{"id":1891,"date":"2021-01-16T20:33:13","date_gmt":"2021-01-16T18:33:13","guid":{"rendered":"http:\/\/journals.khnu.km.ua\/vestnik\/?p=1891"},"modified":"2021-04-22T13:42:16","modified_gmt":"2021-04-22T10:42:16","slug":"%d1%86%d0%b8%d0%ba%d0%bb%d1%96%d1%87%d0%bd%d1%96%d1%81%d1%82%d1%8c-%d0%bf%d0%be%d1%81%d0%bb%d1%96%d0%b4%d0%be%d0%b2%d0%bd%d0%be%d1%81%d1%82%d0%b5%d0%b9-%d0%b3%d0%b5%d0%bd%d0%b5%d1%80%d0%be%d0%b2","status":"publish","type":"post","link":"https:\/\/journals.khnu.km.ua\/vestnik\/?p=1891","title":{"rendered":"\u0426\u0438\u043a\u043b\u0456\u0447\u043d\u0456\u0441\u0442\u044c \u043f\u043e\u0441\u043b\u0456\u0434\u043e\u0432\u043d\u043e\u0441\u0442\u0435\u0439, \u0433\u0435\u043d\u0435\u0440\u043e\u0432\u0430\u043d\u0438\u0445 \u043c\u0435\u043c\u0440\u0438\u0441\u0442\u043e\u0440\u043d\u043e\u044e \u0445\u0430\u043e\u0442\u0438\u0447\u043d\u043e\u044e \u0441\u0438\u0441\u0442\u0435\u043c\u043e\u044e"},"content":{"rendered":"

\u0426\u0418\u041a\u041b\u0406\u0427\u041d\u0406\u0421\u0422\u042c \u041f\u041e\u0421\u041b\u0406\u0414\u041e\u0412\u041d\u041e\u0421\u0422\u0415\u0419, \u0413\u0415\u041d\u0415\u0420\u041e\u0412\u0410\u041d\u0418\u0425 \u041c\u0415\u041c\u0420\u0418\u0421\u0422\u041e\u0420\u041d\u041e\u042e \u0425\u0410\u041e\u0422\u0418\u0427\u041d\u041e\u042e \u0421\u0418\u0421\u0422\u0415\u041c\u041e\u042e<\/p>\n

CYCLICITY OF TIME SERIES GENERATED BY MEMRISTOR BASED CHAOTIC CIRCUIT<\/p>\n

<\/a> \u0421\u0442\u043e\u0440\u0456\u043d\u043a\u0438: 110-115. \u041d\u043e\u043c\u0435\u0440: \u21166, 2019 (279)<\/strong>
\n\u0410\u0432\u0442\u043e\u0440\u0438: <\/strong>
\n\u041e.\u0412. \u041a\u0420\u0423\u041b\u0406\u041a\u041e\u0412\u0421\u042c\u041a\u0418\u0419, \u0421.\u0414. \u0413\u0410\u041b\u042e\u041a
\n\u0427\u0435\u0440\u043d\u0456\u0432\u0435\u0446\u044c\u043a\u0438\u0439 \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0456\u043c\u0435\u043d\u0456 \u042e\u0440\u0456\u044f \u0424\u0435\u0434\u044c\u043a\u043e\u0432\u0438\u0447\u0430
\nO.V. KRULIKOVSKYI, S.D. HALIUK
\nYuriy Fedkovych Chernivtsi National University
\nDOI:<\/strong> https:\/\/www.doi.org\/10.31891\/2307-5732-2019-279-6-110-115<\/a>
\n\u0420\u0435\u0446\u0435\u043d\u0437\u0456\u044f\/Peer review :<\/strong> 24.12.2019 \u0440.
\n\u041d\u0430\u0434\u0440\u0443\u043a\u043e\u0432\u0430\u043d\u0430\/Printed :<\/strong> 13.01.2020 \u0440.<\/p>\n

\u0410\u043d\u043e\u0442\u0430\u0446\u0456\u044f \u043c\u043e\u0432\u043e\u044e \u043e\u0440\u0438\u0433\u0456\u043d\u0430\u043b\u0443<\/strong><\/p>\n

\u0412 \u0440\u043e\u0431\u043e\u0442\u0456 \u043d\u0430 \u043f\u0440\u0438\u043a\u043b\u0430\u0434\u0456 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u043d\u043e\u0457 \u043c\u043e\u0434\u0435\u043b\u0456 \u043c\u0435\u043c\u0440\u0438\u0441\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u0445\u0430\u043e\u0442\u0438\u0447\u043d\u0438\u0445 \u043a\u043e\u043b\u0438\u0432\u0430\u043d\u044c \u0432\u0438\u0432\u0447\u0430\u0454\u0442\u044c\u0441\u044f \u0434\u043e\u0446\u0456\u043b\u044c\u043d\u0456\u0441\u0442\u044c \u0437\u0430\u0441\u0442\u043e\u0441\u0443\u0432\u0430\u043d\u043d\u044f \u043c\u0435\u0442\u043e\u0434\u0456\u0432 \u0447\u0438\u0441\u0435\u043b\u044c\u043d\u043e\u0433\u043e \u0440\u0456\u0448\u0435\u043d\u043d\u044f \u0434\u0438\u0444\u0435\u0440\u0435\u043d\u0446\u0456\u0439\u043d\u0438\u0445 \u0440\u0456\u0432\u043d\u044f\u043d\u044c \u0432\u0438\u0441\u043e\u043a\u043e\u0457 \u0442\u043e\u0447\u043d\u043e\u0441\u0442\u0456 \u0432 \u043a\u0440\u0438\u043f\u0442\u043e\u0433\u0440\u0430\u0444\u0456\u0447\u043d\u0438\u0445 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0430\u0445. \u0412\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u044e\u0447\u0438 Simulink-\u043c\u043e\u0434\u0435\u043b\u0456 \u0445\u0430\u043e\u0442\u0438\u0447\u043d\u043e\u0457 \u0441\u0438\u0441\u0442\u0435\u043c\u0438 \u0456 \u0430\u0440\u0438\u0444\u043c\u0435\u0442\u0438\u043a\u0443 \u0437 \u0444\u0456\u043a\u0441\u043e\u0432\u0430\u043d\u043e\u044e \u043a\u043e\u043c\u043e\u044e \u0434\u043e\u0441\u043b\u0456\u0434\u0436\u0435\u043d\u043e \u043f\u0435\u0440\u0456\u043e\u0434\u0438\u0447\u043d\u0456\u0441\u0442\u044c \u0440\u0435\u0430\u043b\u0456\u0437\u0430\u0446\u0456\u0439 \u043e\u0442\u0440\u0438\u043c\u0430\u043d\u0438\u0445 \u0437\u0430 \u0434\u043e\u043f\u043e\u043c\u043e\u0433\u043e\u044e \u043c\u0435\u0442\u043e\u0434\u0456\u0432 \u0415\u0439\u043b\u0435\u0440\u0430 \u0442\u0430 \u0420\u0443\u043d\u0433\u0435-\u041a\u0443\u0442\u0442\u0438 \u0447\u0435\u0442\u0432\u0435\u0440\u0442\u043e\u0433\u043e \u043f\u043e\u0440\u044f\u0434\u043a\u0443. \u041f\u043e\u043a\u0430\u0437\u0430\u043d\u043e, \u0449\u043e \u0437 \u0432\u0440\u0430\u0445\u0443\u0432\u0430\u043d\u043d\u044f\u043c \u0447\u0430\u0441\u043e\u0432\u043e\u0457 \u0441\u043a\u043b\u0430\u0434\u043d\u043e\u0441\u0442\u0456 \u0432\u0438\u043a\u043e\u043d\u0430\u043d\u043d\u044f \u043e\u043f\u0435\u0440\u0430\u0446\u0456\u0439 \u043f\u0440\u0438 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043d\u0456\u0439 \u0456 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043d\u043e-\u0430\u043f\u0430\u0440\u0430\u0442\u043d\u0456\u0439 \u0440\u0435\u0430\u043b\u0456\u0437\u0430\u0446\u0456\u0457 \u043d\u0435\u043f\u0435\u0440\u0435\u0440\u0432\u043d\u0438\u0445 \u0445\u0430\u043e\u0442\u0438\u0447\u043d\u0438\u0445 \u0441\u0438\u0441\u0442\u0435\u043c \u0434\u043e\u0446\u0456\u043b\u044c\u043d\u043e \u043a\u043e\u0440\u0438\u0441\u0442\u0443\u0432\u0430\u0442\u0438\u0441\u044f \u043c\u0435\u0442\u043e\u0434\u043e\u043c \u0415\u0439\u043b\u0435\u0440\u0430.
\n\u041a\u043b\u044e\u0447\u043e\u0432\u0456 \u0441\u043b\u043e\u0432\u0430: \u0445\u0430\u043e\u0442\u0438\u0447\u043d\u0430 \u0441\u0438\u0441\u0442\u0435\u043c\u0430, \u043c\u0435\u043c\u0440\u0438\u0441\u0442\u043e\u0440\u043d\u0430 \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u0430, \u043f\u0435\u0440\u0456\u043e\u0434\u0438\u0447\u043d\u0456\u0441\u0442\u044c, \u043c\u0435\u0442\u043e\u0434 \u0415\u0439\u043b\u0435\u0440\u0430, \u043c\u0435\u0442\u043e\u0434 \u0420\u0443\u043d\u0433\u0435-\u041a\u0443\u0442\u0442\u0438, \u0445\u0430\u043e\u0442\u0438\u0447\u043d\u0430 \u043a\u0440\u0438\u043f\u0442\u043e\u0433\u0440\u0430\u0444\u0456\u044f.<\/p>\n

\u0420\u043e\u0437\u0448\u0438\u0440\u0435\u043d\u0430 \u0430\u043d\u043e\u0442\u0430\u0446\u0456\u044f \u0430\u043d\u0433\u043b\u0456\u0439\u0441\u044c\u043a\u043e\u044e \u043c\u043e\u0432\u043e\u044e<\/strong><\/p>\n

In the paper the solutions periodicity of the mathematical model of the memristor chaotic oscillator and expediency of application different methods of high precision numerical solution of differential equations in cryptographic algorithms is studied. Based on Lyapunov exponent theory the dynamic of chaotic system and its dependencies from system parameters is explored. There are several ranges of system parameters where the largest Lyapunov exponent is greater zero and memeristor system has chaotic modes. The transition from continuous system to discretized model is discussed. Using probability density and atractors it is shown saving of properties of chaotic regimes for different methods of numerical modelling. The periodicity of timeseries obtained by Euler and Runge-Kutta methods is studied by Simulink-model of chaotic systems and fixed-point arithmetic. For timeseries of discrete chaotic system the average period is computed. When timestep is equal \u00a0and fixed-point arithmetic Q8.16 average period is about \u00a0iterations. If discrete-time series save the original chaotic modes of continuous system, then average period do not depend from timestep of discrete model and computation complexity. It is shown that taking into consideration the complexity of computation for hardware implementation of continuous chaotic systems is advisable to use the Euler method. If timestep close to precision of computation, after several tens iterations collapse of chaos of discrete-time systems is appear with a one-step length period.
\nKeywords:<\/strong> chaotic system, memristor system, periodicity, Euler method, Runge-Kutta method, cryptography.<\/p>\n

References<\/strong><\/p>\n

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    \u0426\u0418\u041a\u041b\u0406\u0427\u041d\u0406\u0421\u0422\u042c \u041f\u041e\u0421\u041b\u0406\u0414\u041e\u0412\u041d\u041e\u0421\u0422\u0415\u0419, \u0413\u0415\u041d\u0415\u0420\u041e\u0412\u0410\u041d\u0418\u0425 \u041c\u0415\u041c\u0420\u0418\u0421\u0422\u041e\u0420\u041d\u041e\u042e \u0425\u0410\u041e\u0422\u0418\u0427\u041d\u041e\u042e \u0421\u0418\u0421\u0422\u0415\u041c\u041e\u042e CYCLICITY OF TIME SERIES GENERATED BY MEMRISTOR BASED CHAOTIC CIRCUIT \u0421\u0442\u043e\u0440\u0456\u043d\u043a\u0438: 110-115. \u041d\u043e\u043c\u0435\u0440: \u21166, 2019 (279) \u0410\u0432\u0442\u043e\u0440\u0438: \u041e.\u0412. \u041a\u0420\u0423\u041b\u0406\u041a\u041e\u0412\u0421\u042c\u041a\u0418\u0419, \u0421.\u0414. \u0413\u0410\u041b\u042e\u041a \u0427\u0435\u0440\u043d\u0456\u0432\u0435\u0446\u044c\u043a\u0438\u0439 \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0456\u043c\u0435\u043d\u0456 \u042e\u0440\u0456\u044f \u0424\u0435\u0434\u044c\u043a\u043e\u0432\u0438\u0447\u0430 O.V. KRULIKOVSKYI, S.D. HALIUK Yuriy Fedkovych Chernivtsi National University DOI: https:\/\/www.doi.org\/10.31891\/2307-5732-2019-279-6-110-115 \u0420\u0435\u0446\u0435\u043d\u0437\u0456\u044f\/Peer review : 24.12.2019 \u0440. \u041d\u0430\u0434\u0440\u0443\u043a\u043e\u0432\u0430\u043d\u0430\/Printed : 13.01.2020 \u0440. \u0410\u043d\u043e\u0442\u0430\u0446\u0456\u044f \u043c\u043e\u0432\u043e\u044e […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[19],"tags":[],"_links":{"self":[{"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/posts\/1891"}],"collection":[{"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1891"}],"version-history":[{"count":3,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/posts\/1891\/revisions"}],"predecessor-version":[{"id":6018,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/posts\/1891\/revisions\/6018"}],"wp:attachment":[{"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1891"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1891"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1891"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}