[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85540-en":3,"doc-seo-85540-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},85540,8796095360427,"Lucas Martin","https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d",8,"Research & Report","Feedback-Coupled Memory Systems: A Dynamical Model for Adaptive Coordination","This paper develops a dynamical framework for adaptive coordination in systems of interacting agents called Feedback-Coupled Memory Systems (FCMS). Instead of treating coordination as equilibrium optimization or agent-centric learning, it models a closed-loop interaction among agents, incentives, and a persistent environment that stores accumulated coordination signals. Three results are proved: dissipativity yields bounded forward-invariant viability; incentive rules tied to persistent memory prevent reduction to static optimization; and FCMS requires bidirectional coupling where memory-dependent incentives shape agent updates while agent behavior reshapes environmental state. A minimal-specification analysis identifies a Neimark–Sacker bifurcation, and simulations provide an early warning signature of coordination breakdown with scalability to large populations.","arXiv :2603 . 11560v3 [ cs .MA] 30 Mar 2026  \nFeedback-Coupled Memory Systems: A Dynamical Model for Adaptive Coordination  \nStefano Grassia∗  \na Bangkok University, Phahonyothin Rd, Khlong Nueng, Khlong Luang  \nDistrict, Pathum Thani 12120, Thailand  \nMarch 29, 2026  \nAbstract  \nThis paper develops a dynamical framework for adaptive coordination in systems of interacting agents referred to here as Feedback-Coupled Memory Systems (FCMS) . Instead of framing coordination as equilibrium optimization or agent-centric learning, the model describes a closed-loop interaction between agents, incentives, and a persistent environment. The environment stores accumulated coordination signals, a distributed incentive field transmits them locally, and agents update in response, generating a feedback-driven dynamical system. Three main results are established. First, under dissipativity, the closed-loop system admits a bounded forward-invariant region, ensuring dynamical viability independently of global optimality. Second, when incentives depend on persistent environmental memory, coordination cannot be reduced toa static optimization problem. Third, within the FCMS class, coordination requires a bidirectional coupling in which memory-dependent incentives influence agent updates, while agent behavior reshapes the environmental state. Numerical analysis of a minimal specification identifies a Neimark–Sacker bifurcation at a critical coupling threshold (􁅬􀕾 ), providing a stability boundary for the system. Near the bifurcation threshold, recovery time diverges and variance increases, yielding a computable early warning signature of coordination breakdown in observable time series. Additional simulations confirm robustness under nonlinear saturation and scalability to populations of up to 􀔃 = 106 agents making it more relevant for real-world applications. The proposed framework offers a dynamical perspective on coordination in complex systems, with potential extensions to multi-agent systems, networked interactions, and macro-level collective dynamics.  \nKeywords: Feedback-coupled dynamical systems; Adaptive coordination; Neimark–Sacker bifurcation; Mean-field coordination; Persistent environmental memory; Complex adaptive systems; Dissipative structures.  \n∗ Corresponding author: [stefano.g@bu.ac.th](stefano.g@bu.ac.th)  \n1 Introduction  \nMany real-world systems face a fundamental coordination problem: distributed agents must achieve collective order without centralized control, while operating through environments that evolve in response to their own actions. Markets, institutions, networked infrastructures, and multi-agent artificial intelligence systems all share this feature. Individual actions reshape the environment, and the environment in turn conditions future behavior. The question of how collective order emerges from such decentralized interaction has been central to economic thought since Smith’s [1] account of the invisible hand, and remains unresolved in its full dynamical generality. The stability of such systems, and the emergence of coordinated patterns within them, are questions of both theoretical and practical importance. Such systems naturally fall within the class of non-equilibrium dynamical systems with feedback and memory [2], in which macroscopic coordination arises as an emergent property of the coupled dynamics rather than as the output of any centralized design. Existing approaches typically analyze coordination through either equilibrium-based optimization or agent-centric learning frameworks. In these settings, the environment is often treated as exogenous or memoryless, and coordination is interpreted as the solution to a predefined objective. However, these assumptions limit the ability to capture insights from systems in which the environmental state evolves endogenously and influences future dynamics. As a result, the structural role of persistent environmental memory and its interaction with incentive mechan","cbCailgKzogjbOZ7","https://ap.wps.com/l/cbCailgKzogjbOZ7","pdf",1064819,3,1,23,"English","en",105,"# Introduction\n## System definition and motivation\n## Key structural conditions (coordination and dissipativity)\n# Main results\n## Bounded viability under dissipativity\n## Non-reducibility to static optimization with persistent memory\n## Bidirectional coupling requirements\n## Neimark–Sacker bifurcation and early warning signatures","[{\"question\":\"What makes a Feedback-Coupled Memory System (FCMS) different from equilibrium optimization or agent-centric learning?\",\"answer\":\"FCMS defines coordination through a closed-loop dynamical interaction among agents, incentives, and a persistent environment, rather than through equilibrium optimization or objective-driven learning. The environment stores accumulated coordination signals and continuously affects future dynamics.\"},{\"question\":\"How does dissipativity contribute to the system’s coordination and stability?\",\"answer\":\"Under dissipativity, the closed-loop system admits a bounded forward-invariant region, ensuring dynamical viability without relying on global optimality. This guarantees trajectories remain within a compact absorbing region.\"},{\"question\":\"Why does persistent environmental memory prevent reducing coordination to a static optimization problem?\",\"answer\":\"When incentives depend on persistent environmental memory, coordination cannot be represented as a static optimization of a fixed objective. The incentive mechanism evolves endogenously with the environment state over time.\"}]",1784204301,58,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"feedback-coupled-memory-systems-a-dynamical-model-for-adaptive-coordination","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":20},"https://docshare.wps.com/document/research-report/",{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/feedback-coupled-memory-systems-a-dynamical-model-for-adaptive-coordination/85540/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-25","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What makes a Feedback-Coupled Memory System (FCMS) different from equilibrium optimization or agent-centric learning?","Question",{"text":75,"@type":76},"FCMS defines coordination through a closed-loop dynamical interaction among agents, incentives, and a persistent environment, rather than through equilibrium optimization or objective-driven learning. The environment stores accumulated coordination signals and continuously affects future dynamics.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does dissipativity contribute to the system’s coordination and stability?",{"text":80,"@type":76},"Under dissipativity, the closed-loop system admits a bounded forward-invariant region, ensuring dynamical viability without relying on global optimality. This guarantees trajectories remain within a compact absorbing region.",{"name":82,"@type":73,"acceptedAnswer":83},"Why does persistent environmental memory prevent reducing coordination to a static optimization problem?",{"text":84,"@type":76},"When incentives depend on persistent environmental memory, coordination cannot be represented as a static optimization of a fixed objective. The incentive mechanism evolves endogenously with the environment state over time.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]