The amplitude, frequency and parameter space boosting in a memristor–meminductor-based circuit

Yuan, Fang; Deng, Yue; Li, Yuxia; Wang, Guangyi

doi:10.1007/s11071-019-04795-z

Cited by 98 publications

(30 citation statements)

References 36 publications

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“…In system (2), when the parameters are set as a � 4, b � 6, c � 20, d � 5, e � 0.01, f � 1, 3g � 0.1, and h � 0.1 and initial conditions are set as (1, 0, 0, w(0)), the system can generate various coexisting attractors depending on w(0). e typical chaotic attractors are shown in 22,22], and [32,35] (the last Lyapunov exponent is not displayed because it is always a big negative number). And system (2) can also generate other kinds of attractors and limit cycle attractors, which means the system has heterogeneous multistability.…”

Section: Dynamic Analysis Of Heterogeneous Multistabilitymentioning

confidence: 99%

“…In recent years, multistability [20][21][22][23][24][25] and extreme multistability [26][27][28][29][30][31][32] have become research hotspots in the field of chaotic systems. Multistability means that when the system parameters remain unchanged, the system can generate more than one attractor with different initial values.…”

Section: Introductionmentioning

confidence: 99%

“…In the same year, a memristor-based chaotic system is constructed by introducing an ideal flux-controlled memristor with absolute value nonlinearity into an existing hypogenetic chaotic jerk system, which can exhibit the extreme multistability phenomenon in reference [31]. A simplest third-order memristive chaotic system with hidden attractors is proposed, which exhibits the extreme multistability phenomenon of coexisting infinitely many attractors in reference [32].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Heterogeneous and Homogenous Multistabilities in a Novel 4D Memristor-Based Chaotic System with Discrete Bifurcation Diagrams

et al. 2020

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In this paper, a new 4D memristor-based chaotic system is constructed by using a smooth flux-controlled memristor to replace a resistor in the realization circuit of a 3D chaotic system. Compared with general chaotic systems, the chaotic system can generate coexisting infinitely many attractors. The proposed chaotic system not only possesses heterogeneous multistability but also possesses homogenous multistability. When the parameters of system are fixed, the chaotic system only generates two kinds of chaotic attractors with different positions in a very large range of initial values. Different from other chaotic systems with continuous bifurcation diagrams, this system has discrete bifurcation diagrams when the initial values change. In addition, this paper reveals the relationship between the symmetry of coexisting attractors and the symmetry of initial values in the system. The dynamic behaviors of the new system are analyzed by equilibrium point and stability, bifurcation diagrams, Lyapunov exponents, and phase orbit diagrams. Finally, the chaotic attractors are captured through circuit simulation, which verifies numerical simulation.

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Section: Dynamic Analysis Of Heterogeneous Multistabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Heterogeneous and Homogenous Multistabilities in a Novel 4D Memristor-Based Chaotic System with Discrete Bifurcation Diagrams

et al. 2020

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“…If several or even infinite kinds of coexisting attractors are found in a dynamics system, then the system has heterogeneous multistability [35]. The typical attractors can be obtained as shown in Figure 13, when the system parameter values were set as in Table 1 and the initial conditions are (0, y(0), 0, 0).…”

Section: Heterogeneous Multistabilitymentioning

confidence: 99%

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

Song

Chang

2020

Electronics

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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.

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“…Recently, much attention has been paid to construct memristor-based chaotic circuits and analyze their dynamical behaviors. Reference [19] presented and analyzed a new chaotic circuit, which was composed of a meminductor emulator and an active memristor emulator. Reference [20] constructed a memristor-based hyperchaotic Wien-bridge oscillator and analyzed its dynamical behaviors.…”

Section: Introductionmentioning

confidence: 99%

Coexisting Attractors and Multistability in a Simple Memristive Wien-Bridge Chaotic Circuit

Song

Yuan

2019

Entropy

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In this paper, a new voltage-controlled memristor is presented. The mathematical expression of this memristor has an absolute value term, so it is called an absolute voltage-controlled memristor. The proposed memristor is locally active, which is proved by its DC V–I (Voltage–Current) plot. A simple three-order Wien-bridge chaotic circuit without inductor is constructed on the basis of the presented memristor. The dynamical behaviors of the simple chaotic system are analyzed in this paper. The main properties of this system are coexisting attractors and multistability. Furthermore, an analog circuit of this chaotic system is realized by the Multisim software. The multistability of the proposed system can enlarge the key space in encryption, which makes the encryption effect better. Therefore, the proposed chaotic system can be used as a pseudo-random sequence generator to provide key sequences for digital encryption systems. Thus, the chaotic system is discretized and implemented by Digital Signal Processing (DSP) technology. The National Institute of Standards and Technology (NIST) test and Approximate Entropy analysis of the proposed chaotic system are conducted in this paper.

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The amplitude, frequency and parameter space boosting in a memristor–meminductor-based circuit

Cited by 98 publications

References 36 publications

Heterogeneous and Homogenous Multistabilities in a Novel 4D Memristor-Based Chaotic System with Discrete Bifurcation Diagrams

Heterogeneous and Homogenous Multistabilities in a Novel 4D Memristor-Based Chaotic System with Discrete Bifurcation Diagrams

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

Coexisting Attractors and Multistability in a Simple Memristive Wien-Bridge Chaotic Circuit

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