{"title":"Lorenz system manufacturing with a Butterworth filter","authors":"L.L. Jiménez-Zacarías , I. Campos-Cantón","doi":"10.1016/j.vlsi.2025.102386","DOIUrl":null,"url":null,"abstract":"<div><div>This paper investigates the Lorenz system <span><math><mi>x</mi></math></span> state equation duality, with a first-order <span><math><mrow><mi>R</mi><mi>C</mi></mrow></math></span> passive low-pass filter to propose a new Lorenz type system. This new Lorenz type system is done electronically; to fulfill this objective, an electronic circuit is developed using a Butterworth, Chebyshev, and second order <span><math><mrow><mi>R</mi><mi>C</mi></mrow></math></span> filter replacing the <span><math><mi>x</mi></math></span> state low pass filter. The electronic circuit is simulated using Multisim software. Bifurcation diagrams, Lyapunov exponents, and phase portrait techniques are used to confirm the chaotic circuit behavior. It is found that the Lorenz system produces chaos if the second-order <span><math><mrow><mi>R</mi><mi>C</mi></mrow></math></span> filter associated with the <span><math><mi>x</mi></math></span> state is tuned to a 10 rad/sec cutoff frequency, whereas it should be 28 rad/sec for the Butterworth filter and 40 rad/sec for the Chebyshev filter.</div></div>","PeriodicalId":54973,"journal":{"name":"Integration-The Vlsi Journal","volume":"103 ","pages":"Article 102386"},"PeriodicalIF":2.2000,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Integration-The Vlsi Journal","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167926025000434","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, HARDWARE & ARCHITECTURE","Score":null,"Total":0}
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Abstract
This paper investigates the Lorenz system state equation duality, with a first-order passive low-pass filter to propose a new Lorenz type system. This new Lorenz type system is done electronically; to fulfill this objective, an electronic circuit is developed using a Butterworth, Chebyshev, and second order filter replacing the state low pass filter. The electronic circuit is simulated using Multisim software. Bifurcation diagrams, Lyapunov exponents, and phase portrait techniques are used to confirm the chaotic circuit behavior. It is found that the Lorenz system produces chaos if the second-order filter associated with the state is tuned to a 10 rad/sec cutoff frequency, whereas it should be 28 rad/sec for the Butterworth filter and 40 rad/sec for the Chebyshev filter.
期刊介绍：
Integration''s aim is to cover every aspect of the VLSI area, with an emphasis on cross-fertilization between various fields of science, and the design, verification, test and applications of integrated circuits and systems, as well as closely related topics in process and device technologies. Individual issues will feature peer-reviewed tutorials and articles as well as reviews of recent publications. The intended coverage of the journal can be assessed by examining the following (non-exclusive) list of topics:
Specification methods and languages; Analog/Digital Integrated Circuits and Systems; VLSI architectures; Algorithms, methods and tools for modeling, simulation, synthesis and verification of integrated circuits and systems of any complexity; Embedded systems; High-level synthesis for VLSI systems; Logic synthesis and finite automata; Testing, design-for-test and test generation algorithms; Physical design; Formal verification; Algorithms implemented in VLSI systems; Systems engineering; Heterogeneous systems.
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