Memristor-based Chaotic Circuit Research Articles

Real time hybrid medical image encryption algorithm combining memristor-based chaos with DNA coding

Image encryption is a commonly used method to secure medical data on a public network, playing a crucial role in the healthcare industry. Because of their complex dynamics, memristors are often used in developing novel chaotic systems that can improve the efficiency of encryption algorithms based on chaos. In this work, we propose a novel locally active memristor-based chaotic circuit model and present a real time hybrid image encryption application developed on a PYNQ-Z1 (Python Productivity for Zynq) low-cost FPGA board using Jupiter programming environment. The proposed hybrid algorithm combines memristor-based chaos with a DNA (deoxyribonucleic acid) encryption algorithm exploiting diffusion-confusion technique. We initially present a new compact and inductorless chaotic circuit, derive the model equations, and then verify its chaotic dynamics numerically through the investigation of the phase portraits, Lyapunov exponents and the bifurcation diagrams. We further implement the chaotic circuit experimentally with discrete elements. The randomness of the chaotic sequence is improved using Trivium and von Neumann post-processor algorithms and assessed through the NIST tests. Finally, the performance of the encryption algorithm is evaluated through various metrics, including histogram and correlation analyses, differential attack, information entropy, as well as data-loss and noise attack, demonstrating its security and suitability for real-time encryption systems.

Slow Invariant Manifolds of Memristor-Based Chaotic Circuits

This work presents an efficient approach for computing the slow invariant manifold of the fourth-order canonical memristor-based Chua circuits using the flow curvature method. First, the magnetic-flux and charge characteristic curve is generated from the classical circuit with a piecewise-linear function. Then, the characteristic curve is generated from the circuit with the piecewise-linear function replaced by a cubic function. Further, the duality principle is applied to studying such memristor-based circuits in the three-dimensional flux-linkage and charge phase space and then in the four-dimensional current–voltage phase space. It is demonstrated that the slow invariant manifolds of these fourth-order memristor-based chaotic circuits can be more directly computed for the first case than the second.

Design and implementation of an efficient memristor-based chaotic circuit

Design and implementation of an efficient memristor-based chaotic circuit

Use of memristor-based chaotic circuits in AM-DCSK and FM-DCSK modulation

In this paper, digital communications systems are built by taking advantage of hyperchaotic circuits implemented with an active flux-controlled memristor. The signals produced by these hyperchaotic circuits with rich chaotic dynamics obtained by replacing the nonlinear element with the memristor in the Chua circuit and the Wien bridge oscillator are used as carriers in digital communications systems. The dynamic behavior of memristor-based hyperchaotic circuits has a high degree of disorder. Therefore, they offer better system performance in many practical applications such as broadband signal generation, encryption and secure communications compared to the already used ordinary chaotic systems. To demonstrate the excellent system performance of memristor-based chaotic circuits, they are applied to two variants of differential chaos shift keying (DCSK) communications schemes. Both the Amplitude Modulated Differential Chaos Shift Keying (AM-DCSK) and Frequency-modulated differential chaos shift keying (FM-DCSK) have been considered. The Bit Error Rate (BER) performances of the proposed AM-DCSK and FM-DCSK systems are evaluated in an Additive White Gaussian Noise (AWGN) channel.

Real-time fuzzy-pid synchronization of memristor-based chaotic circuit using graphical coded algorithm in secure communication applications

The main goal of this study is to implement real-time synchronization of a memristor-based chaotic circuit for secure communication on LabVIEW virtual instrument environments. Memristors can be used in chaotic circuits because of their nonlinear behavior. In this paper, an application for secure communication systems is proposed by using the chaotic property of the memristor. Phase portraits, Lyapunov exponential spectrum, and bifurcation diagrams of the memristor-based chaotic circuit were investigated. A Fuzzy-PID controller was used for master-slave synchronization of memristive chaotic circuit and in secure communication application, three images were also used for encryption and decryption. NI 6251 DAQ card was used to obtain real-time results. Information entropy values, correlation coefficients (CC), peak signal to noise ratio (PSNR), structural similarity index (SSIM), correlation coefficients for the horizontal, vertical and diagonal directions from the three encrypted images, number of pixels change rate (NPCR) and unified average changing intensity (UACI) are calculated to test encryption/decryption performance in the designed system. The results obtained from real-time applications and simulations prove that memristor-based chaotic circuits can be used in secure communication systems where privacy is important.

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.

Symmetry Breaking-Induced Dynamics for a Fourth-Order Memristor-Based Chaotic Circuit

Symmetry Breaking-Induced Dynamics for a Fourth-Order Memristor-Based Chaotic Circuit

On a new four-dimensional model of memristor-based chaotic circuit in the context of nonsingular Atangana\u2013Baleanu\u2013Caputo operators

A memristor is naturally a nonlinear and at the same time memory element that may substitute resistors for next-generation nonlinear computational circuits that can show complex behaviors including chaos. A four-dimensional memristor system with the Atangana–Baleanu fractional nonsingular operator in the sense of Caputo is investigated. The Banach fixed point theorem for contraction principle is used to verify the existence–uniqueness of the fractional representation of the given system. A newly developed numerical scheme for fractional-order systems introduced by Toufik and Atangana is utilized to obtain the phase portraits of the suggested system for different fractional derivative orders and different parameter values of the system. Analysis on the local stability of the fractional model via the Matignon criteria showed that the trivial equilibrium point is unstable. The dynamics of the system are investigated using Lyapunov exponents for the characterization of the nature of the chaos and to verify the dissipativity of the system. It is shown that the supposed system is chaotic and it is significantly sensitive to parameter variation and small initial condition changes.

A novel current-controlled memristor-based chaotic circuit

In this paper, a novel third-order autonomous memristor-based chaotic circuit is proposed. The circuit has simple topology and contains only four elements including one linear negative impedance converter-based resistor, one linear capacitor, one linear inductor, and one nonlinear current-controlled memristor. Firstly, the voltage-current characteristic analysis of the memristor emulator for different driving amplitudes and frequencies are presented. With dimensionless system, the symmetry, equilibrium point and its stability are analysed. It is shown that the system has two unstable saddle-foci and one unstable saddle. A set of typical parameters are chosen for the generation of chaotic attractor. Differing from the common period-doubling bifurcation route in smooth dynamical systems, this memristive system shows abrupt transition from the coexisting period-1 limit cycles to robust chaos when varying system parameters. Various dynamical behaviors are analysed using the numerical simulations and circuit verifications.

On the dynamics of chaotic circuits based on memristive diode-bridge with variable symmetry: A case study

• This work addresses the dynamics of a generalized memristive diode bridge-based jerk circuit whose I − V characteristic symmetry can be varied. The main motivation of this work lies in the following three keys points: • To evaluate the effects of symmetry-breaking imperfections on the dynamics of the class of memristive circuits considered in this work; • To verify the predictions of the theoretical investigations by performing out laboratory experimental studies of the physical circuit; • To enrich the literature by highlighting new behaviors engendered in symmetric systems in general and the model considered in particular, in the presence of symmetry-breaking. It is widely accepted that for any physical system, symmetries are rarely exact. Therefore, some symmetry imperfections must be always assumed to be present. The dynamics of memristor-based chaotic circuits with symmetric hysteresis loop is well documented. However, only a few works are devoted to the dynamics of these types of circuits when the current-voltage characteristic of the considered memristor is no longer symmetrical. Accordingly, we consider in this work (as a case study) the dynamics of a generalized memristive diode-bridge-based jerk circuit whose symmetry can be varied. We denote by k the dissymmetry coefficient. The tools used for the analysis are the Routh-Hurwitz criterion, bifurcation diagrams, phase portraits, and basins of attraction. It is shown that in the symmetric configuration (i.e. when k = 1.0 ) there are three symmetric equilibria whereas in the asymmetric configuration (i.e. when k ≠ 1.0 ) we always have two equilibrium with fixed position in state space and a third one whose location varies according to the value of the dissymmetry coefficient. The intrinsic nonlinearity of the memristor is responsible for the plethora of nonlinear and complex behaviours observed in both configurations. These include the coexistence of symmetric and asymmetric attractors, coexisting symmetric and asymmetric bubbles of bifurcation, and symmetric and asymmetric double-scroll chaotic attractors, just to name a few. In addition, the experimental investigations agree well with the results of theoretical and numerical studies.

The Fractional Order Generalization of HP Memristor Based Chaotic Circuit with Dimensional Consistency

For studying the practical memristor-based chaotic circuit with fractional-order dynamic and asserting the importance of dimensional consistency awareness, the dimensional consistency aware fractio...

Coexisting Multi-Dynamics of a Physical SBT Memristor-Based Chaotic Circuit

This paper presents a new physical [Formula: see text] (SBT) memristor-based chaotic circuit. The equilibrium point and the stability of the chaotic circuit are analyzed theoretically. This circuit system exhibits multiple dynamics such as stable point, periodic cycle and chaos by means of Lyapunov exponents spectra, bifurcation diagrams, Poincaré maps and phase portraits, when the initial state or the circuit parameter changes. Specially, the circuit system exhibits coexisting multi-dynamics. This study provides insightful guidance for the design and analysis of physical memristor-based circuits.

Complex Dynamics of a Novel Chaotic System Based on an Active Memristor

On the basis of the bistable bi-local active memristor (BBAM), an active memristor (AM) and its emulator were designed, and the characteristic fingerprints of the memristor were found under the applied periodic voltage. A memristor-based chaotic circuit was constructed, whose corresponding dynamics system was described by the 4-D autonomous differential equations. Complex dynamics behaviors, including chaos, transient chaos, heterogeneous coexisting attractors, and state-switches of the system were analyzed and explored by using Lyapunov exponents, bifurcation diagrams, phase diagrams, and Poincaré mapping, among others. In particular, a novel exotic chaotic attractor of the system was observed, as well as the singular state-switching between point attractors and chaotic attractors. The results of the theoretical analysis were verified by both circuit experiments and digital signal processing (DSP) technology.

Experimental verification of volt-ampere characteristic curve for a memristor-based chaotic circuit

PurposeThe ammeter can measure the direct current and low-frequency alternating current through the wires, but it is difficult to measure complex waveforms. The oscilloscope can measure complex waveforms, but it is easy to measure the voltage waveform and difficult to measure the current waveform. Thus, how to measure complex current waveforms with oscilloscope is an important and crucial issue that needs to be solved in practical engineering applications. To solve the above problems, an active short circuit line method is proposed to measure the volt-ampere characteristic curve of chaotic circuits.Design/methodology/approachIn this paper, an active short circuit line method is proposed to measure the volt-ampere characteristic curve of various chaotic circuits especially for memristive systems. A memristor-based chaotic system is introduced, and the corresponding memristor-based circuit is constructed and implemented by using electronic components.FindingsThe chaotic attractors and volt-ampere characteristic curve of the memristor-based chaotic circuit are successfully analyzed and verified by oscilloscope measurement with the proposed active short circuit line method. Accordingly, the hardware circuit experiments are carried out to validate the effectiveness and feasibility of the active short circuit line method for these chaotic circuits. A good agreement is shown between the numerical simulations and the experimental results.Originality/valueThe primary contributions of this paper are as follows: an active short circuit line method for measuring the volt-ampere characteristic curve of chaotic circuits is proposed for the first time. A memristor-based chaotic system is also constructed by using memristor as nonlinear term. Then, the active short circuit line method is applied to measure the volt-ampere characteristic curve of the corresponding memristor-based chaotic circuit.

A Scheme for Image Encryption And Decryption of Chaotic System Based on memristors

In this paper, a scheme for image encryption and descryption of chaotic system based on memristors has been proposed. A memristor-based chaotic circuit is simulated and demonstrated it has chaotic characteristics. Then, a memristor-based XOR operation is introduced. At last, image encryption and decryption is presented based on these two structures. Simulation results indicate that chaotic system consisting of memristor-based chaotic circuit and memristor-based XOR operator can achieve image encryption and decryption.

Analysis and electronic implementation of an absolute memristor autonomous Van der Pol-Duffing circuit

In this paper, a memristor-based chaotic circuit is built by replacing the nonlinear resistor of a unified Van der Pol-Duffing circuit by an ideal and active flux-controlled memristor with an absolute value nonlinearity. The equilibrium points of the mathematical model describing the proposed absolute memristor Van der Pol-Duffing circuit are determined and their stabilities are analyzed thank to the Routh-Hurwitz criteria. The numerical simulations reveal that the proposed absolute memristor circuit exhibits reverse period-doubling to chaos, bistable one-scroll chaotic attractors, double-scroll chaotic attractor, bistable periodic attractors and antimonotonicity phenomenon. Moreover the proposed absolute memristor circuit is implemented in PSIM software package. The results found using the PSIM software package have a good qualitative agreement with those found during the numerical simulations.

A Nonvolatile Fractional Order Memristor Model and its Complex Dynamics

It is found that the fractional order memristor model can better simulate the characteristics of memristors and that chaotic circuits based on fractional order memristors also exhibit abundant dynamic behavior. This paper proposes an active fractional order memristor model and analyzes the electrical characteristics of the memristor via Power-Off Plot and Dynamic Road Map. We find that the fractional order memristor has continually stable states and is therefore nonvolatile. We also show that the memristor can be switched from one stable state to another under the excitation of appropriate voltage pulse. The volt–ampere hysteretic curves, frequency characteristics, and active characteristics of integral order and fractional order memristors are compared and analyzed. Based on the fractional order memristor and fractional order capacitor and inductor, we construct a chaotic circuit, of which the dynamic characteristics with respect to memristor’s parameters, fractional order α, and initial values are analyzed. The chaotic circuit has an infinite number of equilibrium points with multi-stability and exhibits coexisting bifurcations and coexisting attractors. Finally, the fractional order memristor-based chaotic circuit is verified by circuit simulations and DSP experiments.

Transient and steady coexisting attractors in a new memristor-based 4-D chaotic circuit

In this study, a new current-controlled memristor is proposed and its characteristics are analyzed. Based on this new memristor, a new four-dimensional chaotic circuit is proposed. The complex dynamics of the proposed chaotic circuit are investigated. From the results of the theoretical analysis and the numerical simulations, it is found that the memristor-based chaotic circuit can generate different types of attractors including single-scroll, double-scroll, and periodic attractors for varying circuit parameters. By taking symmetrical initial conditions, symmetric steady coexisting attractors are obtained under the same set of circuit parameters. For certain initial conditions, striking transient coexisting attractors with different timescales can be obtained. In particular, there are two transient changes occurring successively at different time scales respect to the same initial conditions for the proposed chaotic circuit, which is a novel dynamic property. Finally, a practical circuit platform that describes the proposed chaotic circuit on Field Programmable Gate Arrays (FPGA) is designed, and some experimental results are presented for confirmation.

Dynamic Behaviors and the Equivalent Realization of a Novel Fractional-Order Memristor-Based Chaotic Circuit

This paper proposed a novel fractional-order memristor-based chaotic circuit. A memristive diode bridge cascaded with a fractional-order RL filter constitutes the generalized fractional-order memristor. The mathematical model of the proposed fractional-order chaotic circuit is established by extending the nonlinear capacitor and inductor in the memristive chaotic circuit to the fractional order. Detailed theoretical analysis and numerical simulations are carried out on the dynamic behavior of the proposed circuit by investigating the stability of equilibrium points and the influence of circuit parameters on bifurcations. The results show that the order of the fractional-order circuit has a great influence on the dynamical behavior of the system. The system may exhibit complicated nonlinear dynamic behavior such as bifurcation and chaos with the change of the order. The equivalent circuits of the fractional-order inductor and capacitor are also given in the paper, and the parameters of the equivalent circuits are solved by an undetermined coefficient method. Circuit simulations of the equivalent fractional-order memristive chaotic circuit are carried out in order to validate the correctness of numerical simulations and the practicability of using the integer-order equivalent circuit to substitute the fractional-order element.

Bi-stability in a fifth-order voltage-controlled memristor-based Chua's chaotic circuit

Generally, the occurrence of multiple attractors indicates that the multi-stability existing in a nonlinear dynamical system and the long-time motion behavior are essentially different, depending on which basin of attraction the initial condition belongs to. Up to now, due to the emergence of multi-stability, some particular memristor-based nonlinear circuits whose dynamical behaviors are extremely related to memristor initial conditions or other initial conditions have attracted considerable attention. By replacing linear or nonlinear resistors with memristor emulators in some already-existing oscillating circuits or introducing memristor emulators with different nonlinearities into these oscillating circuits, various memristor-based nonlinear dynamical circuits have been constructed and broadly investigated. Motivated by these considerations, we present a novel fifth-order voltage-controlled memristor-based Chua's chaotic circuit in this paper, from which a wonderful phenomenon of bi-stability is well demonstrated by numerical simulations and PSIM circuit simulations. Note that the bi-stability is a special kind of multi-stability, which is rarely reported in the memristor-based chaotic circuits.<br/>The proposed memristor-based Chua's chaotic circuit is constructed by inserting an inductor into the coupled resistor branch in series and substituting the Chua's diode with a voltage-controlled memristor in the classical Chua's circuit. Five-dimensional system model is established, of which the equilibrium point and its stability are investigated. Theoretical derivation results indicate that the proposed circuit owns one or three equilibrium points related to the circuit parameters. Especially, unlike the newly reported memristive circuit with bi-stability, the proposed memristor-based Chua's chaotic circuit has only one zero equilibrium point under the given parameters, but it can generate coexistent chaotic and periodic behaviors, and the bi-stability occurs in such a memristive Chua's circuit. By theoretical analyses, numerical simulations and PSIM circuit simulations, the bi-stability phenomenon of coexistent chaotic attractors and periodic limit cycles with different initial conditions and their formation mechanism are revealed and expounded. Besides, with the dimensionless system equations, the corresponding initial condition-dependent dynamical behaviors are further numerically explored through bifurcation diagram, Lyapunov exponents, phased portraits and attraction basin. Numerical simulation results demonstrate that the proposed memristive Chua's system can generate bi-stability under different initial conditions. The PSIM circuit simulations and numerical simulations are consistent well with each other, which perfectly verifies the theoretical analyses.