Dynamics analysis of Wien-bridge hyperchaotic memristive circuit system

In this paper, a hyperchaotic memristive circuit based on Wien-bridge chaotic circuit was designed. The mathematical model of the new circuit is established by using the method of normalized parameter. The equilibrium point and the stability point of the system are calculated. Meanwhile, the stable interval of corresponding parameter is determined. Using the conventional dynamic analysis method, the dynamical characteristics of the system are analyzed. During the analysis, some special phenomenon such as coexisting attractor is observed. Finally, the circuit simulation of system is designed and the practical circuit is realized. The results of theoretical analysis and numerical simulation show that the Wien-bridge hyperchaotic memristive circuit has very rich and complicated dynamical characteristics. It provides a theoretical guidance and a data support for the practical application of memristive chaotic system.     

Antimonotonicity,chaos and multiple attractors in a novel autonomous memristor-based jerk circuit

A novel memristor-based oscillator derived from the autonomous jerk circuit (Sprott in IEEE Trans Circuits Syst II Express Briefs 58:240–243, 2011) is proposed. A first-order memristive diode bridge replaces the semiconductor diode of the original circuit. The complex behavior of the oscillator is investigated in terms of equilibria and stability, phase space trajectories plots, bifurcation diagrams, graphs of Lyapunov exponents, as well as frequency spectra. Antimonotonicity (i.e. concurrent creation and destruction of periodic orbits), chaos, periodic windows and crises are reported. More interestingly, one of the main features of the novel memristive jerk circuit is the presence of a region in the parameters’ space in which the model develops hysteretic behavior. This later phenomenon is marked by the coexistence of four different (periodic and chaotic) attractors for the same values of system parameters, depending solely on the choice of initial conditions. Basins of attractions of various competing attractors display complex basin boundaries thus suggesting possible jumps between coexisting solutions in experiment. Compared to previously published jerk circuits with similar behavior, the novel system distinguishes by the presence of a single equilibrium point and a relatively simpler structure (only off-the-shelf electronic components are involved). Results of theoretical analyses are perfectly traced by laboratory experimental measurements.     

Chaotic behavior in fractional-order memristor-based simplest chaotic circuit using fourth degree polynomial

In this paper, a memristor with a fourth degree polynomial memristance function is used in the simplest chaotic circuit which has only three circuit elements: a linear passive inductor, a linear passive capacitor, and a nonlinear active memristor. We use second order exponent internal state memristor function and fourth degree polynomial memristance function to increase complexity of the chaos. So, the system can generate double-scroll attractor and four-scroll attractor. Systematic studies of chaotic behavior in the integer-order and fractional-order systems are performed using phase portraits, bifurcation diagrams, Lyapunov exponents, and stability analysis. Simulation results show that both integer-order and fractional-order systems exhibit chaotic behavior over a range of control parameters.     

Dynamics of a cantilever arm actuated by a nonlinear electrical circuit

The idea in this paper is to present some analytical and numerical results on the investigation of the dynamics of a nonlinear electromechanical system including a cantilever robot arm manipulator, harmonically actuated through an electric circuit. We use the method of harmonic balance to derive oscillatory solutions. Forced vibrations are analyzed showing that numerical results are in agreement with those obtained analytically for the stationary response. The system presents various types of nonlinear behaviors including chaos.     

Double-compound synchronization of six memristor-based Lorenz systems

In this paper, a new type of double-compound synchronization, which is based on combination–combination synchronization and compound synchronization of four chaotic systems, is investigated for six memristor-based Lorenz systems. Using Lyapunov stability theory and adaptive control, some sufficient conditions are attained to ensure our conclusions hold. The corresponding theoretical proofs and numerical simulations are supplied to verify the effectiveness and feasibility of our synchronization design. Due to the complexity of our synchronization, it will be more secure to transmit and receive signals in application of communication.     

Implementation and study of the nonlinear dynamics of a memristor-based Duffing oscillator

An electronic model of Duffing oscillator with a characteristic memristive nonlinear element is proposed instead of the classical cubic nonlinearity. The memristive Duffing oscillator circuit system is mathematically modeled, and the stability analysis presents the evolution of the proposed system. The dynamical behavior of this circuit is investigated through numerical simulations, statistical analysis, and real-time hardware experiments, which have been carried out under the external periodic force. The chaotic dynamics of the circuit is studied by means of phase diagram. It is found that the proposed circuit system shows complex behaviors, like bifurcations and chaos, three tori, transient chaos, and intermittency for a certain range of circuit parameters. The observed phenomena and scenario are illustrated in detail through experimental and numerical studies of memristive Duffing oscillator circuit. The existence of regular and chaotic behaviors is also verified by using 0–1 test measurements. In addition, the robustness of the signal strength is confirmed through signal-to-noise ratio. The numerically observed results are confirmed from the laboratory experiment.     

Dynamics,circuit realization,control and synchronization of a hyperchaotic hyperjerk system with coexisting attractors

Although different hyperjerk systems have been discovered, a few hyperjerk systems can exhibit hyperchaotic behavior. In this work, we introduce a new hyperjerk system with hyperchaotic attractors. By investigating dynamics of the system, we have observed the different coexisting attractors such as coexistence of period-2 attractors, or coexistence of period-2 attractor and quasiperiodic attractor. It is worth noting that this striking phenomenon is rarely reported in a hyperjerk system. The proposed system has been realized with electronic components. The agreement between the simulation and experimental results indicates the feasibility of the hyperjerk system. Moreover, chaos control and synchronization of such hyperjerk system have been also reported.     

Finite-time projective synchronization of memristor-based delay fractional-order neural networks

Nonlinear Dynamics - This paper mainly investigates the finite-time projective synchronization problem of memristor-based delay fractional-order neural networks (MDFNNs). By using the definition of...     

Hard and soft excitation of oscillations in memristor-based oscillators with a line of equilibria

Nonlinear Dynamics - A model of memristor-based Chua’s oscillator is studied. The considered system has infinitely many equilibrium points, which build a line of equilibria. Bifurcational...     

Nonlinear dynamics and chaos in a simplified memristor-based fractional-order neural network with discontinuous memductance function

Nonlinear Dynamics - In this paper, a simplified memristor-based fractional-order neural network (MFNN) with discontinuous memductance function is proposed. It is essentially a switched system with...     

Global exponential stability of stochastic memristor-based complex-valued neural networks with time delays

In recent years, the dynamic behaviors of complex-valued neural networks have been extensively investigated in a variety of areas. This paper focuses on the stability of stochastic memristor-based complex-valued neural networks with time delays. By using the Lyapunov stability theory, Halanay inequality and Itô formula, new sufficient conditions are obtained for ensuring the global exponential stability of the considered system. Moreover, the obtained results not only generalize the previously published corresponding results as special cases for our results, but also can be checked with the parameters of system itself. Finally, simulation results in three numerical examples are discussed to illustrate the theoretical results.     

Finite-time stability analysis of fractional-order complex-valued memristor-based neural networks with time delays

In this paper, the problem of finite-time stability of fractional-order complex-valued memristor-based neural networks (NNs) with time delays is extensively investigated. We first initiate the fractional-order complex-valued memristor-based NNs with the Caputo fractional derivatives. Using the theory of fractional-order differential equations with discontinuous right-hand sides, Laplace transforms, Mittag-Leffler functions and generalized Gronwall inequality, some new sufficient conditions are derived to guarantee the finite-time stability of the considered fractional-order complex-valued memristor-based NNs. In addition, some sufficient conditions are also obtained for the asymptotical stability of fractional-order complex-valued memristor-based NNs. Finally, a numerical example is presented to demonstrate the effectiveness of our theoretical results.     

Global stabilization of fractional-order memristor-based neural networks with incommensurate orders and multiple time-varying delays: a positive-system-based approach

Nonlinear Dynamics - This paper addresses global stabilization of fractional-order memristor-based neural networks (FMNNs) with incommensurate orders and multiple time-varying delays (MTDs), where...     

Self-sustained oscillation in a memristor circuit

Nonlinear Dynamics - In this paper, we consider dynamical behavior of a comparatively simple self-oscillating circuit only with an inductor, a capacitor and a memristor, but this circuit can...     

Dynamics of a gravity stonewall

Treated is the dynamics of a gravity stonewall. The wall is excited by a transient damped periodic oscillation simulating an earthquake. The model adopts a stick-slip friction constitutive law. Sensitivity of energy dissipation to parameters such as number of blocks, friction coefficient, sticktion and slipping stiffness and excitation amplitude and frequency is determined. A 2-D model of the monolithic wall is also analyzed to compare displacement and shear stress of the two constructions.     

Electronic circuit equivalent of a mechanical impacting system

Nonlinear Dynamics - Mechanical impacting systems exhibit a large array of interesting dynamical behaviors including a large amplitude chaotic oscillation close to the grazing condition. This...     

Multistability analysis,circuit implementations and application in image encryption of a novel memristive chaotic circuit

A novel memristive chaotic circuit is proposed by replacing the Chua’s diode in modified Chua’s circuit with a smooth active memristor, and the corresponding memristive model is analyzed and validated. The equilibrium point set, dissipativity and stability of this new chaotic circuit are developed theoretically. The dynamic characteristics for the new system are presented by means of phase diagrams, Lyapunov exponents, bifurcation diagrams and Poincaré maps. The coexistence of the memristive system is carried out from the perspective of asymmetric coexistence and symmetry coexistence. In addition, the coexistence of multiple states is studied by a more direct method with initial value as the system variable to gain a more intuitive observation. The circuit model of the memristive chaotic system is designed through Multisim simulation software. Finally, the memristive chaotic sequence is used to encrypt the image, and the influence of multistability on the encryption is investigated by the histogram, correlation and key sensitivity. The results show that the proposed new memristive chaotic system has high security.