Chaotic Signal Generator Research Articles

CCII current conveyor and dormand-prince-based chaotic oscillator designs for secure communication applications

Chaos is one of the important research areas in recent years. The chaotic signal generator is one of the most basic structure in the chaos-based researches and applications. In this study, Sundarapandian-Pehlivan Chaotic Oscillator (SPCO) designs have been implemented in 2 different platforms as analog-based using Second-Generation Current Controlled Current Conveyor (CCII) and FPGA-based with one of the chaotic oscillator that has been presented to the literature namely Sundarapandian-Pehlivan system. The structure used for the design of CCII-based chaotic oscillator and the results obtained from the study have been presented. In the second phase, the design of SPCO has been realized in order to utilize for running in FPGA chips using Dormand-Prince (DP) numeric algorithm. The design has been coded in VHDL using 32-bit IEEE-754-1985 floating point representation. The designed system has been tested by synthesizing it in Xilinx ISE Design Tools program. Then, the test results obtained from DP-based SPCO structure have been presented. In the last phase, the designed system has been synthesized for VIRTEX-7 FPGA. FPGA chip resource consumption values that obtained after the Place-Route process are presented. According to the results, the maximum operating frequency of DP-based SPCO unit on FPGA is obtained as 362.608 MHz. In future studies, the designs of Pseudo Random Number Generator (RNG) and True RNG can be performed using DP-based SPCO unit implemented successfully in this study.

Generation of multi-channel chaotic signals with time delay signature concealment and ultrafast photonic decision making based on a globally-coupled semiconductor laser network

We propose and demonstrate experimentally and numerically a network of three globally coupled semiconductor lasers (SLs) that generate triple-channel chaotic signals with time delayed signature (TDS) concealment. The effects of the coupling strength and bias current on the concealment of the TDS are investigated. The generated chaotic signals are further applied to reinforcement learning, and a parallel scheme is proposed to solve the multiarmed bandit (MAB) problem. The influences of mutual correlation between signals from different channels, the sampling interval of signals, and the TDS concealment on the performance of decision making are analyzed. Comparisons between the proposed scheme and two existing schemes show that, with a simplified algorithm, the proposed scheme can perform as well as the previous schemes or even better. Moreover, we also consider the robustness of decision making performance against a dynamically changing environment and verify the scalability for MAB problems with different sizes. This proposed globally coupled SL network for a multi-channel chaotic source is simple in structure and easy to implement. The attempt to solve the MAB problem in parallel can provide potential values in the realm of the application of ultrafast photonics intelligence.

Simultaneous Generation of Multi-Channel Broadband Chaotic Signals Based on Two Unidirectionally Coupled WRC-FPLDs

We propose and demonstrate experimentally a scheme for simultaneously generating multi-channel broadband chaotic signals based on two unidirectionally coupled weak-resonant-cavity Fabry-Perot laser diodes (WRC-FPLDs) with almost the same mode interval, where one WRC-FPLD is utilized as master WRC-FPLD (M-WRC-FPLD) and the other is used as slave WRC-FPLD (S-WRC-FPLD). Under the optical injection from the M-WRC-FPLD with suitable injection parameters, multiple longitudinal modes of the S-WRC-FPLD can be simultaneously driven into chaotic states, which can provide multi-channel chaotic signals. Via a tunable optical filter, we inspect the performances of 9-channel chaotic signals, the results show that the chaotic bandwidths are within the range of 8∼15 GHz for all the 9-channel chaotic signals. Furthermore, the influences of the injection power and frequency detuning on the performances of the chaotic output from one of the channels are also analyzed.

SIP Network Secure Communication Model Based on Improved SIP Protocol

The hot topics of session initiation protocol (SIP) authentication are mainly hypertext transfer protocol (HTTP) digest authentication mechanism and public-key cryptography standards (PKI) authentication mechanism. Among them, the PKI authentication mechanism encounters problems such as long encryption and decryption time and difficult actual deployment. Aiming at the shortcomings of the existing identity authentication mechanism of SIP, start with the chaotic sequence generated by chaotic equations, the dynamic password generation is optimised during the authentication process. A SIP security authentication mechanism based on chaotic equations is proposed. Firstly, improved security authentication scheme is applied in the video intercom system, then the chaotic signal generator on the microcontroller is designed, and finally the improved security authentication scheme is applied into the system. The results show that the system can realise all the functions at design time based on the improved SIP certification.

Хаотизация обработки и формирования сигналов в технологии DRFM: учёт ресурсных ограничений

Хаотизация обработки и формирования сигналов в технологии DRFM: учёт ресурсных ограничений

Generation of Chaotic Signal for Scrambling Matrix Content

Very well evolved, information technology made so easy the transfer of all types of data over public channels. For this reason, ensuring data security is certainly a necessary requirement. Scrambling data is one solution to hide information from non authorized users. Presenting matrix content, image scrambling can be made by only adding a mask to the real content. A user, having the appropriate mask, can recognize the image content by only subtracting it. Chaotic function is recently used for image encryption. In this paper, an algorithm of image scrambling based on three logistic chaotic functions is proposed. Defined by its initial condition and parameter, each chaotic function will generate a random signal. The set of initial conditions and parameters is the encryption key. The performance of this technique is ensured for two great reasons. First, using masks on the image makes unintelligible its content. Second, using three successive encryption processes makes so difficult attacks. This point reflects, in one hand, a sufficient key length to resist to brute force attack. In the other hand, it reflects the random aspect of the pixel distribution in the scrambled image. That means, the randomness in one mask minimizes the correlations really existent between neighboring pixels. That makes our proposed approach resistant to known attacks and suitable for applications requiring secure data transfer such as medical image exchanged between doctors

Phased-array assisted time-delay signature suppression in the optical chaos generated by an external-cavity semiconductor laser

An external-cavity semiconductor laser (ECSL) outputs high-dimensional chaos, which has potential for various applications, but the unwanted time-delay signature (TDS) might compromise the performance. In this work, a highly integrated and extensible framework of phased-array semiconductor lasers, operating in a steady state when isolated, is employed to postprocess the original chaos generated by an ECSL. Our results demonstrate that such a compact active device enables TDS suppression over wide parameter space. Better performance can be achieved in the proposed scheme compared with the conventional, discrete semiconductor laser subjected to optical chaotic injection. The influence of the injection parameters and the laser separation is studied, which further confirms the feasibility of the proposed scheme for TDS suppression. The phased array can be readily extended to include a large number of elements, and thus the current scheme allows for the generation of multiple independent chaotic signals with no discernible TDS in parallel. This means that the current study may pave the way for parallel random number generation based on optical chaos.

Adaptation of dynamical properties of time series data and its applications in deep brain stimulation

The chaotic nature of the brain can be observed by electroencephalogram signals. This chaotic behavior can be affected by the progressive nature of neurodegenerative disorders like Parkinson disease. The gradual changes in dynamical behavior of brain can be tracked to facilitate effective and timely treatment. Deep brain stimulation (DBS) is used in therapy when the medication stops working. We investigate the use of chaotic signal as stimulus in DBS. We stimulate a simulated model of isolated neuron with different types of stimuli to see if periodicity in neuronal spiking can be disrupted and show that neuron, when stimulated with chaotic signal, does fire up in non-periodic/chaotic manner. Furthermore, as a step toward the development of our system for estimation of chaotic behavior of brain, we investigate the use of recurrent neural networks to adapt the chaotic characteristics of a chaotic time series in this research work. We explore two different setups of long short-term memory (LSTM). In first setup, we define three unique topologies of LSTM network and analyze those for chaotic parameter estimation in seven different test cases for shallow and deep networks. We show that the deep LSTM networks are capable of modeling the chaotic behavior of a wide range of parameters and that the network performs the best when the architecture is driven by chaotic attributes of the time series data. In second setup, we use LSTM network in a traditional configuration to predict the chaotic time series data and demonstrate that the LSTM network can make prediction over a range of chaotic parameters with adequate accuracy. This provides the basis for the generation of chaotic stimulation signals when required.

Numerical investigations on multi-channel wideband chaotic signal generation by a multi-transverse mode vertical-cavity surface-emitting laser subject to chaotic optical injection.

A multi-channel wideband chaotic signal generation scheme is proposed and numerically investigated based on a slave multi-transverse mode vertical-cavity surface-emitting laser (SL) subject to chaotic optical injection from a master multi-transverse mode vertical-cavity surface-emitting laser (ML) with optical feedback. Taking two low-order transverse modes, LP01 and LP11, as an example for numerical calculations, the simulated results show that under suitable optical feedback both the LP01 and LP11 modes (two-channel) of a ML can be driven into the chaotic states where their bandwidths are relatively narrow at a level about 8 GHz. Further injecting the two chaotic signals into a SL, for the case of the globally chaotic optical injection, the SL can output two-channel chaotic signals with wide bandwidths above 20 GHz under appropriate operation parameters. Moreover, the case of SL with mode-selective chaotic optical injection is also analyzed.

Dynamical analysis, sliding mode synchronization of a fractional-order memristor Hopfield neural network with parameter uncertainties and its non-fractional-order FPGA implementation

Recent developments in the applications of neural networks in various engineering and technology applications have motivated researchers to study the nonlinear behavior of such networks. In this work we investigate a fractional-order Hopfield neural network with memristor synaptic weight. The dynamical properties of the proposed system are examined and the memristor neural network shows hyperchaotic attractors in fractional orders with hidden oscillations. We also propose an adaptive sliding mode control technique to synchronize the proposed fractional-order systems with uncertainties. Numerical simulations are derived to show the effectiveness of the synchronization algorithm. Moreover, the designed chaotic memristor Hopfield neural network system is realized on FPGA using the 4th-order Runge–Kutta (RK4) numerical algorithm. The FPGA-based chaotic memristor HNN is coded in VHDL using the 32-bit IEEE-754-1985 floating point standard. The chaotic memristor neural network designed on FPGA is synthesized and tested using Xilinx ISE. The chip statistics of Xilinx XC6VLX240T-1-FF1156 kit obtained from Place & Route operation for the designed RK4-based system is presented. The operating frequency of newly modeled FPGA-based memristor neural network chaotic signal generator is 231.616 MHz.

A Monolithically Integrated Laser-Photodetector Chip for On-Chip Photonic and Microwave Signal Generation

An Indium-phosphide-based monolithically integrated photonic chip comprising of an amplified feedback laser (AFL) and a photodetector was designed and fabricated for on-chip photonic and microwave generation. Various waveforms including single tone, multi-tone, and chaotic signal generation were demonstrated by simply adjusting the injection currents applied to the controlling electrodes. The evolution dynamics of the photonic chip was characterized. Photonic microwave with frequency separation tunable from 26.3 GHz to 34 GHz, chaotic signal with standard bandwidth of 12 GHz were obtained. An optoelectronic oscillator (OEO) based on the integrated photonic chip was demonstrated without using any external electrical filter and photodetector. Tunable microwave outputs ranging from 25.5 to 26.4 GHz with single sideband (SSB) phase noise less than −90 dBc/Hz at a 10-kHz offset from the carrier frequency were realized.

Wavelength-Tunable Chaotic Signal Generation With On-Chip O/E Conversion

A wavelength-tunable chaotic optical signal generation and on-chip O/E conversion scheme based on an integrated laser-photodiode chip subject to filtered optical feedback is proposed and experimentally demonstrated. The integrated chip consists of a Fabry–Perot (FP) gain section and a photodiode, which was fabricated on an n-InP substrate with the same active material. By applying a filtered feedback signal to the FP gain section, wavelength-tunable chaotic carrier ranging from 1576 to 1587 nm was achieved. On-chip microwave chaotic signal generation with a standard bandwidth over 5.5 GHz was obtained using the integrated photonic chip.

Spectral characteristics of a general piecewise linear chaotic signal generator

The Power Spectral Density (PSD) of the transmitted signals is a fundamental aspect in the performance evaluation of general communication systems. This way, when it comes to chaos-based communication systems, it is relevant to analytically obtain the PSD of chaotic signal generators. In particular, a number of results for piecewise-linear maps were recently obtained. In the present paper, we deduce the PSD for a general family of such maps composed by an arbitrary number of segments, with positive or negative slopes. Numerical examples illustrate the analytical results and show the diversity of attainable spectra.

Equalization in chaos-based communication systems using kernel adaptive filtering

Chaos-based communication systems have attracted attention of researchers in academy and industry in the last decades. A particular family of such systems has as basic idea to use the transmitted message to modify a known nonlinear chaotic signal generator (CSG). In the receiver, the knowledge of the employed nonlinear CSG in conjunction with chaotic synchronization permits to recover the original message. These systems are an alternative for spread spectrum communication with a possible increase in the security in the physical layer, since it is necessary to perfectly know the CSG in the receiver to decode the message. However, the lack of robustness of chaotic synchronization in relation to channel noise and intersymbol interference still poses a barrier for their practical use. The problem of equalization for such systems have been tackled for a while, and algorithms based on the normalized least-mean squares have presented auspicious results for linear channels. For nonlinear channels, Kernel Adaptive Filters (KAFs) have been used since they are able to solve nonlinear problems implicitly projecting the input vector into a larger dimension space, where they can be linearly solved. Therefore, in this paper, we propose the use of KAFs with two purposes: to equalize linear and nonlinear channels and, at the same time, decode the message without knowledge of the CSG in the receiver. Simulation results show that the proposed solution is able to perform these tasks.

Current-Starved Cross-Coupled CMOS Inverter Rings as Versatile Generators of Chaotic and Neural-Like Dynamics Over Multiple Frequency Decades

The generation of chaotic signals is relevant to a multitude of applications across telecommunications, random number generation, control, and the realization of distributed sensing systems; in addition, networks of coupled chaotic oscillators replicate diverse emergent phenomena occurring in considerably larger biological neural systems. However, to date, the generation of chaotic signals by means of complementary metal-oxide-silicon (CMOS) integrated circuits has been hampered largely by the need to implement reactive elements, and by limited flexibility. In this paper, we introduce a pure CMOS implementation of a chaos generator based on three inverter rings having lengths equal to the smallest odd prime numbers, i.e., 3, 5, and 7. These rings are cross-coupled via diodes of diverse strengths enabled through pass-gates, and the inverters in the rings are independently current-starved. Through numerical simulations and experiments, it is shown that this new topology can generate chaotic signals over at least four frequency decades. Furthermore, it is demonstrated that the experimental devices have access to a multitude of qualitatively-different dynamical behaviors as a function of the starving currents. In particular, the generation of spiking and bursting signals reminiscent of action potentials are observed, both with and without slower fluctuations which resemble field potentials. Furthermore, instances of oscillation quenching are found, wherein the circuit acts as a nonlinear amplifier yielding 1/ ${f}$ -like stochastic signals. This compact and flexible topology promises to become a foundational cell in the design of integrated circuits requiring area-efficient, low-power, and controllable chaos generation.

Analysis of the Chaotic Dynamics of MEMS/NEMS Doubly Clamped Beam Resonators with Two-Sided Electrodes

We investigate the chaotic dynamics of micro- and nanoelectromechanical (MEMS/NEMS) beam resonators actuated electrostatically by two-sided electrodes, considering devices with realistic physical parameters. We model the resonators using the Euler–Bernoulli beam theory with the addition of viscous damping, midplane stretching and the electrostatic force. For the purpose of numerical simulations, the partial differential equation describing the system is reduced to a one degree of freedom model using the Galerkin method. The resulting nonlinear ordinary differential equation incorporates the main effects of the beam curvature. A comparison with the widely used parallel plate approximation (PPA) evidences the significant effects of the beam curvature. It is also concluded that in the case of resonators with two-sided electrodes special care must be taken when using the PPA. A detailed numerical analysis reveals the region in the relevant parameter space where chaos can be found. Phase portraits, Poincaré sections and bifurcation diagrams are used to characterize the chaotic attractors. The effects of gap asymmetry and damping are also investigated, showing that a stronger chaotic dynamics is favored by small asymmetries and smaller damping. In general, a more complex chaotic dynamics was found, compared to what was initially expected. The results are relevant in view of the potential practical applications in the generation of pseudo-random numbers and chaotic signals for secure communications. The proposed improved model can be easily implemented numerically, helping in the design and simulation of resonators, and the comparison between theoretical and experimental results.

Hidden Coexisting Attractors in a Chaotic System Without Equilibrium Point

This paper proposes a new three-dimensional chaotic system with no equilibrium point but can generate hidden chaotic attractors. Dynamic characteristics of the system are analyzed in detail by theoretical analysis and simulating experiments, including hidden attractors, transient period and coexisting attractors. Different hidden coexisting attractors exist in this system, which shows abundant and complex dynamic characteristics and can be used to generate pseudorandom sequences for encryption fields. Besides, the presented system is realized by the digital signal processing (DSP) technology to construct a chaotic signal generator, whose statistical properties are tested by National Institute of Standards and Technology (NIST) software. The obtained results are better than that of the Lorenz system and imply the presented system can be used in the encrypted fields.

Chaotic Spreading Sequence for Linear Frequency Modulation

In the presented article the use of chaotic signals as spreading sequences for linear-frequency modulation is proposed. An example of a simplified block diagram for a chaotic signal generator constructed on the basis of linear and switching elements is given, as well as equations describing the operation of the circuit. The results of calculation and simulation of processes with specific specified parameters of the circuit are shown. The calculation of differential equations is carried out by a numerical method of Runge-Kutt of the fourth order of accuracy. It is shown that carrier frequency varies linearly, according to the scanning voltage. To maintain the full range of changes the beginning of each linear variable voltage function can be shifted for certain time interval. It is shown that when forming a range of frequency changes, it is necessary to take into account the presence of a "dead zone". The dependence of the transition from one frequency to another is random and depends on the values of correlation coefficient. A bifurcation diagram and display functions for processes with two and three attraction points are presented, The first zone of chaotic oscillations corresponds to the value of the coefficient, which is approximately in the range from 15 to 19. The second zone of chaotic oscillations correspond to the coefficient values from 40 to 59. The third zone of chaotic oscillations correspond to the coefficient values from 117 to 173. Between these zones regular oscillations are presented in the system. With an increase of correlation coefficient the number of attraction points and the corresponding display points can increase or decrease. The formulas for the calculation and the graph of the change in the correlation coefficient are given. It is shown that the correlation function is close to zero, some of its periodicity and the difference from zero is probably due to the existence of repeating areas of transient process. An example of an integer sequence for a process with two attraction points is given. For a process with two attraction points an example of integer sequences is given, which it is proposed to use to identify the type of chaotic process. The feature of generated chaotic sequences is shown – the sequence of integer function periods, which are enclosed between two attraction points is chaotic and unique. With using the deterministic equations with switching functions, a chaotic spreading sequence of linear frequency modulation is build, for identification of which it is proposed to use integer sequences of the number of periods that are enclosed between the points of generated frequencies.Ref. 7, fig. 4, table 1.

Performance Testing and Feature Expression of New Chaotic Circuit with 5-Connection Modes and 4-Signal Outputs

Experts of circuits have always wanted to quickly judge the characteristics of the output signals of the chaotic circuits designed. This work proposed briefly an example of the simplest chaotic circuit design methodology. An inductor and a capacitor, an operational amplifier and a multiplier are applied to construct a chaotic signal generator assisted by six resistors. This new circuit is characterized by two bi-directional power sources, five connection-modes and four output-signals. These signals features in time domain waveform, voltage phase diagram and pq-plot and our new pqs-plot. The tested results show that (1) four-path chaotic output signals are complex, (2) the signals’ evolution times are in 60-second level, (3) the new criterion of graphic expression uses short data of 1390 points. This case study will become a significant exploring work in future engineering education of brain health micro-nano-electronics.

Ultrawideband Millimeter-Wave Oscillators Based on Two Coupled Gyro-TWTs With Helical Waveguide

We are considering the possibility of ultrawideband millimeter-wave generation in microwave oscillators consisting of two coupled helical-waveguide gyro-TWTs, one of which operating as an amplifier whereas the other acting as a saturable absorber or as a nonlinear converter. In the first case, the regime of passive mode-locking is realized when the radiation represents a periodical train of ultrashort electromagnetic pulses. The spectral domain corresponds to the formation of a microwave “frequency comb.” On the other hand, if the second gyro-TWT acts as a nonlinear converter with a fast variation of the phase characteristic, it leads to the generation of chaotic signals with quasi-continuous spectrum and a bandwidth of up to ~10% which is defined by the bandwidth of the gyro-TWTs.