CC BY
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Visiiyk NTIJU KP1 Servia Radiolekhnika Radioaparat.obuduuannia, "2019, Iss. 77, pp. 13—16
Design, modeling and research of the new non-autonomous chaotic generator
Rusyn V. B.1, Pavlyukevich I. 2, Pribylova L. 3 Sktadas H. Ch.A
i-Yuriy Fedkovych Chernivtsi National University, Ukraine 2Friedrich Schiller University Jena, Germany 3Masaryk University, Czech Republic 4Technical University of Crete, Greece
E-mail: rusyn_ v&ukr.ncl■
Introduction. General scientific fields where can be used non-autonomous circuits that, realize chaotic behavior and generate chaotic oscillations are presented. Main characteristic about non-autonomous chaotic circuits is described. For modelling, analysis and demonstrate results was selected MultiSim software environment.
Modelling of Non-Linear Element. The simplest chaotic non-autonomous second-order circuit which belongs to the single-loop RL-diode series circuit, system of equations has described RLC circuit and theoretical nonlinear characteristic and circuit for realization of nonlinear characteristic, nominal components, parameters are presented. This non-linear element has designed to have a piecewise-linear characteristic and built only in one opamp. For realization of nonlinearit.y use only one bipolar power source for the opamp is enough. Results of computer modelling and simulation using MultiSim, i.e. the volt-ampere characteristic (VAC) at certain values of the components of the scheme's nominal values, is presented. Modelling and Analysis of the New Non-Autonomous Chaotic Circuit. System's behaviour is investigated through numerical simulations, by using well-known tools of nonlinear theory, such as chaotic attract.or and time distributions of the chaotic coordinates. This designed non-autonomous circuit, which generate a chaotic attract.or, can be used in modern transmission and reception systems of information. Conclusions. For the first, time was designed a new non-autonomous circuit, that, generate chaotic oscillations. The circuit., system of equations that, describe circuit, and nominal of components are presented. This circuit, that, generate chaotic oscillations can be used as one of the main part, of modern telecommunication systems for masking and decrypt, of information carrier.
Key words: chaos: non-autonomous generator: MultiSim
DOI: 10.20535/RADAP.2019.77.13-16
Introduction
Chaos is a very interesting complex nonlinear phenomenon which has been intensively studied in the different of science, mathematics and engineer-
ing communities. Chaos has been found to be very-useful and has great potential in many technological disciplines such as in information and computer sciences. power systems protection, flow dynamics, liquid mixing, biomedical systems analysis fl 15]. Chaotic signals can be generated with simple electronic circuits. Chaotic signal depends very sensitively on initial conditions, have unpredictable features and wide band spectrum. Chaotic systems are deterministic, highly sensitive to system parameters. A circuit is said to be non-autonomous if it is driven by at least one AC signal. A first-order non-autonomous circuit cannot be chaotic because its state equation can be transformed into an equivalent second-order autonomous system. However, a non-autonomous second-order circuit can become chaotic.
1 Modelling Element
of Non-Linear
The simplest chaotic non-autonomous second-order circuit is the single-loop RL-diode series circuit shown in Fig. 1.
Following system of equations has described RLC circuit:
J dvc dt
íl - g(Vc)
L^ = -R ■ iL -Vc + F ■ sinnt,
(1)
where g(Vc) - nonlinear function.
A great interest is the simulation that using different software environments allows to demonstration different information properties of chaotic oscillations flC 18]. Nonlinear elements these are elements in which the relation between voltage and current is a nonlinear function. An example is a diode, in which the current is an exponential function of the voltage. Circuits with nonlinear elements are harder to analyse
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Rusyn V. tí., Pavlyukovich 1. , Pribylova L. , Skiadas H. Ch.
arid design, often requiring circuit simulation computer programs snch as SPICE.
GB/ 1 l' Bp y V
/
zero. The circuit values shown and nsed in simulation are the measured values of nominal components.
The circuit realization of the above is displayed in Fig. 3. with component: one operational amplifier DA1-TL082, R2 = R3 = 1,2 kQ, R4 = 2,4 kQ, two diodes 1N4148. Voltage - ± 12 V. Probe X correspond current /, probe Y correspond voltage U, respectively.
Fig. 1. Electrical circuit: R, L, C - linear elements; g -nonlinear element; F sin(Qt) - sinusoidal generator
A single-port network having the characteristic of a linear negative resistance, terminated at both ends with linear positive resistance (Fig. 2) was chosen as the nonlinear element.
Fig. 3. Circuit for realization of nonlinear characteristic
Nonlinear characteristic was modeled by the following parameters: GB1 = 9 V, / = 1 kHz, R1 = 1000 Q.
Fig. 2. Nonlinear characteristic
It possesses the advantage that it may be realized, approximately, using an op-amp and three resistors, with two back-to-back diodes to set the break points (Fig. 2) or more precisely, by the switching-in of the series combination of an appropriate resistor and voltagc-sonrcc at the break-point voltages. With carefnl design this version can exhibit close to ideal behavior.
The network's DC, V/I characteristic, is that of a voltage-controlled, short-circuit stable, negative resistance. It has been shown by Chua and Lin that, in dynamic operation, where, when what nsed to be called "jumps" occur, that, both in modeling this characteristic, and in reality, to provide a path for the continuity of current, a transit capacitor, however small, must exist across the terminals of the device. This suggested the placing of a capacitor in this position. The remainder of the circuit is the series combination of a periodic voltage source, a linear inductor and a resistor. The resistor comprises an actual resistor and the DC resistance of the inductor. The total resistance value was chosen to be greater than l/Ga so that the circuit was not capable of starting or maintaining sustained oscillation when the driving voltage was reduced to
Fig. 4. Nonlinear characteristic
Fig. 4 show result of modeling of nonlinear element nsing MnltiSim. The simulation parameters: U1 5 V/div, U2 1 V/div.
2 Modelling and Analysis of the New Non-Autonomous Chaotic Circuit
Fig. 5 shows proposed of the new chaotic non-autonomous scheme of the simplest chaotic generator.
Circuit was realized on the one operational amplifier DAI TL082, powered by a 12V, two diodes 1N4148, resistors R1 = 500 Q, R2 = R3 = 1.2 kQ, R4 = 2.4 kQ, capacitor CI 10 nF, inductor LI 7 niH. Sinusoidal source GB1 1.5 V. f 2 kHz.
Design, modeling and research of the new non-autonomous chaotic generator
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Fig. 5. Circuit of a now non-autonomous chaotic generator
Fig. 6. Chaotic attractor
Fig. 6 shows the result of circuit simulation. Generated chaotic signal in the plane XY presented on the virtual oscilloscope. Coordinate X in the circuit correspond "plus" of the sinusoidal generator VI, coordinate Y the non-inverting input of operational amplifier DAI.
In Fig. 7 and Fig. 8 shows time dependences of the coordinates X and Y respectively.
■SB
Fig. 7. Time dependence of the coordinate X
Fig. 8. Time dependence of the coordinate Y
Conclusions
Many circuits realize chaotic generators. For the first time was presented a new chaotic non-autonomous circuit. Using MnltiSim software environment conducted scheme technical analysis circuit of a nonlinear element that consist one operational amplifier with two diodes and generator that implements a chaotic behavior. Submitted by a chaotic attractor and time distributions of two chaotic coordinates.
This circuit that generate chaotic oscillations can be nsed as one of the main part of modern telecommunication systems for masking and decrypt of information carrier.
References
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[7] Frank Z. Wang, Lupins Shi, Huaqiang Wu, Na Helian and Loon O. Chua ("2017) Fractional momristor Appl. Phys. Lett., Vol. Ill, pp. 243502. DOl: 10.1063/1.5000919
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Розроблення, моделювання та досль дження нового неавтономного хаотичного генератора
Русин В., Павлюкевич I., Привалова Л., СкгдасХ. Ч.
У дашй робот! представлена нова вероя схеми неавтономного хаотичного генератора з пелшшшетю "дюд-операциший шдсилювач". Це свого роду одна 1з пай-иросташих схем. яка проявляв хаотичпу поведшку. Дана
схема неавтономного хаотичного генератора micthtb чо-тири резистора, один конденсатор, одну котушку ищу-ктивпоста, два дюди з одним операгцйпим шдсилювачем i зовшшшо перюдичпу силу. Найпросташнй пелипйпий елемепт, спроектовапий таким чипом, щоби отрима-ти кусково-лшшпу характеристику, тобто комбшацпо одного операцшпого шдсилювача з двома дюдами, що BBiMKiieni пазустр!ч одип одному. Для реал!зацп пель шйпоста, для двох дюд!в по потр1бпо окремого джерела живлеппя, а тгльки достатпьо лише одного двополярпо-го живлеппя для операцшпого шдсилювача. Приведено схему для шд'едпаппя та досл1джеппя пелшшпого еле-меиту. а також результати комп'ютерпого моделюваппя. тобто вольт-амперпу характеристику (ВАХ) при певпих зпачеш1ях помшал1в компопепт1в схеми. За допомогото одного 1з пайсучасшших програмпих середовищ проведено схемотехп1чппй апал!з та представлено результати комп'ютерпого моделюваппя нового неавтономного генератора, що геперуе хаотичш колгшашш. В дапому ви-падку було застосовапо програмпе середовище MultiSim компаш! National Instruments. Досл1джепа поведшка си-стеми за допомогото чиселыгого моделюваппя, викори-стовуючи в1дом! 1пструмепти пел1шйпо1 Teopii, так! як фазовий портрет (хаотичпий атрактор) i часов! розпо-д!ли хаотичпих коордгшат. Тобто представлено сигнал до пелипйпого елемеита (сипусощальпий), i в1дпов1дно згеиерований шеля пелш1йпого елемепту хаотичш ко-ливаш1я. Заиропоиовапа неавтономна схема генератора, що геперуе хаотичш коливаппя, може бути використа-па як осповпа частгша сучаишх систем передаваппя i приймаппя 1пформацп для маскуваппя i дешифруваш1я пос1я ¡пфорМсЩП.
Клюноог слова: хаос: пеавтопомпий генератор: MultiSim
Разработка, моделирование и исследование нового неавтономного хаотического генератора
Русый В., Павлюкевич П., Прибьишва Л., СкиОасХ. Ч.
В работе представлена разработанная новая неавтономная хаотичная схема, которая реализует хаотическое поведение. Эта схема имеет простой нелинейный элемент, спроектированный так, чтобы получить кусочпо-липейпую характеристику. Даппая разработанная схема может использоваться в современных системах передачи и приема информации. Генерируемый ею аттрактор может применяться для маскировки информационного носителя и его восстановления. С помощью программной среды MultiSim проведен схемотехнический анализ и представлены результаты моделирования нелинейного элемента и разработанной повой неавтономной хаотической схемы. Исследовано поведение системы с помощью численного моделирования, используя известные инструменты нелинейной теории, такие как хаотичный аттрактор и временные распределения хаотических коордгшат.
Ключевые слова: хаос: неавтономный генератор: MultiSim
