Complex Dynamics in a Memristive Diode Bridge-Based MLC Circuit: Coexisting Attractors and Double-Transient Chaos
20 Mar 2021-International Journal of Bifurcation and Chaos (World Scientific Publishing Company)-Vol. 31, Iss: 03, pp 2150049
TL;DR: In this article, a memristive diode bridge-based Murali-Lakshmanan-Chua (MLC) circuit was investigated and some striking and new complex phenomena were uncovered.
Abstract: This paper uncovers some striking and new complex phenomena in a memristive diode bridge-based Murali–Lakshmanan–Chua (MLC) circuit. These striking dynamical behaviors include the coexistence of mu...
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6 citations
TL;DR: In this article , the coexistence of chaos and hyperchaos and their control based on a non-invasive temporal feedback method for attractor selection in a multistable non-autonomous memristive Murali-Lakshamanan-Chua (MLC) system is reported.
Abstract: This paper reports both the coexistence of chaos and hyperchaos and their control based on a noninvasive temporal feedback method for attractor selection in a multistable non-autonomous memristive Murali-Lakshamanan-Chua (MLC) system. Numerical simulation methods such as bifurcation diagrams, the spectrum of Lyapunov exponents, phase portraits, and cross-section basins of initial states are used to examine several striking dynamical features of the system, including torus, chaos, hyperchaos, and multistability. Of most interest, the rare phenomenon of the coexistence of hyperchaos and chaos has been uncovered based on bifurcation techniques and nonbifurcation scheme like offset boosting. Further analyses based on intermittent feedback-based control in the time domain help to drive the system from the multistable state to a monostable one where only the hyperchaotic attractor survives. Since the attractor’s internal dynamics are retained, this control method is non-invasive. At the end of our analyses, the results of both PSpice and that of the microcontroller-based digital calculator of the circuit match perfectly with the numerical investigations.
4 citations
TL;DR: In this article , a sixth-order memristive hyperchaotic system with two flux-controlled and one charge-controlled memristor was designed to enhance the order and Kolmogorov entropy.
Abstract: To enhance the order and Kolmogorov entropy of the memristive hyperchaotic system and improve the realizability of the circuit, a sixth-order memristive hyperchaotic system that consists of two flux-controlled memristors and one charge-controlled memristor is designed. Combined with Lyapunov exponential spectrum, phase trajectory diagram and bifurcation diagram, dynamic characteristics of the system are analyzed, and the effects of system control parameters and initial state on the system dynamic behavior are explored. Equivalent circuit models of flux-controlled and charge-controlled memristors with cubic nonlinear characteristics are constructed by the basic operation modules, and the hardware simulation design of the memristive hyperchaotic system is completed. The experimental results show that the proposed system can exhibit kinds of attractors, such as periodic-loop, single-scroll, double-scroll and superposition by adjusting system control parameters, and the system can show the behavior of period doubling bifurcation entering chaos and anti-period doubling exiting chaos under the different system initial states, which corresponds to the multistable coexistence phenomena of the system, such as quasi-period and hyperchaos. Meanwhile, the sixth-order hyperchaotic system is implemented by hardware circuit simulation. The phase diagrams of the circuit simulation are consistent with that of the numerical simulation, which verifies the physical realizability of the hyperchaotic system. Based on the strong initial value sensitivity and large K entropy, the memristive hyperchaotic system can be applied to the image encryption, and the confidentiality and security of images can be effectively enhanced.
3 citations
TL;DR: In this paper , a simple memristor emulator consisting of a diode bridge and a capacitor was investigated, and a higher-frequency Colpitts circuit was established based on the proposed memristors.
Abstract: This paper investigates a simple memristor emulator consisting of a diode bridge and a capacitor. It exhibits pinched hysteresis loops, and what is more striking is the higher frequency, as it operates up to greater than 5 MHz. Based on the proposed memristor, a higher-frequency Colpitts circuit was established. According to the mathematical model of the system, the system only possesses one unstable equilibrium point. Period doubling bifurcation, reverse periodic doubling bifurcation, different types of periodic and chaotic orbits, transient chaos, coexisting bifurcations and offset boosting are depicted. More interestingly, it has coexisting multiple attractors with different topologies, such as a chaotic attractor accompanied with periodic orbits, period-1 orbits with bicuspid structure and periodic-2 orbits with tridentate structure. Moreover, a hardware circuit using discrete components was fabricated and experimental measurements were consistent with the MATLAB numerical results, further confirming the real feasibility of the proposed circuit.
2 citations
TL;DR: In this paper , a chaotic system with non-hyperbolic equilibrium was introduced and its sensitivity to different numerical integration techniques prior to implementing it on an FPGA was studied, showing that the discretization method used in numerically integrating the set of differential equations in MATLAB and Mathematica does not yield chaotic behavior except when a low accuracy Euler method is used.
Abstract: We introduce a new chaotic system with nonhyperbolic equilibrium and study its sensitivity to different numerical integration techniques prior to implementing it on an FPGA. We show that the discretization method used in numerically integrating the set of differential equations in MATLAB and Mathematica does not yield chaotic behavior except when a low accuracy Euler method is used. More accurate higher-order numerical algorithms (such as midpoint and fourth-order Runge–Kutta) result in divergence in both MATLAB and Mathematica (but not Python), which agrees with the divergence observed in an analog circuit implementation of the system. However, a fixed-point digital FPGA implementation confirms the chaotic behavior of the system using Euler and fourth-order Runge–Kutta realizations. Therefore, the increased sensitivity of chaotic systems with nonhyperbolic equilibrium should be carefully considered for reproducibility.
2 citations
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TL;DR: In this article, the authors present the first algorithms that allow the estimation of non-negative Lyapunov exponents from an experimental time series, which provide a qualitative and quantitative characterization of dynamical behavior.
8,128 citations
TL;DR: The performance requirements for computing with memristive devices are examined and how the outstanding challenges could be met are examined.
Abstract: Memristive devices are electrical resistance switches that can retain a state of internal resistance based on the history of applied voltage and current. These devices can store and process information, and offer several key performance characteristics that exceed conventional integrated circuit technology. An important class of memristive devices are two-terminal resistance switches based on ionic motion, which are built from a simple conductor/insulator/conductor thin-film stack. These devices were originally conceived in the late 1960s and recent progress has led to fast, low-energy, high-endurance devices that can be scaled down to less than 10 nm and stacked in three dimensions. However, the underlying device mechanisms remain unclear, which is a significant barrier to their widespread application. Here, we review recent progress in the development and understanding of memristive devices. We also examine the performance requirements for computing with memristive devices and detail how the outstanding challenges could be met.
3,037 citations
01 Feb 1976
TL;DR: In this article, a broad generalization of memristors to an interesting class of nonlinear dynamical systems called memristive systems is introduced, which are unconventional in the sense that while they behave like resistive devices, they can be endowed with a rather exotic variety of dynamic characteristics.
Abstract: A broad generalization of memristors--a recently postulated circuit element--to an interesting class of nonlinear dynamical systems called memristive systems is introduced. These systems are unconventional in the sense that while they behave like resistive devices, they can be endowed with a rather exotic variety of dynamic characteristics. While possessing memory and exhibiting small-signal inductive or capacitive effects, they are incapable of energy discharge and they introduce no phase shift between the input and output waveforms. This zero-crossing property gives rise to a Lissajous figure which always passes through the origin. Memristive systems are hysteretic in the sense that their Lissajous figures vary with the excitation frequency. At very low frequencies, memristive systems are indistinguishable from nonlinear resistors while at extremely high frequencies, they reduce to linear resistors. These anomalous properties have misled and prevented the identification of many memristive devices and systems-including the thermistor, the Hodgkin-Huxley membrane circuit model, and the discharge tubes. Generic properties of memristive systems are derived and a canonic dynamical system model is presented along with an explicit algorithm for identifying the model parameters and functions.
2,159 citations
TL;DR: By utilizing a memristor to substitute a coupling resistor in the realization circuit of a three-dimensional chaotic system having one saddle and two stable node-foci, a novel memristive hyperchaotic system with coexisting infinitely many hidden attractors is presented in this paper.
Abstract: By utilizing a memristor to substitute a coupling resistor in the realization circuit of a three-dimensional chaotic system having one saddle and two stable node-foci, a novel memristive hyperchaotic system with coexisting infinitely many hidden attractors is presented. The memristive system does not display any equilibrium, but can exhibit hyperchaotic, chaotic, and periodic dynamics as well as transient hyperchaos. In particular, the phenomenon of extreme multistability with hidden oscillation is revealed and the coexistence of infinitely many hidden attractors is observed. The results illustrate that the long term dynamical behavior closely depends on the memristor initial condition thus leading to the emergence of hidden extreme multistability in the memristive hyperchaotic system. Additionally, hardware experiments and PSIM circuit simulations are performed to verify numerical simulations.
305 citations
TL;DR: In this article, the multiple attractors with different initial states are revealed and with the dimensionless system equations, complex dynamics with various initial conditions are further discussed and theoretical derivation results indicate that the normalized memristive Chua's system has two stable nonzero saddle-foci in globally adjusting normalized parameter region and exhibits the unusual and striking dynamical behavior of multiple attractor with multistability.
Abstract: Multiple attractors can be found in many nonlinear dynamical system with multistability. Recently, experimental attractors with two stable saddle-foci were reported to find in a non-ideal active voltage-controlled memristor based Chua's circuit. In this paper we focus on the multiple attractors found in the proposed memristive Chua's circuit. Concretely, by numerical simulations of mathematical model, hardware circuit experiments and PSIM circuit simulations, multiple attractors with different initial states are revealed and with the dimensionless system equations, complex dynamics with different initial conditions are further discussed. Theoretical derivation results indicate that the normalized memristive Chua's system has two stable nonzero saddle-foci in globally adjusting normalized parameter region and exhibits the unusual and striking dynamical behavior of multiple attractors with multistability.
218 citations