{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,26]],"date-time":"2026-06-26T04:51:37Z","timestamp":1782449497615,"version":"3.54.5"},"reference-count":76,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2026,6,26]],"date-time":"2026-06-26T00:00:00Z","timestamp":1782432000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100020963","name":"Moonshot Research and Development Program","doi-asserted-by":"publisher","award":["JPMJMS2021"],"award-info":[{"award-number":["JPMJMS2021"]}],"id":[{"id":"10.13039\/501100020963","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100009538","name":"Council for Science, Technology and Innovation","doi-asserted-by":"publisher","award":["JPJ012207"],"award-info":[{"award-number":["JPJ012207"]}],"id":[{"id":"10.13039\/501100009538","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003051","name":"New Energy and Industrial Technology Development Organization","doi-asserted-by":"publisher","award":["JPNP14004"],"award-info":[{"award-number":["JPNP14004"]}],"id":[{"id":"10.13039\/501100003051","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Netw. Physiol."],"abstract":"<jats:sec>\n                    <jats:title>Introduction<\/jats:title>\n                    <jats:p>Energy landscapes provide a useful lens for understanding multistability and state transitions in self-organizing systems, but systematic characterization of the energy landscapes for coupled oscillator networks remains less well developed. Here, we study a frustrated Stuart\u2013Landau oscillator network on a 2D toroidal lattice with competing local coupling and global frustration and characterize how its macroscopic states and noise-driven transitions reorganize as the frustration strength is varied.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Method<\/jats:title>\n                    <jats:p>We combine a mode-based, phase-decoupled approximation with homotopy continuation and track representative families of equilibria from the approximation to the full model. In singular cases where the leading XY-Hamiltonian phase interaction yields non-isolated critical points, we impose a second-order phase equilibrium condition and solve it in a constrained-solvability sense to ensure that continuation is well posed.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>Numerical continuation shows partial selectivity of this homotopy, in which lower-energy initializations tend to continue to similarly lower-energy, lower-index equilibria in the full system. Across frustration regimes, continuation shows how approximate equilibria split and reorder by energy and index; at intermediate frustration, extensive runs reveal multistability between an isolated global minimum and multiple 1D troughs contained within the edges of a multigraph. Guided by the resulting landscape-level picture, simulations demonstrate distinct noise-dependent synergetic phenomena, including noise-induced synchronization, noise-induced desynchronization, and persistent switching among coexisting macrostates. Stationary transition kinetics exhibit both Arrhenius\u2013Kramers-like (activated) and diffusion-limited scaling with respect to noise.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Discussion<\/jats:title>\n                    <jats:p>These results support a coupled-oscillator-based framework for analyzing the energy landscape of multivariate time series, with potential applications in neuroscience, physiology, and beyond.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.3389\/fnetp.2026.1778380","type":"journal-article","created":{"date-parts":[[2026,6,26]],"date-time":"2026-06-26T04:38:55Z","timestamp":1782448735000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Energy landscapes and synergetic state transitions in frustrated Stuart\u2013Landau oscillator networks: a homotopy continuation study"],"prefix":"10.3389","volume":"6","author":[{"given":"Yang","family":"Li","sequence":"first","affiliation":[{"name":"International Research Center for Neurointelligence (WPI-IRCN), The University of Tokyo","place":["Tokyo, Japan"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kazuyuki","family":"Aihara","sequence":"additional","affiliation":[{"name":"International Research Center for Neurointelligence (WPI-IRCN), The University of Tokyo","place":["Tokyo, Japan"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1965","published-online":{"date-parts":[[2026,6,26]]},"reference":[{"key":"B1","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1016\/S0893-6080(96)00061-5","article-title":"Associative dynamics in a chaotic neural network","volume":"10","author":"Adachi","year":"1997","journal-title":"Neural Netw."},{"key":"B2","doi-asserted-by":"publisher","first-page":"1195","DOI":"10.1142\/S0218127404009806","article-title":"Heteroclinic contours in neural ensembles and the winnerless competition principle","volume":"14","author":"Afraimovich","year":"","journal-title":"Int. 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