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Waveforms of input sine wave with amplitude of 1 V and frequency of 1 kHz. (a) transmitting and receiving waveform, (b) synchronous phase diagram, (c) superimposed signal waveform, (d) carrier signal waveform.
Source publication
In this paper, a scheme for chaotic modulation secure communication is proposed based on chaotic synchronization of an improved Lorenz system. For the first time, the intensity limit and stability of the transmitted signal, the characteristics of broadband and the requirements for accuracy of electronic components are presented by Multisim simulati...
Contexts in source publication
Context 1
... Given an input sine wave with amplitude of 1 V and frequency of 1 kHz, the simulation results are shown as Fig 4. In order to verify that the proposed circuit can transmit various sig- nals without distortion, square wave and triangular wave with amplitude of 1 V and frequency of 1 kHz were input. Simulation results show that, no matter what kind of signal is input, the two chaotic circuits can be completely synchronized if the component parameters of the trans- mitting circuit are entirely same as the receiving circuit. ...
Context 2
... results show that, no matter what kind of signal is input, the two chaotic circuits can be completely synchronized if the component parameters of the trans- mitting circuit are entirely same as the receiving circuit. The modulation-demodulation signal waveform and the synchronous phase diagram of the receiver and the transmitter are shown in Fig 4(a), 4(b) and 4(c). Negligible distortion can be observed. ...
Citations
... In this secure communication, the intensity limit, stability of the transmitted signal, characteristics of broadband, and requirements for the accuracy of electronic components have been presented by simulation and experiments. Following this work, Xiong et al. [43] proposed some improvements to the measurement method and the experimental circuit to facilitate the synchronization, with and without the signal. The possibility of synchronizing coupled analog and digital systems was experimentally proven. ...
Chaos-based encryption is a promising approach to secure communication due to its complexity and unpredictability. However, various challenges lie in the design and implementation of efficient, low-power, attack-resistant chaos-based encryption schemes with high encryption and decryption rates. In addition, Machine learning (ML) has emerged as a promising tool for enhancing the growing security and efficiency concerns and maximizing the potential of emerging computing platforms across diverse domains. With the rapid advancements in technology and the increasing complexity of computing systems, ML offers a unique approach to addressing security challenges and optimizing performance. This paper presents a comprehensive study on the application of ML techniques to secure chaotic communication for wearable devices, with an emphasis on chaos-based encryption. The theoretical foundations of ML for secure chaotic communication are discussed, including the use of ML algorithms for signal synchronization, noise reduction, and encryption. Various ML algorithms, such as deep neural networks, support vector machines, decision trees, and ensemble learning methods, are explored for designing chaos-based encryption algorithms. This paper places a greater emphasis on methodological aspects, metrics, and performance evaluation of machine learning algorithms. In addition, the paper presents an in-depth investigation into state-of-the-art ML-assisted defense and attacks on chaos-based encryption schemes, covering their theoretical foundations and practical implementations. Furthermore, a review of the potential advantages and limitations associated with the utilization of ML techniques in secure communication systems and encryption is provided. The study extends to exploring the diverse range of applications that can benefit from ML-assisted encryption, such as secure communication in the Internet of Things (IoTs), cloud computing, and wireless networks. Overall, we provide insights into the applications of ML for secure chaotic communication in wearable devices, its challenges, and opportunities, offering a foundation for further research and development and facilitating advancements in the field of secure chaotic communication.
... A number of studies are dedicated to creating efficient and precise electronic implementations of chaotic systems, including fractionalorder systems and systems with memristors [14][15][16][17][18][19][20][21][22]. A plethora of possible applications of analog chaotic circuits is known: accurate sensing [23,24], measurement [2,25] and secure communication [26,27]. ...
Chaotic analog circuits are commonly used to demonstrate the physical existence of chaotic systems and investigate the variety of possible applications. A notable disparity between the analog circuit and the computer model of a chaotic system is usually observed, caused by circuit element imperfectness and numerical errors in discrete simulation. In order to show that the major component of observable error originates from the circuit and to obtain its accurate white-box model, we propose a novel technique for reconstructing ordinary differential equations (ODEs) describing the circuit from data. To perform this task, a special system reconstruction algorithm based on iteratively reweighted least squares and a special synchronization-based technique for comparing model accuracy are developed. We investigate an example of a well-studied Rössler chaotic system. We implement the circuit using two types of operational amplifiers. Then, we reconstruct their ODEs from the recorded data. Finally, we compare original ODEs, SPICE models, and reconstructed equations showing that the reconstructed ODEs have approximately 100 times lower mean synchronization error than the original equations. The proposed identification technique can be applied to an arbitrary nonlinear circuit in order to obtain its accurate empirical model.
... With the research on rich and colorful nonlinear dynamic characteristics [24][25][26][27][28] of nonlinear circuits containing memristors, scholars pay more and more attention to the potential function and value of memristors in practical engineering applications. ...
In this paper, a memristive circuit system is proposed and its dynamical characteristics are analyzed by two-parameters bifurcation diagrams, Lyapunov exponent spectrum, SE complexity and C0 complexity. The numerical analysis results illustrate that the chaotic state of the memristive system is distributed in a large range of parameters, which is especially suitable for image encryption application. Then, in view of the fact that the traditional method of observing three-dimensional chaotic attractors can not give full play to the essence of human eyes cooperating with brain information processing, a new method to obtain the brain information of complete three-dimensional chaotic attractors by using red–blue 3D glasses is proposed. The results show that compared with the traditional method based on the memristive system, the visual effect of chaotic attractors observed by red–blue 3D glasses is shocking. In addition, an image encryption algorithm is designed to verify the image encryption application of the memristive system based on DNA variation. A series of security performance analysis experiments are performed to verify the effectiveness and reliability of the designed algorithm such as the secret key space analysis, histogram distribution analysis, information entropy analysis, correlation analysis and key sensitivity analysis. Finally, the hardware circuit based on the memristive system is implemented with some common electronic devices, which has the advantages of simple structure and low cost.
... This was done in a manner similar to that discussed in [31], where Kirchhoff's laws may be used to create a standard, voltagemode opamp integrator configuration paired with voltage multipliers. This also resembles the analog circuit implementations shown in [32]. where V P (t) = [a sin(Ot + ϕ 0 )) − xα] is an external stimulus. ...
Adaptive oscillators (AOs) are nonlinear oscillators with plastic states that encode information. Here, an analog implementation of a four-state adaptive oscillator, including design, fabrication, and verification through hardware measurement, is presented. The result is an oscillator that can learn the frequency and amplitude of an external stimulus over a large range. Notably, the adaptive oscillator learns parameters of external stimuli through its ability to completely synchronize without using any pre-or post-processing methods. Previously , Hopf oscillators have been built as two-state (a regular Hopf oscillator) and three-state (a Hopf oscillator with adaptive frequency) systems via VLSI and FPGA designs. Building on these important implementations, a continuous-time, analog circuit implementation of a Hopf oscillator with adaptive frequency and amplitude is achieved. The hardware measurements and SPICE simulation show good agreement. To demonstrate some of its func-tionality, the circuit's response to several complex waveforms, including the response of a square wave, a sawtooth wave, strain gauge data of an impact of a nonlinear beam, and audio data of a noisy microphone recording, are reported. By learning both the frequency and amplitude, this circuit could be used to enhance applications of AOs for robotic gait, clock oscillators, analog frequency analyzers, and energy harvesting.
... Fractional order chaotic systems exhibit higher nonlinearity, more degrees of freedom and more complex dynamics than their corresponding integer-order systems because of fractional derivative parameters. Many chaotic systems have been confirmed by electronic circuit experiments [14][15][16] . ...
... (15) numerically at selected values to show the chaos and hyperchaos in the system. Phase portraits for system Eq.(15) with the initial conditions (1 , 0 . ...
A novel fractional nonautonomous system is proposed by introducing fractional order meminductor-memristor based circuit. Four circuit models are presented by different arrangements for the elements and the dynamic behaviors for each circuit are explored. It is observed that the four systems exhibit chaotic and hyperchaotic behaviors which have been verified using Lyapunov exponents. Bifurcation diagrams and phase portraits are employed to examine the effects of parameters variation on the qualitative dynamics of each model. An image encryption scheme is presented based on pseudo chaos orbit generated by two interval extensions of chaotic circuit model. The security analysis is carried out to verify the robustness and efficiency of the encryption scheme against possible attacks.
... According to the literature, the nonlinearities can be piecewise nonlinear function [3], trigonometric function [4], absolute value function [5], or power function [6]. With different nonlinearities, the chaotic system can have various strange attractors as single-scroll [7], double-scroll [8], multi-scroll [9], etc. The majority of such chaotic systems are known for many years, and some chaotic systems with hidden attractors are derived from them [10][11][12]. ...
In recent years, exploring and investigating chaotic systems with hyperbolic sine nonlinearity has gained the interest of many researchers. With two back-to-back diodes to approximate the hyperbolic sine nonlinearity, these chaotic systems can achieve simplicity of the electrical circuit without any multiplier or sub-circuits. In this chapter, the genesis of chaotic systems with hyperbolic sine nonlinearity is introduced, followed by the general method of generating nth-order (n > 3) chaotic systems. Then some derived chaotic systems/torus-chaotic system with hyperbolic sine nonlinearity is discussed. Finally, the applications such as random number generator algorithm, spread spectrum communication and image encryption schemes are introduced. The contribution of this chapter is that it systematically summarizes the design methods, the dynamic behavior and typical engineering applications of chaotic systems with hyperbolic sine nonlinearity, which may widen the current knowledge of chaos theory and engineering applications based on chaotic systems.
... Jovic (2011) described an operation process of secure communication based on chaotic synchronization technique in detail. Xiong et al. (2016) used chaotic synchronization to achieve the robust secure communication through analog electronic circuits. It is known that the chaotic system of the synchronization scheme is completely exposed to the public channel, which increases the risk of being identified or even cracked. ...
With emerge of smart navigation, the secure communication issues have drawn extensive attention on maritime agendas between ships or with the shore. This paper presents a chaotic secure communication scheme by using observer design for maritime navigation and transportation systems. The proposed scheme involves three key factors: chaotic encryption, state observer, and chaotic decryption. The chaotic system, as the encryption keys carrying confidential information, will be sent from transmitter to the receiver through a public channel. It is obvious that the fewer signals are transmitted on the public channel, the higher security of the communication system is possible. A state observer is designed to estimate all system states when only partial states are detectable on the public channel. The robust observer gain is implemented in terms of linear matrix inequality (LMI) for convex optimization. The process of information encryption and recovery has been discussed in detail. From the simulation results, it is found that the observer-based method can robustly estimate full state variables by using system output signals with LMI optimization. Based on these updated states with the the state observer, the original information is accurately recovered for safe navigation of vessels with reliability and efficiency.
... Additionally, most of researches center on theoretical analysis and numerical simulation for the chaotic system (Mahmoud, 2013;Mahmoud, 2012;Mahmoud and Mahmoud, 2010a;Ma et al., 2017;Sundarapandian, 2011;Wu and Zeng, 2017;Wang et al., 2014;Ma et al., 2014), and the study on corresponding chaotic circuit implementation (Wang and Xu, 2016;Zhang et al., 2014;Bao et al., 2018;Xu et al., 2018;Lu et al., 2018;Xiong et al., 2016;Xiong et al., 2017a) is less. Especially, the circuit realization for chemical oscillating system is rarely seen. ...
Purpose
This paper is aimed at investigating a novel chemical oscillating chaotic system with different attractors at fixed parameters. The typical dynamical behavior of the new chemical oscillating system is discussed, and it is found that the state selection is dependent on initial values. Then, the stabilization problem of the chemical oscillating attractors is investigated analytically and numerically. Subsequently, the novel electronic circuit of the proposed chemical oscillating chaotic system are constructed, and the influences of the changes of circuit parameters on chemical oscillating chaotic attractors are investigated.
Design/methodology/approach
The different attractors of the novel chemical oscillating chaotic system are investigated by changing the initial values under fixed parameters. Moreover, the active control and adaptive control methods are presented to make the chemical oscillating chaotic systems asymptotically stable at the origin based on the Lyapunov stability theory. The influences on chemical oscillating chaotic attractors are also verified by changing the circuit parameters.
Findings
It is found that the active control method is easier to be realized by using physical components because of its less control signal and lower cost. It is also confirmed that the adaptive control method enjoys strong anti-interference ability because of its large number of selected controllers. What can be seen from the simulation results is that the chaotic circuits are extremely dependent on circuit parameters selection. Comparisons between MATLAB simulations and Multisim simulation results show that they are consistent with each other and demonstrate that changing attractors of the chemical oscillating chaotic system exist. It is conformed that circuit parameters selection can be effective to control and realize chaotic circuits.
Originality/value
The different attractors of the novel chemical oscillating chaotic system are investigated by changing the initial values under fixed parameters. The characteristic of the chemical oscillating attractor is that the basin of attraction of the three-dimensional attractor is located in the first quadrant of the eight quadrants of the three-dimensional space, and the ranges of the three variables are positive. This is because the concentrations of the three chemical substances are all positive.
... Moreover, in order to meet the security requirements of chaotic secure communication, researchers proposed a method to improve the predictability and complexity of the system by constructing hyperchaotic systems [24][25][26] and memristor-based chaotic systems, since memristor is a nonlinear component, whose memory ability [27][28][29][30][31] of the current by convection is not available in conventional chaotic circuit elements. In this way, it is especially suitable for the chaotic secure communication field [32][33][34][35][36]. Although the application research of memristor is just the beginning in the field of chaotic secure communication, it has great potentials and advantages in improving the confidentiality and security of chaotic secure communication system. ...
... where y 1 , y 2 , y 3 , y 4 are the states and u 1 , u 2 , u 3 , u 4 are the designed controllers, whereas the synchronization error based on the active control method is defined as follows: 4 37 According to (37), the synchronization error system between the memductor-based drive system (35) and the memductor-based response system (36) is easily obtained as follows: ...
This paper is expected to introduce a novel memductor-based chaotic system. The local dynamical entities, such as the basic dynamical behavior, the divergence, the stability of equilibrium set, and the Lyapunov exponent, are all investigated analytically and numerically to reveal the dynamic characteristics of the new memductor-based chaotic system as the system parameters and the initial state of memristor change. Subsequently, an active control method is derived to study the synchronous stability of the novel memductor-based chaotic system through making the synchronization error system asymptotically stable at the origin. Further to these, a memductor-based chaotic circuit is designed, realized, and applied to construct a new memductor-based secure communication circuit by employing the basic electronic components and memristor. Furthermore, the design principle of the memductor-based chaotic circuit is thoroughly analyzed and the concept of “the memductor-based chaotic circuit defect quantification index” is proposed for the first time to verify whether the chaotic output is consistent with the mathematical model. A good qualitative agreement is shown between the simulations and the experimental validation results.
... In Optical Engineering 106101-3 October 2018 • Vol. 57 (10) general, value of C 2 n is almost constant for near-ground horizontal links with typical values ranging from 10 −17 to 10 −13 m −3∕2 representing weak-to-strong turbulence conditions. 2,5,33,[37][38][39][40] In practice, the refractive index structure parameter is usually calculated from measurements of optical wave characteristics, such as the turbulence-induced angleof-arrival and intensity fluctuations (scintillations) of the optical wave at the receiver detector plane. ...
... The approach here shows the degradation experienced by the received signal RðtÞ ¼ γðtÞsðtÞ þ αðtÞ þ ηðtÞ as it passes through the FSO channel while the noise level has been Fig. 7 A sampled original binary message, mðt Þ, and the corresponding reconstructed message,mðt Þ. Optical Engineering 106101-6 October 2018 • Vol. 57 (10) increased by a factor of 10 dB for three different scenarios as shown in Fig. 10. Based on the DSNR definition Eq. (12), the variance of AWGN has been increased while all other noise sources have not been changed. ...
... Optical Engineering 106101-12 October 2018 • Vol. 57 (10) ...
This paper aims to present a Lorenz chaotic free-space optical (FSO) communication system (LC-FSO-CS), and to study the impact of FSO channel on a transmitted Lorenz chaotic signal infused by an arbitrary random binary message. It examines and corroborates the LC-FSO-CS by an analytical approach, using autocorrelation and power spectral density in the presence of the channel's multiplicative noise. To achieve this task, the paper exploits an autocorrelation model for the multiplicative scintillation noise while approximating the transmitted chaotic signal modeled by a quasirandom telegraph signal. The method presented here considers the effect of the additive noise in the FSO channel as negligible, while successfully employing the linear system concepts and logarithmic operation to analyze the influence of scintillation noise on the transmitted chaotic waveform. The emphasis of this work is on last-mile FSO communication with simulation experiments performed and results presented throughout the paper to validate the LC-FSO-CS. © 2018 Society of Photo-Optical Instrumentation Engineers (SPIE).
