{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T17:42:23Z","timestamp":1790876543467,"version":"4.1.0"},"reference-count":33,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2018,3,27]],"date-time":"2018-03-27T00:00:00Z","timestamp":1522108800000},"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>Chaotic systems with hyperbolic sine nonlinearity have attracted the attention of researchers in the last two years. This paper introduces a new approach for generating a class of simple chaotic systems with hyperbolic sine. With nth-order ordinary differential equations (ODEs), any desirable order of chaotic systems with hyperbolic sine nonlinearity can be easily constructed. Fourth-order, fifth-order, and tenth-order chaotic systems are taken as examples to verify the theory. To achieve simplicity of the electrical circuit, two back-to-back diodes represent hyperbolic sine nonlinearity without any multiplier or subcircuits. Thus, these systems can achieve both physical simplicity and analytic complexity at the same time.<\/jats:p>","DOI":"10.3390\/e20040230","type":"journal-article","created":{"date-parts":[[2018,3,27]],"date-time":"2018-03-27T12:17:24Z","timestamp":1522153044000},"page":"230","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["An Approach for the Generation of an Nth-Order Chaotic System with Hyperbolic Sine"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8303-2619","authenticated-orcid":false,"given":"Jizhao","family":"Liu","sequence":"first","affiliation":[{"name":"School of Information Science and Engineering, Lanzhou University, Lanzhou 730000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jun","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Physics and Electronic Information Engineering, Qinghai Normal University, Xining 810008, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jing","family":"Lian","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Lanzhou University, Lanzhou 730000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pengbin","family":"Chang","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Lanzhou University, Lanzhou 730000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yide","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Lanzhou University, Lanzhou 730000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2018,3,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Fiori, S., and Di Filippo, R. 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