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In this paper, a nine-dimensional chaotic system is designed and applied to secure communication.

Firstly, the equilibrium characteristics, dissipativity, bifurcation diagram and Lyapunov exponent spectrum are used to analyze the relevant characteristics of the proposed nine-dimensional chaotic system. In the analysis of Lyapunov exponential spectrum, when changing the linear parameters, the system shows two states, hyperchaos and chaos. For secure communication, there is a large secret key space. Secondly, C0 complexity and SEcomplexity of the system are analyzed, which shows that the system has sequences closer to random sequences.

The proposed nine-dimensional system has a large key space and more complex dynamic characteristics

The results show that the proposed nine-dimensional hyperchaotic system has excellent encryption capabilities and can play an important role in the field of secure communication.

This paper introduces an audio encryption algorithm based on permutation of audio samples using discrete modified Henon map followed by substitution operation with keystream generated from the modified Lorenz-Hyperchaotic system. In this work, the audio file is initially compressed by Fast Walsh Hadamard Transform (FWHT) for removing the residual intelligibility in the transform domain. The resulting file is then encrypted in two phases. In the first phase permutation operation is carried out using modified discrete Henon map to weaken the correlation between adjacent samples. In the second phase it utilizes modified-Lorenz hyperchaotic system for substitution operation to fill the silent periods within the speech conversation. Dynamic keystream generation mechanism is also introduced to enhance the correlation between plaintext and encrypted text. Various quality metrics analysis such as correlation, signal to noise ratio (SNR), differential attacks, spectral entropy, histogram analysis, keyspace and key sensitivity are carried out to evaluate the quality of the proposed algorithm. The simulation results and numerical analyses demonstrate that the proposed algorithm has excellent security performance and robust against various cryptographic attacks.

The purpose of this paper is to construct a proportion-integral-type (PI-type) memristor, which is different from that of the previous memristor emulator, but the constructing memristive chaotic circuit possesses line equilibrium, leading to the emergence of the initial conditions-related dynamical behaviors.

This paper presents a PI-type memristor emulator-based canonical Chua’s chaotic circuit. With the established mathematical model, the stability region for the line equilibrium is derived, which mainly consists of stable and unstable regions, leading to the emergence of bi-stability because of the appearance of a memristor. Initial conditions-related dynamical behaviors are investigated by some numerically simulated methods, such as phase plane orbit, bifurcation diagram, Lyapunov exponent spectrum, basin of the attraction and 0-1 test. Additionally, PSIM circuit simulations are executed and the seized results validate complex dynamical behaviors in the proposed memristive circuit.

The system exhibits the bi-stability phenomenon and demonstrates complex initial conditions-related bifurcation behaviors with the variation of system parameters, which leads to the occurrence of the hyperchaos, chaos, quasi-periodic and period behaviors in the proposed circuit.

These memristor emulators are simple and easy to physically fabricate, which have been increasingly used for experimentally demonstrating some interesting and striking dynamical behaviors in the memristor-based circuits and systems.

The purpose of this paper is to construct a multiwing chaotic system that has hidden attractors with multiple stable equilibrium points. Because the multiwing hidden attractors chaotic systems are safer and have more dynamic behaviors, it is necessary to construct such a system to meet the needs of developing engineering.

By introducing a multilevel pulse function into a three-dimensional chaotic system with two stable node–foci equilibrium points, a hidden multiwing attractor with multiple stable equilibrium points can be generated. The switching behavior of a hidden four-wing attractor is studied by phase portraits and time series. The dynamical properties of the multiwing attractor are analyzed via the Poincaré map, Lyapunov exponent spectrum and bifurcation diagram. Furthermore, the hardware experiment of the proposed four-wing hidden attractors was carried out.

Not only unstable equilibrium points can produce multiwing attractors but stable node–foci equilibrium points can also produce multiwing attractors. And this system can obtain 2N + 2-wing attractors as the stage pulse of the multilevel pulse function is N. Moreover, the hardware experiment matches the simulation results well.

This paper constructs a new multiwing chaotic system by enlarging the number of stable node–foci equilibrium points. In addition, it is a nonautonomous system that is more suitable for practical projects. And the hardware experiment is also given in this article which has not been seen before. So, this paper promotes the development of hidden multiwing chaotic attractors in nonautonomous systems and makes sense for applications.

This study aims to improve the complexity of chaotic systems and the security accuracy of information encrypted transmission. Applying five-dimensional memristive Hopfield neural network (5D-HNN) to secure communication will greatly improve the confidentiality of signal transmission and greatly enhance the anticracking ability of the system.

Chaos masking: Chaos masking is the process of superimposing a message signal directly into a chaotic signal and masking the signal using the randomness of the chaotic output. Synchronous coupling: The coupled synchronization method first replicates the drive system to get the response system, and then adds the appropriate coupling term between the drive The synchronization error and the coupling term of the system will eventually converge to zero with time. The synchronization error and coupling term of the system will eventually converge to zero over time.

A 5D memristive neural network is obtained based on the original four-dimensional memristive neural network through the feedback control method. The system has five equations and contains infinite balance points. Compared with other systems, the 5D-HNN has rich dynamic behaviors, and the most unique feature is that it has multistable characteristics. First, its dissipation property, equilibrium point stability, bifurcation graph and Lyapunov exponent spectrum are analyzed to verify its chaotic state, and the system characteristics are more complex. Different dynamic characteristics can be obtained by adjusting the parameter k.

A new 5D memristive HNN is proposed and used in the secure communication

With the development of integrated circuit and communication technology, digital secure communication has become a research hotspot. This paper aims to design a five-dimensional fractional-order chaotic secure communication circuit with sliding mode synchronous based on microcontroller (MCU).

First, a five-dimensional fractional-order chaotic system for encryption is constructed. The approximate numerical solution of fractional-order chaotic system is calculated by Adomian decomposition method, and the phase diagram is obtained. Then, combined with the complexity and 0–1 test algorithm, the parameters of fractional-order chaotic system for encryption are selected. In addition, a sliding mode controller based on the new reaching law is constructed, and its stability is proved. The chaotic system can be synchronized in a short time by using sliding mode control synchronization.

The electronic circuit is implemented to verify the feasibility and effectiveness of the designed scheme.

It is feasible to realize fractional-order chaotic secure communication using MCU, and further reducing the synchronization error is the focus of future work.

The purpose of this paper is to develop a simple chaotic circuit. The circuit can be fabricated by less discrete electronic components, within which complex dynamical behaviors can be generated.

A second-order non-autonomous inductor-free chaotic circuit is presented, which is obtained by introducing a sinusoidal voltage stimulus into the classical Wien-bridge oscillator. The proposed circuit only has two dynamic elements, and its nonlinearity is realized by the saturation characteristic of the operational amplifier in the classical Wien-bridge oscillator. After that, its dynamical behaviors are revealed by means of bifurcation diagram, Lyapunov exponent and phase portrait and further confirmed using the 0-1 test method. Moreover, an analog circuit using less discrete electronic components is implemented, and its experimental results are measured to verify the numerical simulations.

The equilibrium point located in a line segment varies with time evolution, which leads to the occurrence of periodic, quasi-periodic and chaotic behaviors in the proposed circuit.

Unlike the previously published works, the significant values of the proposed circuit with simple topology are inductor-free realization and without extra nonlinearity, which make the circuit can be used as a paradigm for academic teaching and experimental illustraction for chaos.

The purpose of this paper is to propose a new algorithm for detection of chaos in oscillatory circuits. The algorithm is based on the wavelet transform.

The proposed detection is developed by using a specific measure obtained by averaging wavelet coefficients. This measure exhibits various values for chaotic and periodic states.

The proposed algorithm is applied to signals from autonomous systems such as the Chua’s oscillatory circuit, the Lorenz chaotic system and non-autonomous systems such as the Duffing oscillator. In addition, the detection is applied to sequences obtained from the logistic map. The results are compared to those obtained with a detrended fluctuation analysis and a time-frequency signal analysis based on detectors of chaotic states.

In this paper, a new algorithm is proposed for the detection of chaos from a single time series. The proposed technique is robust to the noise influence, having smaller calculation complexity with respect to the state-of-the-art techniques. It is suitable for real-time detection with delay that is about half of the window width.

The purpose of this paper is with delay-independent stabilization of nonlinear systems with multiple time-delays and its application in chaos synchronization of Rössler system.

Based on linear matrix inequality and algebra Riccati matrix equation, the stabilization result is derived to guarantee asymptotically stable and applicated in chaos synchronization of Rössler chaotic system with multiple time-delays.

A controller is designed and added to the nonlinear system with multiple time-delays. The stability of the nonlinear system at its zero equilibrium point is guaranteed by applying the appropriate controller signal based on linear matrix inequality and algebra Riccati matrix equation scheme. Another effective controller is also designed for the global asymptotic synchronization on the Rössler system based on the structure of delay-independent stabilization of nonlinear systems with multiple time-delays. Numerical simulations are demonstrated to verify the effectiveness of the proposed controller scheme.

The introduced approach is interesting for delay-independent stabilization of nonlinear systems with multiple time-delays and its application in chaos synchronization of Rössler system.

This paper aims to classify the inductorless Chua’s circuits into two types from the topological structures and construct a chaotic circuit under this new classification framework.

In this paper, two types of inductorless Chua’s circuit models are presented from topological structure, among which the first type of inductorless Chua’s circuit (FTICC) model is much closer to the original Chua’s circuit. Under this classification framework, a new inductorless Chua’s circuit that belongs to the FTICC model is built by replacing LC parallel resonance of the original Chua’s circuit with a second order Sallen–Key band pass filter.

Compared with a paradigm of a reported inductorless Chua’s circuit that belongs to the second type of inductorless Chua’s circuit (STICC) model, the newly proposed circuit can present the attractors which are much more closely to the original Chua’s attractors. The dynamical behaviors of coexisting period-doubling bifurcation patterns and boundary crisis are discovered in the newly proposed circuit from both numerical simulations and experimental measurements. Moreover, a crisis scenario is observed that unmixed pairs of symmetric coexisting limit cycles with period-3 traverse through the entire parameter interval between coexisting single-scroll chaotic attractors and double-scroll chaotic attractor.

The newly constructed circuit enriches the family of inductorless Chua’s circuits, and its simple topology with small printed circuit board size facilitates the various types of engineering applications based on chaos.