Chaotic Duffing Oscillator Research Articles

Positive semi-definite Lyapunov function-based adaptive control for nonlinear discrete-time systems with application to chaotic Duffing oscillator

Positive semi-definite Lyapunov function-based adaptive control for nonlinear discrete-time systems with application to chaotic Duffing oscillator

Research on the Threshold Determination Method of the Duffing Chaotic System Based on Improved Permutation Entropy and Poincaré Mapping.

The transition from a chaotic to a periodic state in the Duffing chaotic oscillator detection system is crucial in detecting weak signals. However, accurately determining the critical threshold for this transition remains a challenging problem. Traditional methods such as Melnikov theory, the Poincaré section quantitative discrimination method, and experimental analyses based on phase diagram segmentation have limitations in accuracy and efficiency. In addition, they require large computational data and complex algorithms while having slow convergence. Improved permutation entropy incorporates signal amplitude information on the basis of permutation entropy and has better noise resistance. According to the characteristics of improved permutation entropy, a threshold determination method for the Duffing chaotic oscillator detection system based on improved permutation entropy (IPE) and Poincaré mapping (PM) is proposed. This new metric is called Poincaré mapping improved permutation entropy (PMIPE). The simulation results and the verification results of real underwater acoustic signals indicate that our proposed method outperforms traditional methods in terms of accuracy, simplicity, and stability.

Novel Duffing chaotic oscillator and its application to privacy data protection

Traditional Compressive Sensing (CS) achieves both compression and encryption of digital data. However, most existing compressive sensing methods present some shortcomings, including weak resistance to chosen-plaintext attacks and heavy key management burden. To overcome these shortcomings, this work presents a new combination of CS with optical transformation for digital image compression and encryption. The proposed compression-encryption scheme utilizes the interesting properties of CS and permutation-diffusion techniques to reduce the image size and encrypt the image data. A Novel Duffing Oscillator (NDO) is proposed, its dynamics is deeply analyzed, and its sequences are exploited to build a hardware-friendly measurement matrix for the CS process. This also contributes to reducing the total size of secret key sent to the receiving end. In addition, the final image compression-encryption output is obtained by applying one of the most significant optical encryption methods, namely Double Random Phase Encoding (DRPE). This contributes to further strengthen the security of the proposed scheme. Eventually, the experimental results imply that our scheme is effective in improving the resistance against various attacks, while guaranteeing good imperceptibility and reconstruction performance. It can then be employed in the information security communication field.

A novel method for frequency feature extraction of ship radiated noise based on variational mode decomposition, double coupled Duffing chaotic oscillator and multivariate multiscale dispersion entropy

The processing of ship radiated noise is a research hotspot in the field of military and marine resource exploration. Frequency characteristic is an important characteristic of ship radiated noise. Ship radiated noise consists of line spectrum and continuous spectrum, and the frequency features are mainly reflected by line spectrum. Accurate extraction of line spectrum frequency feature is of great significance to realize ship target classification and recognition. This paper proposes a novel method for frequency feature extraction of ship radiated noise based on variational mode decomposition (VMD), double coupled Duffing chaotic oscillator (DCDCO) and multivariate multiscale dispersion entropy (mvMDE), named VMD-DCDCO-mvMDE. For the first time, DCDCO and mvMDE are applied to the feature extraction of ship radiated noise. Firstly, ship radiated noise is decomposed into a series of intrinsic mode functions (IMFs) by VMD. The decomposition layers K of VMD are determined according to the decomposition results of EMD. Secondly, adjust γand let d = 2 to leave DCDCO in critical chaotic state and detect the frequency of low frequency IMF. The mvMDE of the output signal of chaotic oscillator is calculated in the frequency range of DCDCO in the large scale periodic state, and the accurate frequency is determined by the minimum value of mvMDE. Finally, the extracted frequency feature parameters are input into the self-organizing mapping (SOM) neural network to classify and recognize different ship targets. In the analog signal experiment, the maximum frequency error of VMD-DCDCO-MVMDE extraction is only 0.01%, while the minimum error of the current method is 0.33%. The proposed method can extract frequency feature more accurately. In the measured signal experiment, the results show that the correct rate of the proposed method can reach 100% for the classification and recognition of the three groups of ship radiated noise, while the correct rate of the current method is the highest at 84%. The proposed method can effectively extract the line spectrum frequency feature of ship radiated noise, and the classification accuracy is higher, and the recognition effect is better.

Anti-Chaos control of a servo system using nonlinear model reference adaptive control

Abstract This work presents a method for anti-chaos control of a servo system affected by parametric uncertainty and constant disturbances. It is based on Nonlinear Model Reference Adaptive Control where the reference model corresponds to a chaotic Duffing oscillator. Only upper and lower bounds on the servo system input gain are assumed known beforehand. It is shown that the solutions of the closed-loop system are Uniformly Ultimately Bounded. Moreover, the chaotic behaviour of the servo system position is verified through the Largest Lyapunov Exponent. The proposed control methodology is tested through experiments.

Poincaré maps design for the stabilization of limit cycles in non-autonomous nonlinear systems via time-piecewise-constant feedback controllers with application to the chaotic Duffing oscillator

Abstract In this paper, a design of Poincare maps and time–piecewise–constant state–feedback control laws for the stabilization of limit cycles in periodically–forced, non–autonomous, nonlinear dynamical systems is achieved. Our methodology is based mainly on the linearization of the nonlinear dynamics around a desired period–m unstable limit cycle. Thus, this strategy permits to construct an explicit mathematical expression of a controlled Poincare map from the structure of several local maps. An expression of the generalized controlled Poincare map is also developed. To make comparisons, we design three different time–piecewise–constant control laws: an mT–piecewise–constant control law, a T–piecewise–constant control law and a T n –piecewise–constant control law. As an illustrative application, we adopt the chaotic Duffing oscillator. By applying the designed piecewise–constant control laws to the Duffing oscillator, the system is stabilized on its desired period–m limit cycle and hence the chaotic motion is controlled.

A Novel Linear Spectrum Frequency Feature Extraction Technique for Warship Radio Noise Based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise, Duffing Chaotic Oscillator, and Weighted-Permutation Entropy.

Warships play an important role in the modern sea battlefield. Research on the line spectrum features of warship radio noise signals is helpful to realize the classification and recognition of different types of warships, and provides critical information for sea battlefield. In this paper, we proposed a novel linear spectrum frequency feature extraction technique for warship radio noise based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), duffing chaotic oscillator (DCO), and weighted-permutation entropy (W-PE). The proposed linear spectrum frequency feature extraction technique, named CEEMDAN-DCO-W-PE has the following advantages in comparison with other linear spectrum frequency feature extraction techniques; (i) as an adaptive data-driven algorithm, CEEMDAN has more accurate and more reliable decomposition performance than empirical mode decomposition (EMD) and ensemble EMD (EEMD), and there is no need for presetting parameters, such as decomposition level and basis function; (ii) DCO can detect the linear spectrum of narrow band periodical warship signals by way of utilizing its properties of sensitivity for weak periodical signals and the immunity for noise; and (iii) W-PE is used in underwater acoustic signal feature extraction for the first time, and compared with traditional permutation entropy (PE), W-PE increases amplitude information to some extent. Firstly, warship radio noise signals are decomposed into some intrinsic mode functions (IMFs) from high frequency to low frequency by CEEMDAN. Then, DCO is used to detect linear spectrum of low-frequency IMFs. Finally, we can determine the linear spectrum frequency of low-frequency IMFs using W-PE. The experimental results show that the proposed technique can accurately extract the line spectrum frequency of the simulation signals, and has a higher classification and recognition rate than the traditional techniques for real warship radio noise signals.

A Fusion Frequency Feature Extraction Method for Underwater Acoustic Signal Based on Variational Mode Decomposition, Duffing Chaotic Oscillator and a Kind of Permutation Entropy

In order to effectively extract the frequency characteristics of an underwater acoustic signal under sensor measurement, a fusion frequency feature extraction method for an underwater acoustic signal is presented based on variational mode decomposition (VMD), duffing chaotic oscillator (DCO) and a kind of permutation entropy (PE). Firstly, VMD decomposes the complex multi-component underwater acoustic signal into a set of intrinsic mode functions (IMFs), so as to extract the estimated center frequency of each IMF. Secondly, the frequency of the line spectrum can be obtained by using DCO and a kind of PE (KPE). DCO is used to detect the actual frequency of the line spectrum for each IMF and KPE can determine the accurate frequency when the phase space track is in the great periodic state. Finally, the frequency characteristic parameters acted as the input of the support vector machine (SVM) to distinguish different types of underwater acoustic signals. By comparing with the other three traditional methods for simulation signal and different kinds of underwater acoustic signals, the results show that the proposed method can accurately extract the frequency characteristics and effectively realize the classification and recognition for the underwater acoustic signal.

Duffing oscillators for secure communication

This paper introduces a new technique for using chaotic Duffing oscillators in secure communication. The secret message is encrypted using the parameters of the Duffing oscillator that indirectly affect the generated chaotic orbits. The mathematical model of the chaotic transmitter uses three parameters that can be altered between two levels, depending on the binary sequence of the digital secret message and the corresponding cipher. Consequently, a total of eight chaotic attractors are used to scramble the binary-based signal. Two different structures, for the synchronization and encryption mechanisms, between the transmitter and the receiver, are introduced. The first one uses the time series of the two chaotic signals generated by the Duffing transmitter, while implementing a cipher-less encryption mechanism. The second one uses a single time series of the Duffing transmitter, while allowing one of its parameters to act as a digital cipher. Better utilization of the communication channel is proved for the second method, while using a new adaptive Lyapunov-based technique to implement both the state synchronization and the parameters estimation at the receiver side. Both simulation and experimental case studies are presented to illustrate the proposed techniques and their applicability to securely transmit various multimedia digital signals.

Locating and imaging contact delamination based on chaotic detection of nonlinear Lamb waves

Abstract We propose a novel method for locating and imaging contact delaminations in composite plates, using a network of PZT transducers and the nonlinear Lamb waves. Being immune to noise and sensitive to weak signal, the Duffing chaotic oscillator is utilized to detect the nonlinear harmonics of Lamb waves generated at the contact delamination interfaces. The Lyapunov exponent of the Duffing system output is calculated to quantify the relative intensity of nonlinear second harmonic. Its normalized value is taken as the damage index to locate and image the delaminations by combining with the probabilistic imaging algorithm. The numerical simulation study on the proposed method is performed. Compared with the nonlinearity parameter and the conventional damage index, the Lyapunov damage index (LDI) can image the single delamination or multiple delaminations more effectively, especially under the noise interference. The experiment using the LDI is also conducted on a composite laminated plate with multiple internal delaminations. The results show that the proposed imaging method based on LDI is also valid to the practical delaminations in the composite plate. It has the following advantages: immunity to noise, needlessness of baseline data, high imaging resolution and location accuracy.

Synchronisation phenomenon in three blades rotor driven by regular or chaotic oscillations

The goal of the paper is to analysed the influence of the different types of excitation on the synchronisation phenomenon in case of the rotating system composed of a rigid hub and three flexible composite beams. In the model is assumed that two blades, due to structural differences, are de-tuned. Numerical calculation are divided on two parts, firstly the rotating system is exited by a torque given by regular harmonic function, than in the second part the torque is produced by chaotic Duffing oscillator. The synchronisation phenomenon between the beams is analysed both either for regular or chaotic motions. Partial differential equations of motion are solved numerically and resonance curves, time series and Poincaré maps are presented for selected excitation torques.

A parallel image encryption algorithm based on chaotic Duffing oscillators

Image encryption has been a popular research field in recent decades. This paper presents a novel parallel image encryption algorithm, which is based on the chaotic duffing oscillators. Image encryption systems based on chaotic Duffing oscillators are show some better performances. In order to be more efficient and secure, we divided the plain-images (original-image) into several pieces. The speed of encryption and decryption is very fast. We use well-known ways to perform the security and performance analysis of the proposed image encryption scheme. The results of the fail-safe analysis are inspiring and it can be concluded that, the proposed scheme is efficient and secure.

Research on Weak Signal Detection with Duffing Oscillator Based on Virtual Instrument Technology

In the process of oil field development, acoustic telemetry system is an important means to realize the wireless communication between underground and ground. However, due to the attenuation of acoustic waves in the transmission process, the signal becomes very weak when it reaches the ground, so, weak signal detection is very important for acoustic telemetry system. This paper proposed a weak signal detection with chaotic oscillator based on virtual instrument technology. Firstly, analyzed the principle of the weak sinusoidal signal detection with Duffing chaotic oscillator. Especially the influence of the signal initial phase was discussed; and then the multi-phase- capture method based on virtual instrument technology was proposed, it was achieved by programming with LabVIEW. The results indicate that the method not only could effectively detect the weak inputted signal with random phase, but also it features progressiveness and practicability used for downhole acoustic telemetry system.

Indirect Model Reference Fuzzy Control of SISO Fractional Order Nonlinear Chaotic Systems

This paper presents a novel indirect model reference fuzzy control for the control of a fractional order chaotic nonlinear dynamic system. The proposed control scheme benefits from a fractional order reference model which has more degrees of freedom. Takagi-Sugeno fuzzy model is used to model the nonlinear dynamic system under control. Some adaption laws are proposed to estimate the parameters of the Takagi-Sugeno fuzzy model. The stability of the proposed structure and the proposed adaptation laws are proved using a novel Lyapunov function. In order to show the implementability and effectiveness of the proposed controller, it is simulated on the control of a fractional order chaotic Duffing oscillator.

Study on Traveling Wave Signal Anti-Interference and a New Detection Method

Traveling wave in transit, wave head is easy to produce distortion and affected by environmental interference, so accurately measuring the head of traveling wave singularity occurrence time become extremely difficult. The key to improve the precision of traveling wave detection is to accurately capture the happening time of wave head of singular points. Recently, traveling wave singularity detection usually use wavelet, EMD-HHT transform technique, but both have mixing phenomenon, affecting the accuracy of detection. In this paper, we propose a new method that use Duffing chaotic oscillator to suppress traveling wave interference signal. By Matlab simulation and it is proved that this method can effectively suppress noise singular point. Meanwhile, we propose an anti-mixing EEMD-HHT wave head detection technology. Through simulation experiment and field test, it is proved that, compared with EMD, EEMD can more accurately identify the traveling wave arrival time, detection accuracy increasing by 1.52%.

A Method for Weak Multi-Frequency Signal Feature Extraction Based on Chaotic Duffing Oscillator

In this paper, we study the scale-transformation weak signal detection method based on chaotic Duffing oscillator. Based on this, the frequency characteristics of the weak single-frequency signal with arbitrary frequency and initial phase can be extracted. Furthermore, we propose a signal frequency interception preprocessing method for analyzing weak multi-frequency signal. After combing the preprocessing method with the weak signal detection method based on chaotic Duffing oscillator, we further propose a novel detection method for weak multi-frequency signal. Based on this novel method, we can extract the frequency characteristics and initial phase characteristics of the weak multi-frequency signal. In this research, we also study the automatic detection of unknown multi-frequency signal. According to the numerical simulation, the novel method we propose in this paper is helpful to extract the frequency parameters and initial phase information of each signal component of the weak multi-frequency signal.

Fuzzy adaptive modular design of uncertain chaotic Duffing oscillators

This paper proposes a fuzzy adaptive control approach based on a modular design for uncertain chaotic Duffing oscillators. Using fuzzy logic, the unknown nonlinear function in the Duffing oscillator is approximated. Subsequently, a modular adaptive controller is derived consisting of an inputtostate stabilizing (ISS) control module and a passive identifier module. Since the modular design allows for independent design of the controller and identifier, the proposed method provides substantial flexibility in the choice of a parameter identifier. Additionally, the modularity of the controller-identifier pair provides simplicity in the control system derivation. Simulation results are included to illustrate the effectiveness of the proposed approach.

A secure communication scheme based on chaotic Duffing oscillators and frequency estimation for the transmission of binary-coded messages

This work presents a new technique to securely transmit and retrieve a message signal via chaotic systems. The main contribution of this paper is two-fold: the way that the message signal is encrypted in the frequency of a sinusoidal term and a novel frequency estimator for retrieving the message. In our system, a two-valued message signal modulates the frequency of the Duffing oscillator sinusoidal term. Then, two chaotic signals generated by the oscillator are encrypted with a Delta modulator and sent through a noisy channel. A Lyapunov-based observer is used in the receiver side to retrieve the sinusoidal term that contains the message and a novel frequency estimator is then used to retrieve the confidential message signal. The system was implemented in Matlab/Simulink in order to analyze its performance.

Simulation and Examination of a Signal Masking Chaotic Communication System, Based on the Duffing Oscillator

The study in this paper is focused on the applications of the chaotic Duffing oscillator to signal masking communication scheme. Using the concept of synchronized chaotic systems the signal masking approach is demonstrated with the Duffing oscillator implemented in both the transmitter and receiver. The chaotic masking signal is added at the transmitter to the information signal, and at the receiver, the masking is regenerated and subtracted from the received signal. Chaotic behavior and chaotic masking scheme are designed and simulated using Simulink/Matlab program. All the results are used to illustrate the effectiveness and the applicability of the Duffing oscillator in signal masking communication.

DISORDER INDUCED ORDER IN AN ARRAY OF CHAOTIC DUFFING OSCILLATORS

This paper addresses the issue of disorder induced order in an array of coupled chaotic Duffing oscillators which are excited by harmonic parametric excitations. In order to investigate the effect of phase disorder on dynamics of the array, we take into account that individual uncoupled Duffing oscillator with a parametric excitation is chaotic no matter what the initial phase of the excitation is. It is shown that phase disorder by randomly choosing the initial phases of excitations can suppress spatio-temporal chaos in the system coupled by chaotic Duffing oscillators. When all the phases are the same and deterministic, the oscillators remain chaotic and asynchronous no matter what the common phase is. When driven asynchronously by introducing phase disorder, the oscillators coupled in the array appear more regular with increase of the amplitude of random phase, and the highest level of synchrony between them is induced by intermediate phase disorder, displaying a resonance like phenomenon caused from the transition of the coupled oscillators from chaos to periodic motion. Since varying the initial phases of excitations is more feasible than altering parameters intrinsic to the oscillators coupled in an array, this study provides a practical method for control and synchronization of chaotic dynamics in high-dimensional, spatially extended systems, which might have potential applications in engineering, neuroscience and biology.