Memristor-based Chaotic System Research Articles

Analysis of a time-dependent memristor-based chaotic system and its application in image encryption

Abstract Compared with ordinary chaotic systems, memristor-based chaotic systems have more complex dynamic behaviors and are more suitable for image encryption algorithms. In this paper, a four-dimensional chaotic system is constructed by introducing a cubic nonlinear memristor into a three-dimensional chaotic system. Firstly, the dynamic characteristics of the constructed memristor-based chaotic system are analyzed in detail, and the simulation results show that the system has different attractors with different topological structures at different simulation times. Within a fixed simulation time, the system has 15 attractors with different topological structures under different parameter values, and there is a phenomenon of multiple stability in the system, indicating high complexity. Based on the above discoveries, a color image encryption algorithm including scrambling and diffusion is designed. Experimental results show that this algorithm can perfectly hide the information of the plaintext image, and the decrypted image is consistent with the plaintext image. Finally, the security of the algorithm is analyzed by using key space and so on. The analysis results indicate that the encryption algorithm designed in this paper can effectively resist external attacks and has high security.

Extreme Homogeneous and Heterogeneous Multistability in a Novel 5D Memristor-Based Chaotic System with Hidden Attractors

This paper proposes a novel five-dimensional (5D) memristor-based chaotic system by introducing a flux-controlled memristor into a 3D chaotic system with two stable equilibrium points, and increases the dimensionality utilizing the state feedback control method. The newly proposed memristor-based chaotic system has line equilibrium points, so the corresponding attractor belongs to a hidden attractor. By using typical nonlinear analysis tools, the complicated dynamical behaviors of the new system are explored, which reveals many interesting phenomena, including extreme homogeneous and heterogeneous multistabilities, hidden transient state and state transition behavior, and offset-boosting control. Meanwhile, the unstable periodic orbits embedded in the hidden chaotic attractor were calculated by the variational method, and the corresponding pruning rules were summarized. Furthermore, the analog and DSP circuit implementation illustrates the flexibility of the proposed memristic system. Finally, the active synchronization of the memristor-based chaotic system was investigated, demonstrating the important engineering application values of the new system.

Memristör Tabanlı Kaotik Sistemler ve DNA Kodlama Kullanılarak Görüntü Şifreleme Uygulaması

The rapid advancement of internet technologies has accentuated the need for robust data security mechanisms, particularly in the realm of image transmission. Addressing this, our study introduces a cutting-edge encryption system that blends arithmetic operations with DNA-inspired biological processes and the complexity of chaotic systems, presenting a significant evolution in encryption methodologies. The system employs a synergetic fusion of DNA-based encryption and XOR operations, bolstered by a memristor-based chaotic system, to heighten the security barriers of image encryption. This innovative approach not only provides a secure means to transmit images over the internet but also lays new groundwork in the field of cryptographic research. Rigorous security analyses, including correlation, histogram, and differential attack assessments, are performed, with the findings validating the robustness and efficacy of the encryption process. The outcomes of this research extend the discourse on data security, offering a fortified method that could revolutionize the protection of information in an increasingly digitalized world.

A 3D memristor-based chaotic system with transition behaviors of coexisting attractors between equilibrium points

A 3D symmetric memristor-based chaotic system (SMCS) is constructed by introducing a smooth quadratic flux control memristor model into the jerk chaotic system (JCS). The dynamics of SMCS are investigated by means of Lyapunov exponents, bifurcation diagrams, multistability, transient behavior, and spectral entropy complexity. It is found that SMCS is sensitive to parameter b included in the normalized equation. Transition behaviors of coexisting attractors between the equilibrium points will be observed when parameter b changes in a specific interval. Its complexity is demonstrated by the types of three multi-stable behaviors and four types of transient behaviors and distinctly enhanced by the spectral entropy complexity as two parameters variations. Additionally, the physical realizability of SMCS is verified by the implementation of the analog circuit and digital hardware. Finally, the pseudo-random sequence based on JCS and SCMS is compared by NIST testing.

A physical memristor-based chaotic system and its application in colour image encryption scheme

This work proposes a physical memristor (TaOx) based new 4D chaotic system with 3D multi-scroll, no equilibrium point, spiking behaviour, coexistence bursting oscillation and multistability. Using this physical memristor-based chaotic system, a novel and efficient colour image encryption algorithm has been developed using a unique box scrambling method and bit-wise XOR operations. Many interesting and new dynamics of a material-based memristive chaotic system are reported here, like 3D multi-scroll chaotic attractors, bursting characteristics, multistability, a neuronal system like spiking behaviours etc using Lyapunov spectrum and bifurcation plots. It is observed that the number of scrolls is changed with the total simulation time. This novel memristive chaotic system has limit cycles with controllable spikes and bursting oscillation. In addition, the system shows chaotic bursting oscillation under a different set of parameters and initial conditions. The coexistence of the bursting phenomena is studied here. The bursting and spiking characteristic is important for material-based memristors in neuromorphic applications. 3D Chaotic multi-scroll and multistability properties make the image encryption method more efficient and secure. Such characteristics are rare in physical memristor-based chaotic systems and using this, the image encryption algorithm is also rare in recent findings. Therefore, a new secure image encryption algorithm for colour images is proposed here, based on the unique box scrambling method, bitwise XOR operation and pseudo-random number generation using the proposed memristive chaotic system. Various tests like NPCR, UACI, histogram analysis, correlation study, information entropy analysis, robustness against external noise, etc have been performed to check the algorithm’s robustness and efficiency and test the capability to resist statistical and differential attacks.

A novel memristor-based chaotic system with infinite coexisting attractors and controllable amplitude

A novel memristor-based chaotic system with infinite coexisting attractors and controllable amplitude

A memristor-based VB2 chaotic system: Dynamical analysis, circuit implementation, and image encryption

A new asymmetric memristor-based chaotic system with only one equilibrium point is obtained by introducing a smooth quadratic flux control memristor module into the VB2 chaotic system. The analysis of the Lyapunov exponent spectra and bifurcation diagrams reveals that this memristor-based system is sensitive to all 5 parameters and has 14 types of attractors with fantastic shapes. The high complexity of the system is reflected in two types of multi-stable behaviors and two types of transient behaviors, especially the attractor merging behavior caused by change of the initial values. As a three-dimensional model, this system nevertheless has an excellent SE value. A circuit was designed to verify the physical feasibility of this system. Finally, this memristor-based system is applied to image encryption whose security is analyzed from both histogram and correlation perspectives. These findings provide a reliable reference for the application of memristor-based systems in the field of encryption.

Tri-valued memristor-based hyper-chaotic system with hidden and coexistent attractors

Recently, the nonlinear dynamics of memristor has attracted much attention. In this paper, a novel four-dimensional hyper-chaotic system (4D-HCS) based on a tri-valued memristor is found. Theoretical analysis shows that the 4D-HCS has complex hyper-chaotic dynamics such as hidden attractors and coexistent attractors. We also experimentally analyze the dynamics behaviors of the 4D-HCS in aspects of the phase diagram, bifurcation diagram, Lyapunov exponential spectrum, power spectrum and the correlation coefficient. To rigorously verify the chaotic behavior, we analyze the topological horseshoe of the system and calculate the topological entropy. In addition, the comparison with binary-valued memristor-based chaotic system shows that a chaotic system with a tri-valued memristor can generate hyper-chaos and coexistent attractors, while the one with a binary-valued memristor cannot. This finding suggests that applying three- or multi-value memristors in chaotic circuits can produce more complex dynamic properties than binary-valued memristors. To show the easy implementation of the 4D-HCS, we implement the 4D-HCS in an analogue circuit-based hardware platform, and the implementation results are consistent with the theoretical analysis. Finally, using the 4D-HCS, we design a pseudorandom number generator to explore its potential application in cryptography.

Hidden dynamics, synchronization, and circuit implementation of a fractional-order memristor-based chaotic system

Hidden dynamics, synchronization, and circuit implementation of a fractional-order memristor-based chaotic system

Adaptive Sliding-Mode Synchronization of the Memristor-Based Sixth-Order Uncertain Chaotic System and Its Application in Image Encryption

This article presents a memristor-based sixth-order chaotic circuit which is designed based on Chua¡ ¯ s circuit using flux-controlled memristors and charge-controlled memristors. The chaotic characteristics are analyzed, and the chaotic phase diagrams are drawn. The specific upper bound information of the model uncertainty and external disturbance is unknown. We design an adaptive terminal sliding-mode control law for such chaotic systems, which not only compensates the influence of the uncertainty and disturbance but also ensures that the synchronization error system is fixed-time stable when the sliding motion takes place. Also, the accessibility of the sliding surface is guaranteed. Thus, the sufficient conditions for the synchronization of the considered systems are derived. Simulation examples show the significance and superiority of the control scheme. The synchronization strategy is applied to image encryption, and the results show that the encryption effect is excellent and has strong anti-disturbance ability.

Analysis of a chaotic system using fractal-fractional derivatives with exponential decay type kernels

<abstract><p>In this article, we introduce and analyze a novel fractal-fractional chaotic system. We extended the memristor-based chaotic system to the fractal-fractional mathematical model using Atangana-Baleanu–Caputo and Caputo-Fabrizio types of derivatives with exponential decay type kernels. We established the uniqueness and existence of the solution through Banach's fixed theory and Schauder's fixed point. We used some new numerical methods to derive the solution of the considered model and study the dynamical behavior using these operators. The numerical simulation results presented in both cases include the two and three-dimensional phase portraits and the time-domain responses of the state variables to evaluate the efficacy of both kernels.</p></abstract>

Memristor-based chaotic system with abundant dynamical behaviors and its application

Memristor-based chaotic system with abundant dynamical behaviors and its application

A novel memristor-based chaotic system with line equilibria and its complex dynamics

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 [Formula: see text] 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.

Hidden Attractor and Multistability in a Novel Memristor-Based System Without Symmetry

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.

Design and multistability analysis of five-value memristor-based chaotic system with hidden attractors* *Project supported by the National Natural Science Foundation of China (Grant No. 61203004), the Natural Science Foundation of Heilongjiang Province, China (Grant No. F201220), and the Heilongjiang Provincial Natural Science Foundation of Joint Guidance Project (Grant No. LH2020F022).

A five-value memristor model is proposed, it is proved that the model has a typical hysteresis loop by analyzing the relationship between voltage and current. Then, based on the classical Liu–Chen system, a new memristor-based four-dimensional (4D) chaotic system is designed by using the five-value memristor. The trajectory phase diagram, Poincare mapping, bifurcation diagram, and Lyapunov exponent spectrum are drawn by numerical simulation. It is found that, in addition to the general chaos characteristics, the system has some special phenomena, such as hidden homogenous multistabilities, hidden heterogeneous multistabilities, and hidden super-multistabilities. Finally, according to the dimensionless equation of the system, the circuit model of the system is built and simulated. The results are consistent with the numerical simulation results, which proves the physical realizability of the five-value memristor-based chaotic system proposed in this paper.

Chaotic Attractors Generated by a Memristor-Based Chaotic System and Julia Fractal

Abstract A chaotic system has many applications in random number generator, image encryption, and secure communication. It is essential to present abundant chaotic attractors in a single chaotic system. Thus a novel 3D chaotic system based on memristor is designed and analyzed. The system's key advantages are as follows: firstly, both the multi-scroll and extended chaotic attractors are produced by merely modifying system parameters. The complex dynamical phenomena, such as coexisting multiple multi-scroll chaotic attractors, transient phenomenon and state transformation, can be observed; secondly, the proposed system combines with the classical Julia fractal and Julia deformation forms, respectively, and fascinating and various circular chaotic attractors are generated, which take good advantage of the combination of a memristor-based chaotic system and Julia fractal. Meanwhile, by applying both dynamic analysis and numerical simulation, basic behaviors of the system, such as stability of equilibrium point, dissipation and symmetry, Poincare maps, instantaneous phase, 0-1 test and power spectrum are employed to illustrate the superiority of the system. Some rather impressive and promising applications of the proposed chaotic system to chaotic confidential communication and image encryption will be achieved later.

Synchronization, circuit and secure communication implementation of a memristor-based hyperchaotic system using single input controller

In this paper, we investigate a circuit implementation of memristor-based chaotic synchronization with a single input controller. Firstly, based on the cubic function model of memristor, a circuit with the grounded flux-control memristor-based hyperchaotic system is designed and implemented. Secondly, a single input controller is proposed to synchronize the two memristor-based hyperchaotic systems, and a sufficient condition of the synchronized system is obtained by the Routh-Hurwitz criterion and minimum phase theory. Then, a circuit of the proposed controller for memristor-based chaotic synchronization system is designed and implemented. Finally, secure communication based on memristor-based chaotic synchronization system is given to show the feasibility of the signal encryption scheme.

A novel non-equilibrium memristor-based system with multi-wing attractors and multiple transient transitions.

Based on the pure mathematical model of the memristor, this paper proposes a novel memristor-based chaotic system without equilibrium points. By selecting different parameters and initial conditions, the system shows extremely diverse forms of winglike attractors, such as period-1 to period-12 wings, chaotic single-wing, and chaotic double-wing attractors. It was found that the attractor basins with three different sets of parameters are interwoven in a complex manner within the relatively large (but not the entire) initial phase plane. This means that small perturbations in the initial conditions in the mixing region will lead to the production of hidden extreme multistability. At the same time, these sieve-shaped basins are confirmed by the uncertainty exponent. Additionally, in the case of fixed parameters, when different initial values are chosen, the system exhibits a variety of coexisting transient transition behaviors. These 14 were also where the same state transition from period 18 to period 18 was first discovered. The above dynamical behavior is analyzed in detail through time-domain waveforms, phase diagrams, attraction basin, bifurcation diagrams, and Lyapunov exponent spectrum . Finally, the circuit implementation based on the digital signal processor verifies the numerical simulation and theoretical analysis.

Modeling and Analysis of a Three-Terminal-Memristor-Based Conservative Chaotic System.

In this paper, a three-terminal memristor is constructed and studied through changing dual-port output instead of one-port. A new conservative memristor-based chaotic system is built by embedding this three-terminal memristor into a newly proposed four-dimensional (4D) Euler equation. The generalized Hamiltonian energy function has been given, and it is composed of conservative and non-conservative parts of the Hamiltonian. The Hamiltonian of the Euler equation remains constant, while the three-terminal memristor’s Hamiltonian is mutative, causing non-conservation in energy. Through proof, only centers or saddles equilibria exist, which meets the definition of the conservative system. A non-Hamiltonian conservative chaotic system is proposed. The Hamiltonian of the conservative part determines whether the system can produce chaos or not. The non-conservative part affects the dynamic of the system based on the conservative part. The chaotic and quasiperiodic orbits are generated when the system has different Hamiltonian levels. Lyapunov exponent (LE), Poincaré map, bifurcation and Hamiltonian diagrams are used to analyze the dynamical behavior of the non-Hamiltonian conservative chaotic system. The frequency and initial values of the system have an extensive variable range. Through the mechanism adjustment, instead of trial-and-error, the maximum LE of the system can even reach an incredible value of 963. An analog circuit is implemented to verify the existence of the non-Hamiltonian conservative chaotic system, which overcomes the challenge that a little bias will lead to the disappearance of conservative chaos.

Parameter Identification of Memristor-Based Chaotic Systems via the Drive-Response Synchronization Method

Memristor-based chaotic systems have been received great attention from researchers in the last decade. This brief investigates parameter identification of a memristor-based chaotic system (proposed by Muthuswamy in 2010). Uncertain parameter identification has not been studied yet for memristor-based chaotic systems. Using the Lyapunov stability theory and Barbălat lemma, two theorems are established to identify uncertain parameters of the system under the following two cases: i) the memductance is unknown; ii) capacitances and inductances are unknown. Finally, numerical simulations are carried out and the results show that the proposed parameter identification methods are effective.