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5 results on '"Chaotic systems"'

1. METHODS FOR BIFURCATION AND RECURRENT ANALYSIS OF NONLINEAR DYNAMICAL SYSTEMS ON MEMRISTIVE CIRCUIT EXAMPLE

Author

D. N. Butusov, A. V. Tutueva, N. P. Kobyzev, D. O. Pesterev, and V. G. Rybin

Subjects
chaotic systems, numerical integration methods, bifurcation analysis, multi-wing attractors, hidden attractors, memristors, Optics. Light, QC350-467, Electronic computers. Computer science, QA75.5-76.95
Abstract

The subject of this study is the analysis algorithms for studying the behavior of the computer models of electronic circuits with advanced nonlinear elements. The paper gives an experimental comparison of four methods of obtaining two-parametric bifurcation diagrams: histogram of maximal values method, kernel density estimation method, sliding window technique and algorithm based on clusterization of recurrence density plot. The simple memristive circuit with chaotic multi-scroll attractor was chosen as an example for experimental part of the study. The following main results were obtained. Two new algorithms of chaotic system analysis were developed, combining the methods of bifurcation and recurrent analysis with mathematical statistics. New technique for creation of two-parametric high resolution bifurcation diagrams is proposed. This technique is based on sliding average window approach. We also propose the clustering method for plotting precise dynamical maps. The comparative analysis of proposed techniques is described, including the comparison with existing approaches. The study of computational efficiency is performed for integration numerical methods applied for the synthesis of discrete models of the circuit. By comparison of efficiency plots the optimal ordinary differential equation (ODE) solver for computer experiments with discrete models was chosen. The efficiency analysis has shown that the best ODE solver for simple memristive circuit simulation is the semi-implicit extrapolation algorithm of order eight. It is experimentally shown that sliding window average method is the most precise approach for creation of two-parametric bifurcation diagrams. The practical relevance of the obtained results is as follows. New methods of nonlinear systems analysis are applicable for creation of high precision simulation tools for circuits with advanced nonlinear elements. The applications are not limited to the electronic circuits simulation only but also include the possibility to locate hidden attractors in chaotic dynamical systems.

Published
2019
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2. Protection of communication channels through the use of nonlinear systems

Subjects
системы передачи информации, complete synchronization of chaotic generators, lyapunov exponents, Ñ Ð°Ð¾Ñ‚Ð¸Ñ‡ÐµÑÐºÐ¸Ðµ системы, ÑÐ¸Ð½Ñ Ñ€Ð¾Ð½Ð¸Ð·Ð°Ñ†Ð¸Ñ, полная ÑÐ¸Ð½Ñ Ñ€Ð¾Ð½Ð¸Ð·Ð°Ñ†Ð¸Ñ Ñ Ð°Ð¾Ñ‚Ð¸Ñ‡ÐµÑÐºÐ¸Ñ Ð³ÐµÐ½ÐµÑ€Ð°Ñ‚Ð¾Ñ€Ð¾Ð², chaotic systems, Ñ Ð°Ñ€Ð°ÐºÑ‚ÐµÑ€Ð¸ÑÑ‚Ð¸Ñ‡ÐµÑÐºÐ¸Ðµ показатели Ляпунова, synchronization, information transmission systems
Abstract

Целью работы является повышение уровня конфиденциальности и эффективности передачи информации в Ñ‚ÐµÐ»ÐµÐºÐ¾Ð¼Ð¼ÑƒÐ½Ð¸ÐºÐ°Ñ†Ð¸Ð¾Ð½Ð½Ñ‹Ñ ÑÐ¸ÑÑ‚ÐµÐ¼Ð°Ñ . Задачи, которые решаются в работе:1) Анализ методов и ÑÑƒÑ‰ÐµÑÑ‚Ð²ÑƒÑŽÑ‰Ð¸Ñ Ñ€ÐµÑˆÐµÐ½Ð¸Ð¹ по использованию детерминированного Ñ Ð°Ð¾ÑÐ° для передачи информации;2) анализ Ð¼Ð°Ñ‚ÐµÐ¼Ð°Ñ‚Ð¸Ñ‡ÐµÑÐºÐ¸Ñ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ Ð´Ð¸Ð½Ð°Ð¼Ð¸Ñ‡ÐµÑÐºÐ¸Ñ ÑÐ¸ÑÑ‚ÐµÐ¼, которые могут генерировать Ñ Ð°Ð¾Ñ;3) выбор средств и алгоритмов для численного расчета и моделирования Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½Ñ‹Ñ ÑÐ¸ÑÑ‚ÐµÐ¼;4) моделирование ÑÐ¸Ð½Ñ Ñ€Ð¾Ð½Ð½Ð¾ ÑÐ²ÑÐ·Ð°Ð½Ð½Ñ‹Ñ Ñ Ð°Ð¾Ñ‚Ð¸Ñ‡Ð½Ñ‹Ñ ÑÐ¸ÑÑ‚ÐµÐ¼5) моделирование процесса передачи сигналов с помощью Ñ Ð°Ð¾Ñ‚Ð¸Ñ‡Ð½Ñ‹Ñ ÑÐ¸ÑÑ‚ÐµÐ¼6) разработка алгоритма и программная реализация шифрования Ð´Ð°Ð½Ð½Ñ‹Ñ Ð´Ð¸ÑÐºÑ€ÐµÑ‚Ð½Ñ‹Ð¼Ð¸ Ñ Ð°Ð¾Ñ‚Ð¸Ñ‡Ð½Ñ‹Ð¼Ð¸ последовательностями.Объект исследования – процесс конфиденциальной передачи Ð¸Ð½Ñ„Ð¾Ñ€Ð¼Ð°Ñ†Ð¸Ð¾Ð½Ð½Ñ‹Ñ ÑÐ¸Ð³Ð½Ð°Ð»Ð¾Ð² по каналам связи в Ñ‚ÐµÐ»ÐµÐºÐ¾Ð¼Ð¼ÑƒÐ½Ð¸ÐºÐ°Ñ†Ð¸Ð¾Ð½Ð½Ñ‹Ñ ÑÐ¸ÑÑ‚ÐµÐ¼Ð°Ñ . Предмет исследования – методы и средства конфиденциальной передачи Ð¸Ð½Ñ„Ð¾Ñ€Ð¼Ð°Ñ†Ð¸Ð¾Ð½Ð½Ñ‹Ñ ÑÐ¸Ð³Ð½Ð°Ð»Ð¾Ð² с помощью устройств с Ñ Ð°Ð¾Ñ‚Ð¸Ñ‡Ð½Ð¾Ð¹ динамикой.Научно – практическая новизна работы:1) Получил развитие метод шифрования Ð´Ð°Ð½Ð½Ñ‹Ñ Ð½Ð° основе Ð´Ð¸ÑÐºÑ€ÐµÑ‚Ð½Ñ‹Ñ Ñ Ð°Ð¾Ñ‚Ð¸Ñ‡ÐµÑÐºÐ¸Ñ Ð¿Ð¾ÑÐ»ÐµÐ´Ð¾Ð²Ð°Ñ‚ÐµÐ»ÑŒÐ½Ð¾ÑÑ‚ÐµÐ¹. На базе дискретно – временной Динамической модели Лоренца был разработан алгоритм шифрования Ð¸ÑÑ Ð¾Ð´Ð½Ð¾Ð³Ð¾ массива байтов. 2) методов, Ð¾ÑÐ½Ð¾Ð²Ð°Ð½Ð½Ñ‹Ñ Ð´ÐµÑ‚ÐµÑ€Ð¼Ð¸Ð½Ð¸Ñ€Ð¾Ð²Ð°Ð½Ð½Ð¾Ð³Ð¾ Ñ Ð°Ð¾ÑÐ°, с помощью ÐºÐ¾Ñ‚Ð¾Ñ€Ñ‹Ñ Ð²Ð¾Ð·Ð¼Ð¾Ð¶Ð½Ð¾ повысить Представлен теории ряд на эффективность и конфиденциальность передачи информации Ñ‚ÐµÐ»ÐµÐºÐ¾Ð¼Ð¼ÑƒÐ½Ð¸ÐºÐ°Ñ†Ð¸Ð¾Ð½Ð½Ñ‹Ñ ÑÐ¸ÑÑ‚ÐµÐ¼Ð°. На базе динамической системы Лоренца был разработан комплекс Ð¸Ð¼Ð¸Ñ‚Ð°Ñ†Ð¸Ð¾Ð½Ð½Ñ‹Ñ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ Ñ Ð°Ð¾Ñ‚Ð¸Ñ‡Ð½Ñ‹Ñ Ð³ÐµÐ½ÐµÑ€Ð°Ñ‚Ð¾Ñ€Ð¾Ð², систем ÑÐ¸Ð½Ñ Ñ€Ð¾Ð½Ð¸Ð·Ð°Ñ†Ð¸Ð¸ и передачи Ð´Ð¸ÑÐºÑ€ÐµÑ‚Ð½Ñ‹Ñ Ð¸ Ð°Ð½Ð°Ð»Ð¾Ð³Ð¾Ð²Ñ‹Ñ ÑÐ¸Ð³Ð½Ð°Ð»Ð¾Ð² с помощью Ñ Ð°Ð¾ÑÐ°., The purpose of the work is to increase the level of confidentiality and efficiency of information transfer in telecommunication systems. The tasks that are solved in the work:1) Analysis of methods and existing decisions on the use of deterministic chaos for information transfer;2) analysis of mathematical models of dynamic systems that can generate chaos;3) selection of tools and algorithms for numerical calculation and modeling of nonlinear systems;4) simulating synchronously connected chaotic systems5) modeling the process of signal transmission using chaotic systems6) algorithm development and software implementation of data encryption by discrete chaotic sequences.The object of the study is the process of confidential transmission of information signals through communication channels in telecommunication systems.The subject of research is the methods and means of confidential transmission of information signals using devices with chaotic dynamics.Scientific and practical novelty of the work:1) The method of encrypting data based on discrete chaotic sequences has been developed. Based on the discrete-time Dynamic Lorentz model, an algorithm for encrypting the original byte array was developed.2) methods based on deterministic chaos, with the help of which it is possible to increase a number of theories on the efficiency and confidentiality of the transmission of information telecommunications systems. Based on the dynamic Lorentz system, a complex of simulation models of chaotic generators, synchronization and transmission systems of discrete and analog signals using chaos was developed.

Published
2023
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3. The Analysis of Periodic Signal Detection Method Based on Duffing System Chaotic Dynamics

Author

V. V. Martynyuk, Ye. V. Havrylko, J. M. Boiko, and M. V. Fedula

Subjects
weak signal detection, chaotic systems, signal-to-noise ratio, phase portrait, Telecommunication, TK5101-6720
Abstract

This article presents the analysis of periodic signal detection method based on Duffing system sensitivity to weak influences. The described signal detection method is developed with using of Duffing system that oscillates in chaotic state, without transitions to periodic state. The main advantage of such method is the absence of periodic oscillation modes with low sensitivity. The divergence of Duffing system phase trajectories is investigated with influences of different periodic signals under low signal-to-noise ratio values. The estimation of phase trajectories divergence is performed with using of numeric integration. The signal detection method is analyzed with different forms of input signal: sinusoidal, square, triangle. The analysis shows that a reliable detection of periodic signal can be performed for any of the three presented forms of signal with repeating frequency near the frequency of the driving signal. The obtained results show wide capabilities of Duffing system applications for detection of weak periodic signals.

Published
2018
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4. Complete synchronization of chaotic systems based on the control of Lyapunov characteristic indicators

Subjects
Генераторы, Ñ Ð°Ð¾Ñ‚Ð¸Ñ‡ÐµÑÐºÐ¸Ðµ системы, полная ÑÐ¸Ð½Ñ Ñ€Ð¾Ð½Ð¸Ð·Ð°Ñ†Ð¸Ñ Ñ Ð°Ð¾Ñ‚Ð¸Ñ‡ÐµÑÐºÐ¸Ñ Ð³ÐµÐ½ÐµÑ€Ð°Ñ‚Ð¾Ñ€Ð¾Ð², Lyapunov characteristic exponents, chaotic systems, Ñ Ð°Ñ€Ð°ÐºÑ‚ÐµÑ€Ð¸ÑÑ‚Ð¸Ñ‡ÐµÑÐºÐ¸Ðµ показатели Ляпунова, Ð¡Ð¸Ð½Ñ Ñ€Ð¾Ð½Ð¸Ð·Ð°Ñ†Ð¸Ñ, full synchronization of chaotic generators, Функции (мат.) Ляпунова
Abstract

Тема выпускной квалификационной работы: «Полная ÑÐ¸Ð½Ñ Ñ€Ð¾Ð½Ð¸Ð·Ð°Ñ†Ð¸Ñ Ñ Ð°Ð¾Ñ‚Ð¸Ñ‡ÐµÑÐºÐ¸Ñ ÑÐ¸ÑÑ‚ÐµÐ¼ на основе управления Ñ Ð°Ñ€Ð°ÐºÑ‚ÐµÑ€Ð¸ÑÑ‚Ð¸Ñ‡ÐµÑÐºÐ¸Ð¼Ð¸ показателями Ляпунова». Объектом исследования являются генераторы с Ñ Ð°Ð¾Ñ‚Ð¸Ñ‡ÐµÑÐºÐ¾Ð¹ динамикой. Предметом исследования являются методы ÑÐ¸Ð½Ñ Ñ€Ð¾Ð½Ð¸Ð·Ð°Ñ†Ð¸Ð¸ генераторов с Ñ Ð°Ð¾Ñ‚Ð¸Ñ‡ÐµÑÐºÐ¾Ð¹ динамикой. Целью данной работы является установление полной ÑÐ¸Ð½Ñ Ñ€Ð¾Ð½Ð¸Ð·Ð°Ñ†Ð¸Ð¸ между двумя Ñ Ð°Ð¾Ñ‚Ð¸Ñ‡ÐµÑÐºÐ¸Ð¼Ð¸ генераторами Лоренца, с различными параметрами у приемной и передающей сторон. Задачи, которые решались в Ñ Ð¾Ð´Ðµ исследования: 1. Изучение математического аппарата, который используется при полной ÑÐ¸Ð½Ñ Ñ€Ð¾Ð½Ð¸Ð·Ð°Ñ†Ð¸Ð¸ генераторов, Ð¸ÑÐ¿Ð¾Ð»ÑŒÐ·ÑƒÑŽÑ‰Ð¸Ñ Ñ Ð°Ð¾Ñ‚Ð¸Ñ‡ÐµÑÐºÑƒÑŽ динамику. 2. Изучение способов применения ÑÐ¸Ð½Ñ Ñ€Ð¾Ð½Ð¸Ð·Ð°Ñ†Ð¸Ð¸ Ñ Ð°Ð¾Ñ‚Ð¸Ñ‡ÐµÑÐºÐ¸Ñ Ð¾ÑÑ†Ð¸Ð»Ð»ÑÑ‚Ð¾Ñ€Ð¾Ð² для скрытой передачи информации между ними. 3. Анализ, ÑÑƒÑ‰ÐµÑÑ‚Ð²ÑƒÑŽÑ‰Ð¸Ñ Ð½Ð° сегодняшний день, методов ÑÐ¸Ð½Ñ Ñ€Ð¾Ð½Ð¸Ð·Ð°Ñ†Ð¸Ð¸, а также методов полной ÑÐ¸Ð½Ñ Ñ€Ð¾Ð½Ð¸Ð·Ð°Ñ†Ð¸Ð¸ Ñ Ð°Ð¾Ñ‚Ð¸Ñ‡ÐµÑÐºÐ¸Ñ ÑÐ¸ÑÑ‚ÐµÐ¼. 4. Реализация метода установления полной ÑÐ¸Ð½Ñ Ñ€Ð¾Ð½Ð¸Ð·Ð°Ñ†Ð¸Ð¸, основанного на управлении Ñ Ð°Ñ€Ð°ÐºÑ‚ÐµÑ€Ð¸ÑÑ‚Ð¸Ñ‡ÐµÑÐºÐ¸Ð¼Ð¸ показателями Ляпунова совместно с взаимным влиянием. 5. Постройка и тестирование системы с взаимным влиянием и управлением Ñ Ð°Ñ€Ð°ÐºÑ‚ÐµÑ€Ð¸ÑÑ‚Ð¸Ñ‡ÐµÑÐºÐ¸Ð¼Ð¸ показателями Ляпунова. 6. Сравнение системы с взаимным влиянием и с управлением Ñ Ð°Ñ€Ð°ÐºÑ‚ÐµÑ€Ð¸ÑÑ‚Ð¸Ñ‡ÐµÑÐºÐ¸Ð¼Ð¸ показателями Ляпунова с системой, основанной только на взаимном влиянии, без управления ХПЛ. В результате выполнения работы была реализована ÑÐ¸Ð½Ñ Ñ€Ð¾Ð½Ð¸Ð·Ð°Ñ†Ð¸Ñ Ñ Ð°Ð¾Ñ‚Ð¸Ñ‡ÐµÑÐºÐ¸Ñ Ð³ÐµÐ½ÐµÑ€Ð°Ñ‚Ð¾Ñ€Ð¾Ð² с разными значениями параметров с помощью метода синтеза управления на основе решения уравнения Сильвестра совместно с методом обратной связи и построена соответствующая ему модель системы связи в среде Matlab. Также было проведено сравнение этого метода с методом полной ÑÐ¸Ð½Ñ Ñ€Ð¾Ð½Ð¸Ð·Ð°Ñ†Ð¸Ð¸ Ñ Ð°Ð¾Ñ‚Ð¸Ñ‡ÐµÑÐºÐ¸Ñ ÑÐ¸ÑÑ‚ÐµÐ¼ на основе метода взаимного влияния и сделаны выводы о применимости этого метода., The topic of the final qualifying work: "Complete synchronization of chaotic systems based on the control of Lyapunov's characteristic indicators". The object of the study is generators with chaotic dynamics. The subject of the study is the methods of synchronization of generators with chaotic dynamics. The purpose of this work is to establish complete synchronization between two chaotic Lorentz generators, with different parameters at the receiving and transmitting sides. Tasks that were solved during the study: 1. The study of the mathematical apparatus used in the complete synchronization of generators using chaotic dynamics. 2. Study of ways to use synchronization of chaotic oscillators for the hidden transfer of information between them. 3. Analysis of currently existing synchronization methods, as well as methods of complete synchronization of chaotic systems. 4. Implementation of the method of establishing full synchronization, based on the management of Lyapunov's characteristic indicators together with mutual influence. 5. Construction and testing of a system with mutual influence and control of Lyapunov's characteristic indicators. 6. Comparison of the system with mutual influence and with the management of Lyapunov's characteristic indicators with a system based only on mutual influence, without the management of Lyapunov exponents. As a result of the work, synchronization of chaotic generators with different parameter values was implemented using the control synthesis method based on the solution of the Sylvester equation together with the feedback method and a corresponding model of the communication system in the Matlab environment was built. This method was also compared with the method of complete synchronization of chaotic systems based on the method of mutual influence and conclusions were drawn about the applicability of this method.

Published
2022
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5. Estimating noise in financial time series

Author

E.A. Demekhin, M.S. Diudin, and E.N. Kalaidin

Subjects
lcsh:Social Sciences, lcsh:H, correlation integral, financial time series, chaotic systems
Abstract

In this article presented method of estimating noise level in financial time series.

Published
2011

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