Chaotic (nonlinear) oscillations, equations, circuits, memristors, control

In this paper, the designed circuit of the non-autonomous chaotic generator that demonstrates nonlinear behavior and nominal values of the electronic components are presented. This circuit consists of one operational amplifier, two diodes, one inductor, one capacitor, four resistors, a symmetrical power source, and a sinusoidal source. Nominal components, chaotic and controlled attractors, time series, and spectral distributions for two signals are shown. For computer modeling and to demonstrate results we selected the MultiSim software environment.

In this paper, the designed circuit of the non-autonomous chaotic generator that demonstrate nonlinear behavior and nominal values of the electronic components are presented. This circuit consists from one operational amplifier, two diodes, one inductor, one capacitor, four resistors, symmetrical power source, and sinusoidal source. Nominal components, chaotic and controlled attractors, timeseries and spectral distributions for two signals are shown. For computer modelling and demonstrate results was selected MultiSim software environment.

A triple-band single-layer rectenna for outdoor RF energy applications is introduced in this paper. The proposed rectenna operates in the frequency bands of LoRa, GSM-1800, and UMTS-2100 networks. To obtain a triple-band operation, a modified E-shaped patch antenna is used. The receiving module (antenna) of the rectenna system is optimized in terms of its reflection coefficient to match the RF-to-DC rectifier. The final geometry of the proposed antenna is derived by the application of the Moth Search Algorithm and a commercial electromagnetic solver. The impedance matching network of the proposed system is obtained based on a three-step process, including the minimization of the reflection coefficient versus frequency, as well as the minimization of the reflection coefficient variations and the maximization of the DC output voltage versus RF input power. The proposed RF-to-DC rectifier is designed based on the Greinacher topology. The designed rectenna is fabricated on a single layer of FR-4 substrate. Measured results show that our proposed rectenna can harvest RF energy from outdoor (ambient and dedicated) sources with an efficiency of greater than 52%.

In this paper we have studied the case of chaotic synchronization of two identical, bidirectional coupled, nonlinear, 4th order autonomous electric circuits. Each circuit contains one linear negative conductance G and one nonlinear resistor RN with a piecewise-linear υ-i characteristic. 􀂾 Using the capacitance C1 and C2 as the control parameters, we have observed the transition from periodic states to chaotic ones and vise versa, as well as crisis phenomena, when the spiral attractor suddenly widens to a double-scroll attractor. We have observed that chaotic synchronization is possible as the coupling parameter ε=R1/RC is varied.

In this paper, the Malasoma system based cubic function is presented. This system contains operational amplifiers, resistors, capacitors, multipliers, and voltage sources. The first stage, we analyze the Malasoma model and execute its stability. The phase portraits and bifurcation diagram are used to analyze the dynamic behaviors of the Malasoma model. The proposed circuit was modelled by utilizing NI’s MultiSim software environment. The electronic circuit is realized by using off-the-shelf components. MATLAB and MultiSim simulation results show a good agreement.

Circuit realization of the inductance equivalent that contains two operational amplifiers, one capacitor, and four resistors is presented. The mathematical equation that allow convert inductor value to resistance of potentiometer is shown. Computer modeling results of the algorithm for calculate inductance was realized in the modern software LabView. Experimental results of realization of the equivalent of inductance are presented. The designed layout was applied for chaotic Chua’s generator.

In this paper, we study a three-dimensional Lorenz system that demonstrates chaotic behavior. We present the state equations and mathematical analysis of the system. We use a system-design platform, like LabView, to study and analyze main information properties, such as chaotic attractors, time series, bifurcation diagram, and dynamic behavior of the overall system. We implemented an Arduino Uno based design to display chaotic attractors of the Lorenz system. The Arduino is connected to a computer through the USB port, while graphs were uploaded using program software ArduinoIDE. Finally, the connection scheme and programming code are also presented.

In this paper, the circuit of a non-autonomous generator that realizes chaotic behavior is presented. This oscillator-circuit contains four resistors, one capacitor, one inductor, two diodes, one operational amplifier, one bipolar voltage source and one sinusoidal source. All nominal of components are shown. The proposed circuit was modeled by utilizing NI's MultiSim software environment. The system's behavior was investigated through numerical simulations, by using well-known tools of nonlinear theory, such as phase portrait, chaotic attractor and time distributions of two chaotic system-variables. Spectral analysis are also presented.

For demonstrate nonlinear behavior we used new one-dimensional modified logistic system. Analysis, equation and system conditions are presented. For analysis of the iteration series with different parameter r and computer modelling was used one of the modern software environment LabView. Programming code and nominal components are also presented. For visualizing and practical realization of the new modified nonlinear logistic map we used Arduino Uno board and ten light-emitting diodes (LEDs) with ten resistors for each part of segment of the range [0;1]. The Arduino was connected to a computer through the USB port and programmed using a language similar to C++. Sketch was uploaded into Arduino using program software ArduinoIDE.

In this paper, we present computer modelling and analysis of the chaotic Arneodo system. For demonstrate of these results was used modern software environment LabView. Created programming interface allows to generating, analysis and research of the main information properties of chaotic Arneodo system, focusing on time series of the three chaotic coordinates, phase portraits and Lyapunov exponents. Another programming interface demonstrates the algorithm of masking and decrypt of the information.

Circuit realization of the generator that demonstrate chaotic behavior is presented. This circuit contains three operational amplifiers, three capacitors, one diode, eight resistors, and one voltage source. The system's behavior was investigated through numerical simulations, by using well-known tools of nonlinear theory, such as phase portrait, chaotic attractor and time distributions of two chaotic system-variables. This proposed circuit of chaotic generator can be used as a main part of modern systems transmitting and receiving information for masking and decryption of an information carrier.

In this paper, the Malasoma system based cubic function is presented. This system contains operational amplifiers, resistors, capacitors, multipliers, and voltage sources. The first stage, we analyze the Malasoma model and execute its stability. The phase portraits and bifurcation diagram are used to analyze the dynamic behaviors of the Malasoma model. The proposed circuit was modelled by utilizing NI’s MultiSim software environment. The electronic circuit is realized by using off-the-shelf components. MATLAB and MultiSim simulation results show a good agreement.

In this paper, the process of pulse transformation of analog nonlinear signals is presented. For demonstrate of this process we used non-autonomous chaotic generator as a main part that generate nonlinear signals. Components with nominal values and electronic circuit that allows to realization of pulse transformation are presented. This circuit consists from one transistor, one operational amplifier, and five resistors. For modelling and demonstrate computer modeling results was selected MultiSim software environment.

In this paper realization of modified chaotic circuit of the Van der Pol-Duffing generator is presented. Modeling and research chaotic behavior as a function of a variable control parameter. The differential equations has been realized using commonly available op amps and the nonlinearity using diodes. The experiments indicate that chaotic behavior indeed emerges through the period doubling route as the parameter is changed.

Considered duopoly Cournot model, which allows analyze the different possible behavior strategies of each of the market participants. Detected conditions of the market equilibrium under which the income of both market participants-maximum. Also consider getting one duopolist additional revenue, on the condition that another go with the market. The control method of economic Cournot model and simulation results are presented.

Introduction. In this paper is presented a theoretical basis of chaotic Rossler system. Modelling of Chaotic Rossler System in LabView. Submitted programming interface that has been developed in LabView software environment. It allows generating and researching chaotic Rossler system. Submitted by time distribution of three chaotic coordinates and spectral analysis. Also submitted values of variables in which generated different period (controlled) attractors of the chaotic Rossler system. The software interface demonstrates masking and decrypt information carrier of the chaotic Rossler system. Modelling of Chaotic Rossler System in MultiSim. Using MultiSim software environment conducted scheme technical analysis circuit of a generator that implements a chaotic Rossler system. Conclusions. Modelled circuit of generator confirming correspondence scheme-technical solution to mathematical apparatus that describing chaotic Rossler system. Keywords: chaos; control; system; Rossler; LabView; MultiSim

In this paper, we used one-dimensional system that demonstrate chaotic behavior. Equation, analysis and system conditions are presented. Modern software environment LabView was used for analysis of the iteration series with different parameter r. Connection scheme, nominal components and programming code are also presented. For practical realization and visualizing of the logistic map we used Arduino Pro Mini and ten light-emitting diodes (LEDs) with ten resistors for each part of segment of the range [0;1]. The Ardu-ino was connected to a computer through the USB port and programmed using a language similar to C++. Sketch was uploaded into Arduino using program software ArduinoIDE.

The new chaotic generator that consists from two operational amplifiers, one diode, three capacitors and seven resistors is presented. This circuit generate chaotic and controlled oscillations. All nominal components, computer modelling results such as chaotic attractor, time distributions and spectral analysis of the chaotic coordinates are presented. The circuit was modelled by using MultiSim software environment. This designed circuit that generate a chaotic and controlled attractor with a fixed period can be used in modern telecommunication systems. Number of periodic (controlled) attractor can be used as a key for masking of information carrier.

In this paper, a new circuit of a generator that realizes chaotic behavior is presented. This oscillator-circuit contains four resistors, two capacitors, one inductor, one diode, one operational amplifier and one voltage source. The proposed circuit was modeled by utilizing NI's MultiSim software environment. The system's behavior was investigated through numerical simulations, by using well-known tools of nonlinear theory, such as phase portrait, chaotic attractor and time distributions of two chaotic system-variables. This proposed circuit of chaotic generator can be used as a main part of modern systems transmitting and receiving information for masking and decryption of an information carrier.

The modified Chua's circuit that realize chaotic behaviour is presented. This circuit having a simple nonlinear element designed to be accurately piecewise-linear modelled. The circuit was modelled by using MultiSim software environment. System's behaviour is investigated through numerical simulations, by using well-known tools of nonlinear theory, such as chaotic attractor and time distributions of the chaotic coordinates. This modified Chua's circuit that generate a chaotic and controlled attractor with a fixed period can be used in modern systems transmitting and receiving information. Number of periodic (controlled) attractor can be used as a key for masking of information carrier.

A novel simple autonomous optoelectronic circuit that demonstrate chaotic behavior is presented. In this circuit a lightemitting diode is a simple optoelectronic element. The mathematical model that contain exponential nonlinearity and six terms with two parameters is described by three first-order ordinary differential equations. A great interest is the simulation that using different software environments allows to demonstration different information properties of chaotic oscillations. For modelling of information properties of the chaotic system and demonstrate results was selected one of the modern software LabView (LabView-2015 (32-bit version for Windows). Temporal dependence of the system is discussed, the chaotic attractors are found and the signal spectrum is given.

The classical Chua’s circuit that realizes chaotic behavior is presented. This circuit having a simple nonlinear element designed to be accurately piecewise-linear modelled. The circuit was modelled by using MultiSim software environment. The system’s behavior is investigated through numerical simulations, by using well-known tools of nonlinear theory, such as chaotic attractor and time distributions of the chaotic coordinates. Using threshold method was practical realization of the control of chaotic attractor. This classical Chua’s circuit that generates a chaotic and controlled attractor with a fixed period can be used in modern systems transmitting and receiving information. Number of periodic (controlled) attractor can be used as a key for masking of information carrier.

In this paper one of the simplest chaotic circuits is presented. The circuit was modeling by using MultiSim software environment. System's behavior is investigated through numerical simulations, by using well-known tools of nonlinear theory, such as phase portrait, bifurcation diagram, Lyapunov exponents and Kaplan-Yorke dimension. Submitted by chaotic attractor and time distributions of two chaotic coordinates. Submitted values of capacitor C2 in which generated controlled chaotic attractors. Control 2-period and 3-period attractors and time distributions of two chaotic controlled coordinates are also submitted. For the first time was conducted control CCC circuit. For demonstration was applied modern software environment MultiSim. The values of capacitor C2 can be used as keys for masking and decryption of information carrier in modern systems transmitting and receiving information.

This paper describe about general information and properties of memristor based on Chua’s scheme. The circuit of connection of the memristor to obtain I–V characteristics is presented. Practical realization and research of information properties are also presented. Memristor scheme is one of the main part in modern telecommunication systems of transmitting and receiving signals and experimental results can be used for masking and decrypt of information carrier.

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 nonlinearity 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 attractor and time distributions of the chaotic coordinates. This designed non-autonomous circuit, which generate a chaotic attractor, 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.

In this paper proposed a modified experimental control of hyperchaotic oscillations using threshold method. Shows an experimental scheme for control of hyperchaotic oscillations.

This paper presents modeling, analysis and research of chaotic Rucklidge system based on programming interface that has been developed in LabView software environment. This study allows for generating and researching the main properties of chaotic Rucklidge system, focusing on time distribution of three chaotic coordinates and phase portraits. A range of the system parameter with which we can generate different period (controlled) attractors and a number of trajectories of chaotic Rucklidge system are also presented. The programming interface demonstrates the algorithm of masking and decrypt information carrier.