{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:25:38Z","timestamp":1760232338419,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,11,2]],"date-time":"2022-11-02T00:00:00Z","timestamp":1667347200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Natural Science Foundation of Shandong Province","award":["ZR2014FQ019","2017GGX10132"],"award-info":[{"award-number":["ZR2014FQ019","2017GGX10132"]}]},{"name":"the Key Research and Development Plan of Shandong Province","award":["ZR2014FQ019","2017GGX10132"],"award-info":[{"award-number":["ZR2014FQ019","2017GGX10132"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In order to reduce the circuit cost and improve the stability and flexibility of the circuit, a simplified symmetry chaotic circuit was designed and implemented by using an inverse integration circuit and a voltage follower as isolators. The change of different symmetry chaotic dynamic behaviors caused by the change of parameters can be realized by adjusting the time constant. The behavior coexistence characteristics and amplitude control characteristics under different initial conditions were verified. The results of circuit experiments are in good agreement with those of numerical simulation and theoretical analysis. This method is effective and feasible.<\/jats:p>","DOI":"10.3390\/sym14112299","type":"journal-article","created":{"date-parts":[[2022,11,3]],"date-time":"2022-11-03T04:11:31Z","timestamp":1667448691000},"page":"2299","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Design and Implementation of Simplified Symmetry Chaotic Circuit"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6448-5049","authenticated-orcid":false,"given":"Zhonglin","family":"Wang","sequence":"first","affiliation":[{"name":"School of Control Science and Engineering, Shangdong University, Jinan 250200, China"},{"name":"College of Aeronautical Engineering, Binzhou Uinversity, Binzhou 256603, China"},{"name":"Shandong Engineering Research Center of Aeronautical Materials and Devices, Binzhou 256603, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shutang","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Control Science and Engineering, Shangdong University, Jinan 250200, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1175\/1520-0469(1963)020<0130:DNF>2.0.CO;2","article-title":"Deterministic non-perodic flows","volume":"20","author":"Lorenz","year":"1963","journal-title":"Atoms. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1465","DOI":"10.1142\/S0218127499001024","article-title":"Yet another chaotic attractor","volume":"9","author":"Chen","year":"1999","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1142\/S0218127402004620","article-title":"A new chaotic attractor coined","volume":"12","author":"Chen","year":"2002","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2855","DOI":"10.1142\/S0218127406016501","article-title":"A Unified Lorenz-Type System and its Canonical Form","volume":"16","author":"Yang","year":"2006","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1393","DOI":"10.1142\/S0218127408021063","article-title":"A Chaotic System with One saddle and Two Stable Node-Foci","volume":"18","author":"Yang","year":"2008","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1031","DOI":"10.1016\/j.chaos.2004.02.060","article-title":"A new chaotic attracator","volume":"22","author":"Liu","year":"2004","journal-title":"Chaos Solitons Fractals"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2872","DOI":"10.1088\/1009-1963\/15\/12\/018","article-title":"A new chaotic system and its circuit realization","volume":"15","author":"Wang","year":"2006","journal-title":"Chin. Phys. B"},{"key":"ref_8","first-page":"383","article-title":"A simple memristive jerk system","volume":"15","author":"Li","year":"2020","journal-title":"IET Circuits Devices Syst."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Song, Y., Yuan, F., and Li, Y. (2019). Coexisting Attractors and Multistability in a Simple Memristive Wien-Bridge Chaotic Circuit. Entropy, 21.","DOI":"10.3390\/e21070678"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1244","DOI":"10.1016\/j.chaos.2007.11.008","article-title":"Bifurcation analysis of a new Lorenz-like chaotic system","volume":"37","author":"Mello","year":"2008","journal-title":"Chaos Solitons Fractals"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Valencia-Ponce, M.A., Casta\u00f1eda-Avi\u00f1a, P.R., Tlelo-Cuautle, E., Carbajal-G\u00f3mez, V.H., Gonz\u00e1lez-D\u00edaz, V.R., Sandoval-Ibarra, Y., and Nu\u00f1ez-Perez, J.C. (2021). CMOS OTA-based filters for designing fractional-order chaotic oscillators. Fractal Fract., 5.","DOI":"10.3390\/fractalfract5030122"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"68057","DOI":"10.1109\/ACCESS.2022.3181424","article-title":"A Novel 3D Chaotic System with Line Equilibrium: Multistability, Integral Sliding Mode Control, Electronic Circuit, FPGA Implementation and Its Image Encryption","volume":"10","author":"Sambas","year":"2022","journal-title":"IEEE Access"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2885","DOI":"10.1109\/TCSI.2022.3165469","article-title":"FPGA Implementation of Reconfigurable CORDIC Algorithm and a Memristive Chaotic System with Transcendental Nonlinearities","volume":"69","author":"Mohamed","year":"2022","journal-title":"IEEE Trans. Circuits Syst. I Regul. Pap."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"125586","DOI":"10.1109\/ACCESS.2019.2935751","article-title":"Design of a new seven-dimensional hyperchaotic circuit and its application in secure communication","volume":"7","author":"Yu","year":"2019","journal-title":"IEEE Access"},{"key":"ref_15","first-page":"6949703","article-title":"A Novel Voltage-Controlled Tri-Valued Memristor and Its Application in Chaotic System","volume":"2020","author":"Wang","year":"2020","journal-title":"Complexity"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2030019","DOI":"10.1142\/S0218127420300190","article-title":"Extreme Multistability and Complex Dynamics of a Memristor-Based Chaotic System","volume":"30","author":"Chang","year":"2020","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1081","DOI":"10.1109\/JAS.2020.1003252","article-title":"An exponential chaotic oscillator design and its dynamic analysis","volume":"7","author":"Wang","year":"2020","journal-title":"IEEE\/CAA J. Autom. Sin."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"110316","DOI":"10.1016\/j.chaos.2020.110316","article-title":"New chaotic memristive cellular neural network and its application in secure communication system","volume":"141","author":"Xiu","year":"2020","journal-title":"Chaos Solitons Fractals"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"10564","DOI":"10.1109\/TIE.2022.3144592","article-title":"A Self-Reproduction Hyperchaotic Map with Compound Lattice Dynamics","volume":"69","author":"Li","year":"2022","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"845","DOI":"10.1109\/TCSI.2013.2283999","article-title":"Chaotic Characteristics Analysis and Circuit Implementation for a Fractional-Order System","volume":"61","author":"Jia","year":"2014","journal-title":"Circuits Syst. I Regul. Pap. IEEE Trans."},{"key":"ref_21","first-page":"6669956","article-title":"Dynamical Analysis and Simulation of a New Lorenz-Like Chaotic System","volume":"2021","author":"Li","year":"2021","journal-title":"Math. Probl. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"10389","DOI":"10.1016\/j.ijleo.2016.08.046","article-title":"Variable-boostable chaotic flows","volume":"127","author":"Li","year":"2016","journal-title":"Optik"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/j.ins.2019.10.070","article-title":"Design and implementation of a simple dynamical 4-D chaotic circuit with applications in image encryption","volume":"515","author":"Tsafack","year":"2020","journal-title":"Inf. Sci."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"023112","DOI":"10.1063\/1.2723641","article-title":"A simple Lorenz circuit and its radio frequency implementation","volume":"17","author":"Blakely","year":"2007","journal-title":"Chaos"},{"key":"ref_25","first-page":"1837","article-title":"Simplification of Chaotic Circuits with Quadratic Nonlinearity","volume":"69","author":"Wu","year":"2022","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"key":"ref_26","first-page":"3344","article-title":"Simplified Memristive Lorenz Oscillator","volume":"69","author":"Jiang","year":"2022","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/11\/2299\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:09:21Z","timestamp":1760144961000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/11\/2299"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,2]]},"references-count":26,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2022,11]]}},"alternative-id":["sym14112299"],"URL":"https:\/\/doi.org\/10.3390\/sym14112299","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,11,2]]}}}