{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,8]],"date-time":"2026-09-08T13:13:21Z","timestamp":1788873201293,"version":"build-2803163510"},"reference-count":51,"publisher":"AIP Publishing","issue":"9","funder":[{"DOI":"10.13039\/501100001410","name":"Human Resource Development Group","doi-asserted-by":"publisher","award":["09\/0025 (17591)\/2024-EMR-I"],"award-info":[{"award-number":["09\/0025 (17591)\/2024-EMR-I"]}],"id":[{"id":"10.13039\/501100001410","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2026,9,1]]},"abstract":"<jats:p>Deterministic chaotic systems often exhibit highly organized structures in both phase space and parameter space. In this work, we investigate two-dimensional H\u00e9non-like extensions of the discrete Gaussian and cubic maps incorporating a linear feedback channel. The Gaussian-based model admits a natural realization as a nonlinear electronic circuit consisting of a Gaussian-saturating amplifier coupled to a linear memory feedback loop. A detailed bifurcation analysis reveals that, while the classical one-dimensional Gaussian map is primarily organized by fold and flip bifurcations together with period-bubbling routes to chaos, its two-dimensional extension possesses a substantially richer dynamical structure. In particular, the system exhibits Neimark\u2013Sacker bifurcations, quasiperiodic dynamics, Arnold tongues generated through frequency locking, shrimp-shaped periodic stability regions embedded within chaotic regimes, and extensive multistability. The observed Arnold tongues follow the classical Farey-tree hierarchy of rotation numbers and organize the resonance structure of the parameter space. Furthermore, coexistence of attractors is demonstrated through bistability between period-9 and period-14 oscillations for identical parameter values. The corresponding basins of attraction display strong intermingling, and the computed basin entropy (Sb\u2009=\u20090.6032) indicates fractal basin boundaries and pronounced sensitivity to initial conditions. In addition, although the one-dimensional cubic map already exhibits shrimp-shaped periodic windows, its two-dimensional extension reveals nested shrimp families together with resonance tongue structures, substantially enriching the global bifurcation landscape. These results show that low-dimensional nonlinear maps can generate highly organized parameter-space architectures in which periodic, quasiperiodic, and chaotic dynamics coexist through well-defined bifurcation mechanisms.<\/jats:p>","DOI":"10.1063\/5.0346275","type":"journal-article","created":{"date-parts":[[2026,9,8]],"date-time":"2026-09-08T13:03:54Z","timestamp":1788872634000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Organized structures and multiple attractors in chaotic regimes"],"prefix":"10.1063","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-5842-7995","authenticated-orcid":false,"given":"Purbasha","family":"Deb","sequence":"first","affiliation":[{"name":"Department of Mathematics, The University of Burdwan , Burdwan 713104, West Bengal,","place":["India"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0867-5689","authenticated-orcid":false,"given":"G. 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