A new fractional-order hyperchaotic memristor oscillator: Dynamic analysis, robust adaptive synchronization, and its application to voice encryption

ABSTRACTThis paper investigates a three-dimensional autonomous chaotic flow without linear terms. Dynamical behaviour of the proposed system is investigated through eigenvalue structures, phase portraits, bifurcation diagram, Lyapunov exponents and basin of attraction. For a suitable choice of the parameters, the proposed system can exhibit anti-monotonicity, periodic oscillations and double-scroll chaotic attractor. Basin of attraction of the proposed system shows that the chaotic attractor is self-excited. Furthermore, feasibility of double-scroll chaotic attractor in the real word is investigated by using the OrCAD-PSpice software via an electronic implementation of the proposed system. A good qualitative agreement is illustrated between the numerical simulations and the OrCAD-PSpice results. Finally, a finite-time control method based on dynamic sliding surface for the synchronisation of master and slave chaotic systems in the presence of external disturbances is performed. Using the suggested control technique, the superior master–slave synchronisation is attained. Illustrative simulation results on the studied chaotic system are presented to indicate the effectiveness of the suggested scheme.

In this paper, we consider and investigate the dynamics of a fractional-order thin magnetostrictive actuato with quintic nonlinearity. The energy balance method is used to establish the motion equation of the system. Numerical solutions of the system are studied using the Caputo method and Adams Bashforth Moulton scheme. In order to analyze the dynamical behaviors of the proposed system, some mathematical tools including bifurcation diagrams, Lyapunov exponents, two-parameter bifurcation diagrams, time series plots and phase portraits are exploited. The bifurcation diagrams show that the system under consideration exhibits rich and intriguing behaviors including period-doubling route to chaos, complex phase space trajectory and extreme multistability. One of the most novelty of the proposed system is that its exhibits extreme multistability, which was not yet reported in the existing thin magnetostrictive actuators discussed in the literature to the author’s knowledge. The results carried out in this work may help us in better understanding of the thin magnetostrictive actuators.

In this research a new chaotic map which is a modification from composition of MS map and Improved logistics map is proposed. New map’s chaotic behavior is proven by the bifurcation diagram and Lyapunov exponent. This map will be used in chaos-based cryptography as a keystream generator and then it will be processed in the encryption and decryption algorithms through XOR operations. The results of the encryption and decryption processes were evaluated by several tests such as key sensitivity analysis, histogram analysis, correlation analysis, and image quality analysis. All the tests are doing to evaluate the performance new chaotic map in encryption of digital color image. Based on the results of several tests, a conclusion can be drawn that the encryption and decryption process is successful and difficult to attack with various kinds of attacks. The key that built from new chaotic map has a good sensitivity.

We monitored the occupancy of a functionally important non-coordinated water molecule in the distal heme pocket of sperm whale myoglobin over the pH range 4.3-9.4. Water occupancy was assessed by using time-resolved spectroscopy to detect the perturbation of the heme visible band absorption spectrum caused by water entry after CO photodissociation ( Goldbeck, R. A., Bhaskaran, S., Ortega, C., Mendoza, J. L., Olson, J. S., Soman, J., Kliger, D. S., and Esquerra, R. M. (2006) Proc. Natl. Acad. Sci. U. S. A. 103, 1254-1259 ). We found that the water occupancy observed during the time interval between ligand photolysis and diffusive recombination decreased by nearly 20% as the pH was lowered below 6. This decrease accounted for most of the concomitant increase in the observed CO bimolecular recombination rate constant, as the lower water occupancy presented a smaller kinetic barrier to CO entry into the pocket at lower pH. These results were consistent with a model in which the distal histidine, which stabilizes the water molecule within the distal pocket by accepting a hydrogen bond, tends to swing out of the pocket upon protonation and destabilize the water occupancy at low pH. Extrapolation of this model to lower pH suggests that the additional increase in ligand association rate constant observed previously in stopped-flow studies at pH 3 may also be due in part to reduced distal water occupancy concomitant with further His64 protonation and coupled protein conformational change.

Relationship between granitic soil particle-size distribution and shrinkage properties based on multifractal method

Two-neuron-based non-autonomous memristive Hopfield neural network: Numerical analyses and hardware experiments

Brake squeal is a manifestation of friction-induced self-excited instability in disc brake systems. This study investigated non-smooth bifurcations and chaotic dynamics in disc brake systems and elucidated a chaotic control system. Decreasing squeal noise which is dependent on chaos, increases passengers comfort; consequently, suppressing chaos is crucial. First, synchronization was used to estimate the largest Lyapunov exponent to identify periodic and chaotic motions. Next, complex nonlinear behaviors were thoroughly observed for a range of parameter values in the bifurcation diagram. Rich dynamics of the disc brake system were studied using a bifurcation diagram, phase portraits, a Poincare map, frequency spectra, and Lyapunov exponents. Finally, the proposed technique was applied to a chaotic disc brake system through the addition of an external input that is a dither signal. Simulation results demonstrated the feasibility of the proposed approach.

This paper addresses the complex nonlinear dynamics involved in controlling chaos in power systems using bifurcation diagrams, time responses, phase portraits, Poincaré maps, and frequency spectra. Our results revealed that nonlinearities in power systems produce period-doubling bifurcations, which can lead to chaotic motion. Analysis based on the Lyapunov exponent and Lyapunov dimension was used to identify the onset of chaotic behavior. We also developed a continuous feedback control method based on synchronization characteristics for suppressing of chaotic oscillations. The results of our simulation support the feasibility of using the proposed method. The robustness of parametric perturbations on a power system with synchronization control was analyzed using bifurcation diagrams and Lyapunov stability theory.

This paper presents a new 4D system constructed based on the well-known Sprott B system and characterized by high complexity. This system can display chaotic, hyperchaotic, periodic, and quasi-periodic behaviors for some parameter values. The findings demonstrate that the novel system can exhibit multistability and different coexisting attractors. Additionally, the study used Lyapunov exponents, bifurcation diagrams, stability of equilibrium points, dissipativity, phase plots, dynamical maps, and Poincare sections to analyze the dynamical characteristics of this system. Since the novel 4D system is very advantageous for chaos-based applications due to its hyperchaotic dynamics and multistability, an efficient voice encryption scheme that uses the proposed hyperchaotic system in secure voice transmission is presented. Experiments and tests are carried out to evaluate the performance and security of the proposed encryption scheme against various attacks. The simulation results demonstrate the robustness of our voice cryptosystem against cryptographic attacks.

A dynamical model is proposed and the corresponding characteristic aligns are derived for voltage-mode bi-frequency controlled switching converter operating in discontinuous conduction mode. According to the dynamical model, the border-collision bifurcation and multi-period behaviors, such as period-2, period-3, period-4, and so on, are studied using bifurcation diagrams as the circuit parameters are varied. It is found that the converter behaves along the bifurcation route of period-1, multi-period, and period-1, and the change of period state is induced by border-collision bifurcation. Based on the characteristic equation, the converter stability is investigated by the Lyapunov exponent. It is shown that Lyapunov exponent is always smaller than zero with the variation of circuit parameters and the converter operates in stable period state all the time. Also, it is validated that period-3 behavior of voltage-mode bi-frequency controlled switching converter does not predicate its inevitable chaos. Time-domain waveforms, phase portraits, and frequency spectra of voltage-mode bi-frequency controlled switching converter are analyzed by circuit simulation, which validates the feasibility of dynamical model and the correctness of theoretical analysis. Simulation results are verified by experiments in this paper.

In this paper, a new hyperchaotic memristor oscillator is proposed. Different dynamical properties of the proposed system such as dissipativity, equilibrium points, and their stabilities, Lyapunov exponents and Kaplan-Yorke dimension are investigated. The system has a line of equilibria. Thus it belongs to the category of systems with hidden attractors. Investigation of the stability of the line of equilibria shows that the line is stable in some intervals and unstable in some others. Bifurcation analysis of the system reveals several coexisting attractors in some range of parameters which indicates multistability. Various coexisting attractors of the proposed system are studied.

A new 4-D memristive system is presented in this paper. The peculiarity of the model is that it displays a line of equilibrium points and it has hyperjerk dynamics in a particular range of the parameters space. The behavior of the proposed system is investigated through numerical simulations, by using phase portraits, Lyapunov exponents and bifurcation diagrams. Also, its circuital implementation confirms the memristive systems expected dynamics.

Chapter 16 - Dynamics, Synchronization and Fractional Order Form of a Chaotic System With Infinite Equilibria

The design of systems without equilibrium or with line of equilibrium points is a subject which has started to attract the interest of the research community the last decade. In this direction, various chaotic systems with hidden attractors, which are based on memristors or memristive systems, have been proposed. In this chapter a new 4-D memristive system is presented. The peculiarity of the model is that it displays a line of equilibrium points for a range of the parameters as well as no-equilibrium for another range of the parameters. System in both occasions presents a chaotic behavior with hidden attractors. The behavior of the proposed system is investigated through numerical simulations, by using phase portraits, Lyapunov exponents and bifurcation diagrams. The adaptive control scheme of the system is presented in order to prove that the memristive system’s dynamical behavior can be controlled. Also, we have designed an electronic circuit to confirm the feasibility of the system in both cases.

In this research work a novel 4-D memristive system is presented. The proposed system belongs to the category of dynamical systems with hidden attractors as it displays a line of equilibrium points. Also, it has an hyperchaotic dynamical behavior in a particular range of its parameters space. System’s behavior is investigated through numerical simulations, by using well-known tools of nonlinear theory, such as phase portrait, bifurcation diagram, Lyapunov exponents and Poincare map. Next, the case of chaos control of the system with unknown parameters using adaptive control method is investigated. Finally, an electronic circuit realization of the novel hyperchaotic system using Spice is presented in detail to confirm the feasibility of the theoretical model.