{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T11:46:02Z","timestamp":1772192762598,"version":"3.50.1"},"reference-count":43,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T00:00:00Z","timestamp":1772150400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"2025 National College Student Innovation Training Program","award":["202510668538"],"award-info":[{"award-number":["202510668538"]}]},{"name":"Anshun Science and Technology Program","award":["Anshike Fundamental [2025] 03"],"award-info":[{"award-number":["Anshike Fundamental [2025] 03"]}]},{"name":"Featured Scientific Research Territory Construction Project of Guizhou University of Engineering Science","award":["TSXQ202403"],"award-info":[{"award-number":["TSXQ202403"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Signals with flexible control over polarity and frequency provide an essential foundation for reliable and high-speed information transmission. To generate chaotic signals with flexible output characteristics in low-dimensional systems, a novel chaotic system model is proposed by introducing a nonlinear term into the classical Chen chaotic system. Dynamical analysis and MATLAB numerical simulations show that the system is not only highly sensitive to initial conditions but also capable of generating three distinct chaotic attractors. Further simulations confirm that the proposed system demonstrates arbitrary unidirectional and multidirectional offset boosting behaviors, with offset amplitudes in all directions having a wide adjustable range. Furthermore, arbitrary offset constants can effectively control the frequencies of all state variables. This chaotic system, which combines flexible offset control with frequency regulation, is rare in existing research. Additionally, certain parameter ranges in the chaotic regime are relatively narrow. To address this, a method involving control constants to enhance system complexity is proposed, and its effectiveness in increasing system complexity is validated through Lyapunov spectrum and spectral entropy (SE) analysis. Based on the constructed chaotic system, an equivalent circuit model was built using the Multisim 14.0 platform. Experimental results confirm that the system generates chaotic attractors with distinct structures and demonstrates offset boosting behavior in arbitrary directions. Additionally, DSP hardware experiments further validate the physical realizability of the system. To fully exploit the system\u2019s advantages, a synchronization controller was designed for both the drive and response systems, enabling synchronization control of the chaotic system with three offset constants. Based on this, data encryption and transmission experiments were conducted, further establishing the theoretical and experimental foundation for applying the new chaotic system in secure communication.<\/jats:p>","DOI":"10.3390\/e28030260","type":"journal-article","created":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T10:41:02Z","timestamp":1772188862000},"page":"260","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Analysis and Application of a 3D Chaotic System with Flexible Offset and Frequency Control"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-1530-6535","authenticated-orcid":false,"given":"Shuaishuai","family":"Shi","sequence":"first","affiliation":[{"name":"School of Information Engineering, Guizhou University of Engineering Science, Bijie 551700, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiangfan","family":"Xiong","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Guizhou University of Engineering Science, Bijie 551700, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3399-2117","authenticated-orcid":false,"given":"Licai","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Electronics and Information Engineering, Anshun University, Anshun 561000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1568-9464","authenticated-orcid":false,"given":"Chuanhong","family":"Du","sequence":"additional","affiliation":[{"name":"College of Electronics and Information Engineering, Anshun University, Anshun 561000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"116554","DOI":"10.1016\/j.chaos.2025.116554","article-title":"Study on weak signal amplitude detection and circuit simulation based on a new chaotic system","volume":"198","author":"Zhao","year":"2025","journal-title":"Chaos Solitons Fractals"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"19240","DOI":"10.3934\/math.2025860","article-title":"Chaotic dynamics in Sprott\u2019s memristive artificial neural network: Dynamic analysis, circuit implementation and synchronization","volume":"10","author":"Kopp","year":"2025","journal-title":"Aims Math."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1520405","DOI":"10.1007\/s11431-024-2886-4","article-title":"A Morris-Lecar model with novel fast-slow structure and its FPGA implementation","volume":"68","author":"Yu","year":"2025","journal-title":"Sci. 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