{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T18:30:46Z","timestamp":1768415446217,"version":"3.49.0"},"reference-count":47,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,4]],"date-time":"2025-02-04T00:00:00Z","timestamp":1738627200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>System stability control in resource allocation is a critical issue in group robot systems. Against this backdrop, this study investigates the nonlinear dynamics and chaotic phenomena that arise during pricing games among finitely rational group robots and proposes control strategies to mitigate chaotic behaviors. A system model and a business model for group robots are developed based on market mechanism mapping, and the dynamics of resource allocation are formulated as a second-order discrete nonlinear system using game theory. Numerical simulations reveal that small perturbations in system parameters, such as pricing adjustment speed, product demand coefficients, and resource substitution coefficients, can induce chaotic behaviors. To address these chaotic phenomena, a control method combining state feedback and parameter adjustment is proposed. This approach dynamically tunes the state feedback intensity of the system via a control parameter M, thereby delaying bifurcations and suppressing chaotic behaviors. It ensures that the distribution of system eigenvalues satisfies stability conditions, allowing control over unstable periodic orbits and period-doubling bifurcations. Simulation results demonstrate that the proposed control method effectively delays period-doubling bifurcations and stabilizes unstable periodic orbits in chaotic attractors. The stability of the system\u2019s Nash equilibrium is significantly improved, and the parameter range for equilibrium pricing is expanded. These findings provide essential theoretical foundations and practical guidance for the design and application of group robot systems.<\/jats:p>","DOI":"10.3390\/e27020164","type":"journal-article","created":{"date-parts":[[2025,2,4]],"date-time":"2025-02-04T05:55:22Z","timestamp":1738648522000},"page":"164","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The Nonlinear Dynamics and Chaos Control of Pricing Games in Group Robot Systems"],"prefix":"10.3390","volume":"27","author":[{"given":"Chen","family":"Wang","sequence":"first","affiliation":[{"name":"School of Communication and Information Engineering, Xi\u2019an University of Science and Technology, Xi\u2019an 710054, China"},{"name":"Xi\u2019an Key Laboratory of Heterogeneous Network Convergence Communication, Xi\u2019an 710054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yi","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Communication and Information Engineering, Xi\u2019an University of Science and Technology, Xi\u2019an 710054, China"},{"name":"Xi\u2019an Key Laboratory of Heterogeneous Network Convergence Communication, Xi\u2019an 710054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-5316-8762","authenticated-orcid":false,"given":"Ying","family":"Han","sequence":"additional","affiliation":[{"name":"School of Communication and Information Engineering, Xi\u2019an University of Science and Technology, Xi\u2019an 710054, China"},{"name":"Xi\u2019an Key Laboratory of Heterogeneous Network Convergence Communication, Xi\u2019an 710054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chao","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Communication and Information Engineering, Xi\u2019an University of Science and Technology, Xi\u2019an 710054, China"},{"name":"Xi\u2019an Key Laboratory of Heterogeneous Network Convergence Communication, Xi\u2019an 710054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/j.ecolecon.2014.02.014","article-title":"Human and nature dynamics (HANDY): Modeling inequality and use of resources in the collapse or sustainability of societies","volume":"101","author":"Motesharrei","year":"2014","journal-title":"Ecol. 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