeoZcMN3m3SPAa3GRskjhHwxY3znyFazp95BtJiT1jL+R5miJYDOWwgLYkN/G2EbGEzZoT4Jc3Ymsfgf3KbBBshWw4/ZvhQUZfbz3/44W2eP2m2/fwEHMYgkYAmwIYhgg74DxAWGQWjYBSMghEOAEVOQursvFXlAAAAAElFTkSuQmCC","orcid":"","institution":"University of West Attica","correspondingAuthor":true,"prefix":"","firstName":"Nikitas","middleName":"","lastName":"Gerolimos","suffix":""},{"id":535039794,"identity":"dd6e1727-496f-4966-90fb-deef5be56e24","order_by":1,"name":"Vasileios Alevizos","email":"","orcid":"","institution":"Karolinska Institutet","correspondingAuthor":false,"prefix":"","firstName":"Vasileios","middleName":"","lastName":"Alevizos","suffix":""},{"id":535039795,"identity":"359969dc-40e5-412f-b332-e16c230e2e6f","order_by":2,"name":"George A. 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