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High-performance reservoir computing has to rely on its highly rich internal dynamic. Chaotic systems based on memristors are widely employed in reservoir computing because of their wealthy nonlinear dynamic behaviors, but there are few studies and applications related to discrete memristor models compared to continuous memristor models. This paper proposes a brand new discrete memristor model, and a two-dimensional hyper chaotic maps is constructed by coupling the discrete memristor model and a sinusoidal function. The map has rich nonlinear dynamic behaviors which cater to the need for RC, therefore, we apply this map to enhance the richness of the state of the reservoir, and test the reservoir's computing capability by the emulation of NARMA and Santa Fe time series prediction task. For this purpose, using the method of the single node with delayed feedback, the proposed reservoir can avoid the selection of meta-parameters, and fully exploits the time dependence of the map states to replace the interactions between the internal nodes. As far as we know, this is the first time that time series analysis using the discrete memristive map, and the experimental results demonstrate that the hyperchaotic map based on the discrete memristor can effectively optimize the performance of the reservoir computing. Moreover, the proposed reservoir shows several attractive features including simple design, ease to calculate, and robustness. [ABSTRACT FROM AUTHOR]

Since the current general image encryption algorithms based on chaotic systems and classical permutation diffusion structures typically suffer from stochastic degradation, simple algorithm structures, and reduced execution efficiency when dealing with images with large data, this paper proposes a new multiprocess image encryption algorithm based on a new hyperchaotic coupled sine map. To begin with, by performing dynamic analyses of the map, including equilibrium points, bifurcation diagrams, Lyapunov exponent diagrams, and phase diagrams, associated performance analyses show high spectral entropy (SE) values and permutation entropy (PE) values. Meanwhile, sequences generated by the proposed map are able to pass the NIST randomness test, which shows its suitability for the design of encryption algorithms. Then, a chaos-based image encryption algorithm is proposed in this paper: In the preprocessing stage, the images are sparsely sampled using a compressed-sensing method; in the permutation stage, the image is decomposed into eight bit-plane images containing only 0s and 1s and a clockwise cyclic shift operation based on a chaotic sequence is applied in each bit-plane image to achieve a bit-level permutation effect; in the diffusion stage, the block DNA random computing is applied to the permuted image to modify the pixel values and the final cipher image is obtained. In addition, the initial value of the map is determined by the preset initial value, user-defined strings, and the Hash value of the plain image, where the Hash value of the plain image is calculated by the SHA-256 algorithm. Finally, the analysis of the algorithm demonstrates that the algorithm exhibits extremely strong plaintext correlation externally and excellent encryption performance in terms of attack resistance and execution efficiency. [ABSTRACT FROM AUTHOR]

The symmetric Lyapunov exponents (LEs) are known to be an inherent property of continuous-time conservative systems. However, the research on this interesting phenomenon in a discrete-time chaotic map has not been reported. Thus, this paper presents an improved 2D chaotic map based on Gumowski–Mira (GM) transformation, which has a stable fixed point or an unstable fixed point depending on its control parameters. Furthermore, it can display symmetric LEs and an infinite number of coexisting attractors with different amplitudes and different shapes. To demonstrate the complex dynamics of the 2D chaotic map, this paper studies its control parameters related to dynamical behaviors employing numerical analysis methods. Then, the hardware implementation based on STM32 platform is established for illustrating the numerical simulation results. Next, the random performance of the 2D chaotic map is tested by NIST FIPS140-2 suite. Finally, an image encryption algorithm based on the 2D chaotic map is designed, and the results obtained reveal that the proposed chaotic map has excellent randomness and is more suitable for many chaos-based image encryptions. [ABSTRACT FROM AUTHOR]

Over the past few decades, the research of dissipative chaotic systems has yielded many achievements in both theory and application. However, attractors in dissipative systems are easily reconstructed by the attacker, which leads to information security problems. Compared with dissipative systems, conservative ones can effectively avoid these reconstructing attacks due to the absence of attractors. Therefore, conservative systems have advantages in chaos-based applications. Currently, there are still relatively few studies on conservative systems. For this purpose, based on the simplest memristor circuit in this paper, a non-Hamiltonian 3D conservative system without equilibria is proposed. The phase volume conservatism is analyzed by calculating the divergence of the system. Furthermore, a Kolmogorov-type transformation suggests that the Hamiltonian energy is not conservative. The most prominent property in the conservative system is that it exhibits quasi-periodic 3D tori with heterogeneous coexisting and different amplitude rescaling trajectories triggered by initial values. In addition, the results of Spectral Entropy analysis and NIST test show that the system can produce pseudo-random numbers with high randomness. To the best of our knowledge, there is no 3D conservative system with such complex dynamics, especially in a memristive conservative system. Finally, the analog circuit of the system is designed and implemented to test its feasibility as well. [ABSTRACT FROM AUTHOR]

Memristor, as a nonlinear element, provides many advantages thanks to its superior properties to design different chaotic circuits. Thus, a novel four-dimensional double-scroll chaotic system with line equilibria as well as two unstable equilibria based on the flux-memristor model is proposed in this paper. The effects of initial values and parameters on the dynamic characteristics of the system are studied in detail by means of phase diagrams, Lyapunov exponent spectrums, bifurcation diagrams, two-parameter bifurcation diagrams and basins of attraction. Besides, a series of complex phenomena in the system, such as sustained chaos, bistability, transient chaos and coexisting attractors are observed, proving that the chaotic system has rich dynamic characteristics. Also, spectral entropy (SE) complexity algorithm and C 0 complexity algorithm based on structure complexity are adopted to analyze the complexity of the system. Additionally, PSPICE circuit simulation and Micro-Controller Unit (MCU) hardware experiment are carried out to verify the correctness of theoretical analysis and numerical simulation. Finally, the pulse chaos synchronization is achieved from the perspective of maximum Lyapunov exponent, and numerical simulations demonstrate the occurrence of the proposed system and practicability of the pulse synchronization control. [ABSTRACT FROM AUTHOR]

Memristor, as a typical nonlinear element, is able to produce chaotic signals in chaotic systems easily. Chaotic systems have potential applications in secure communications, information encryption, and other fields. Therefore, it is of importance to generate abundant dynamic behaviors in a single chaotic system. In this paper, a novel memristor-based chaotic system without equilibrium points is proposed. One of the essential features is the absence of symmetry in this system, which increases the complexity of the new system. Then, the nonlinear dynamic behaviors of the system are analyzed in terms of chaos diagrams, bifurcation diagrams, Poincaré maps, Lyapunov exponent spectra, the sum of Lyapunov exponents, phase portraits, 0–1 test, recurrence analysis and instantaneous phase. The results of the sum of Lyapunov exponents show that the given system is a quasi-Hamiltonian system with certain initial conditions (IC) and parameters. Next, other critical phenomena, such as hidden multi-scroll attractors, abundant coexistence characteristics, are found characterized through basins of attraction and others. Especially, it reveals some rare phenomena in other systems that multiple hidden hyperchaotic attractors coexist. Finally, the circuit implementation based on Micro Control Unit (MCU) confirms theoretical analysis and the numerical simulation. [ABSTRACT FROM AUTHOR]

The analysis of time series is essential in many fields, and reservoir computing (RC) can provide effective temporal processing that makes it well-suited for time series analysis and prediction tasks. In this study, we introduce a new discrete memristor model and a corresponding two-dimensional hyperchaotic map with complex dynamic properties that are well-suited for reservoir computing. By applying this map to the RC, we enhance the state richness of the reservoir, resulting in improved performance. The paper evaluates the performance of the proposed RC approach using time series data for sunspot, exchange rate, and solar-E forecasting tasks. Our experimental results demonstrate that this approach is highly effective in handling temporal data with both accuracy and efficiency. And comparing with other discrete memristive chaotic maps, the proposed map is the best for improving the RC performance. Furthermore, the proposed RC model is characterized by a simple structure that enables it to fully exploit the time-dependence of the state values of the hyperchaotic map. [ABSTRACT FROM AUTHOR]

Cellular neural network (CNN) is one of the best artificial neural network models due to its hardware implementability and many applications for image processing. The memristor-based cellular neural network (MCNN) combines the distinct benefits of memristors and neural networks, and it excels in mimicking chaotic systems under the effect of electromagnetic induction. In this work, a novel CNN chaotic system based on a flux-controlled memristor (MCNN-CS) with electromagnetic induction effects is constructed. Dynamical behaviors are examined by controlling the magnetic flux leakage strength and the intensity of the electromagnetic induction related to the memristor. Based on stability analyses and numerical simulation, forward and reverse period-doubling bifurcations, various coexisting attractors, multiperiods, chaos, several periodic windows, and chaotic crisis are observed. Besides, a number of complicated phenomena, including transient chaos, intermittent chaos, sustained chaos and bistability are also observed, demonstrating that this chaotic system has a wide range of dynamic properties. Finally, we generate pseudo-random number sequences based on this new system and apply them to image encryption. The obtained results show that this chaotic system offers superior randomness and is hence appropriate for image encryption applications. [ABSTRACT FROM AUTHOR]

At present, researchers only find that memristor-based time-delay (MBTD) chaotic systems have rich dynamic behaviors. However, there are still many difficulties in the analysis and application of the MBTD chaotic system. Therefore, a novel 3-D MBTD chaotic system with extreme multi-stability and line equilibrium points is proposed in this work. First, by applying dynamic analysis and numerical simulation, basic behaviors of the system are employed to illustrate the superiority of the system. Then, some special nonlinear phenomena are observed by two-parameter bifurcation diagrams, such as coexisting hidden attractors of both periodic and chaotic, coexisting multi-scroll hidden attractors, coexisting single-scroll hidden attractors and coexisting periodic attractors, which mean that hidden extreme multi-stability occurs. Moreover, the system which has good autocorrelation and cross-correlation is applied to generate the chaotic pseudo-random sequence. Finally, the approximate entropy of the chaotic pseudo-random sequence is larger than that of other time-delay chaotic systems. The above manifest that this MBTD chaotic system possesses abundant dynamics and good randomness. Hence this system owns latent force in the application of memristor. [ABSTRACT FROM AUTHOR]