A Novel Memcapacitor and Its Application in a Chaotic Circuit

2021 ◽  
Author(s):  
Mei Guo ◽  
Ran Yang ◽  
Meng Zhang ◽  
Renyuan Liu ◽  
Yongliang Zhu ◽  
...  
Keyword(s):  
Steady State ◽  
Transient Chaos ◽  
Bifurcation Diagrams ◽  
Chaotic Circuit ◽  
Coexisting Attractors ◽  
Dynamic Behaviors ◽  
Burst Period ◽  
The Stability ◽  
Fifth Order ◽  
Stable Points

Abstract In this paper, a novel memcapacitor is designed by SBT memristor and two capacitors. A fifth-order memcapacitor and memristor chaotic circuit is proposed. The stability of the equilibrium point of the system is analyzed theoretically. Lyapunov exponents spectra, bifurcation diagrams, poincaré maps and phase diagrams are used to analyze the dynamic behaviors of the system. The results show that under different initial values and parameters, the system produces rich dynamic behaviors such as stable points, limit cycles, chaos, and so on. Specially, coexisting attractors, transient chaos, and steady-state chaos accompanied by burst period phenomenon are also produced in the system. The proposed memcapacitor-based circuit expands the research methods of memcapacitor for application in chaoticcircuits.

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

Electronics ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 410 ◽  
Author(s):  
Qinghai Song ◽  
Hui Chang ◽  
Yuxia Li
Keyword(s):  
Signal Processing ◽  
Complex Dynamics ◽  
Digital Signal ◽  
Chaotic Attractors ◽  
Transient Chaos ◽  
Bifurcation Diagrams ◽  
Chaotic Circuit ◽  
Coexisting Attractors ◽  
State Switching ◽  
Autonomous Differential Equations

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.

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

2020 ◽  
Vol 30 (11) ◽  
pp. 2030043
Author(s):  
Gang Dou ◽  
Hai Yang ◽  
Zhenhao Gao ◽  
Peng Li ◽  
Minglong Dou ◽  
...  
Keyword(s):  
Equilibrium Point ◽  
Lyapunov Exponents ◽  
Phase Portraits ◽  
Circuit Parameter ◽  
Bifurcation Diagrams ◽  
Chaotic Circuit ◽  
Initial State ◽  
Stable Point ◽  
The Stability ◽  
Physical Formula

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.

Effects of Initial Conditions and Circuit Parameters on the SBT-Memristor-Based Chaotic Circuit

2019 ◽  
Vol 29 (12) ◽  
pp. 1950171 ◽  
Author(s):  
Gang Dou ◽  
Huaying Duan ◽  
Wenyan Yang ◽  
Hai Yang ◽  
Mei Guo ◽  
...  
Keyword(s):  
Chaotic System ◽  
Initial Conditions ◽  
Chaotic Circuit ◽  
Mathematical Methods ◽  
Initial State ◽  
Dynamical Characteristics ◽  
Dynamical Behaviors ◽  
Initial States ◽  
The Stability ◽  
Stable Points

In the paper, a fourth-order SBT-memristor-based chaotic system described by the flux-controlled model is investigated. The stability of the chaotic system is analyzed, and the effects of initial conditions and circuit parameters on the SBT-memristor-based chaotic circuit are discussed by mathematical methods of Lyapunov exponents spectra, bifurcation diagrams, phase orbits and Poincaré maps. Through simulations, it is observed that the dynamical characteristics vary with initial states and circuit parameters. Complex dynamical behaviors such as stable points, period cycles and chaos can be found in the SBT-memristor-based system. It is also found that the system exhibits multistability, which is closely dependent on the initial state of the SBT memristor. This study provides insightful guidance for the design and analysis of memristor-based circuits towards potential real applications.

The Stability of Steady-State Depth Distributions of Marine Phytoplankton

1974 ◽  
Vol 108 (963) ◽  
pp. 679-687 ◽  
Author(s):  
W. O. Criminale, ◽  
D. F. Winter
Keyword(s):  
Steady State ◽  
Marine Phytoplankton ◽  
The Stability ◽  
Depth Distributions

scholarly journals Steady-state $$\dot{V}{\text{O}}_{2}$$ above MLSS: evidence that critical speed better represents maximal metabolic steady state in well-trained runners

2021 ◽  
Author(s):  
Rebekah J. Nixon ◽  
Sascha H. Kranen ◽  
Anni Vanhatalo ◽  
Andrew M. Jones
Keyword(s):  
Steady State ◽  
Critical Speed ◽  
Lactate Concentration ◽  
Practical Interest ◽  
Blood Lactate Concentration ◽  
Distance Runners ◽  
Severe Intensity ◽  
The Stability ◽  
Trained Runners ◽  
Over Time

AbstractThe metabolic boundary separating the heavy-intensity and severe-intensity exercise domains is of scientific and practical interest but there is controversy concerning whether the maximal lactate steady state (MLSS) or critical power (synonymous with critical speed, CS) better represents this boundary. We measured the running speeds at MLSS and CS and investigated their ability to discriminate speeds at which $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 was stable over time from speeds at which a steady-state $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 could not be established. Ten well-trained male distance runners completed 9–12 constant-speed treadmill tests, including 3–5 runs of up to 30-min duration for the assessment of MLSS and at least 4 runs performed to the limit of tolerance for assessment of CS. The running speeds at CS and MLSS were significantly different (16.4 ± 1.3 vs. 15.2 ± 0.9 km/h, respectively; P < 0.001). Blood lactate concentration was higher and increased with time at a speed 0.5 km/h higher than MLSS compared to MLSS (P < 0.01); however, pulmonary $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 did not change significantly between 10 and 30 min at either MLSS or MLSS + 0.5 km/h. In contrast, $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 increased significantly over time and reached $$\dot{V}{\text{O}}_{2\,\,\max }$$ V ˙ O 2 max at end-exercise at a speed ~ 0.4 km/h above CS (P < 0.05) but remained stable at a speed ~ 0.5 km/h below CS. The stability of $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 at a speed exceeding MLSS suggests that MLSS underestimates the maximal metabolic steady state. These results indicate that CS more closely represents the maximal metabolic steady state when the latter is appropriately defined according to the ability to stabilise pulmonary $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 .

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

Entropy ◽  
2019 ◽  
Vol 21 (7) ◽  
pp. 678 ◽  
Author(s):  
Yixuan Song ◽  
Fang Yuan ◽  
Yuxia Li
Keyword(s):  
Chaotic System ◽  
Analog Circuit ◽  
Random Sequence ◽  
Mathematical Expression ◽  
Digital Signal ◽  
Approximate Entropy ◽  
Chaotic Circuit ◽  
Coexisting Attractors ◽  
Key Space ◽  
Sequence Generator

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.

scholarly journals Nonlinear Dynamics and Stability Analysis of a Three-Cell Flying Capacitor DC-DC Converter

2021 ◽  
Vol 11 (4) ◽  
pp. 1395
Author(s):  
Abdelali El Aroudi ◽  
Natalia Cañas-Estrada ◽  
Mohamed Debbat ◽  
Mohamed Al-Numay
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Monodromy Matrix ◽  
Dynamical Behavior ◽  
Period Doubling ◽  
Simple Expression ◽  
Buck Converter ◽  
State Variables ◽  
Bifurcation Phenomena ◽  
The Stability

This paper presents a study of the nonlinear dynamic behavior a flying capacitor four-level three-cell DC-DC buck converter. Its stability analysis is performed and its stability boundaries is determined in the multi-dimensional paramertic space. First, the switched model of the converter is presented. Then, a discrete-time controller for the converter is proposed. The controller is is responsible for both balancing the flying capacitor voltages from one hand and for output current regulation. Simulation results from the switched model of the converter under the proposed controller are presented. The results show that the system may undergo bifurcation phenomena and period doubling route to chaos when some system parameters are varied. One-dimensional bifurcation diagrams are computed and used to explore the possible dynamical behavior of the system. By using Floquet theory and Filippov method to derive the monodromy matrix, the bifurcation behavior observed in the converter is accurately predicted. Based on justified and realistic approximations of the system state variables waveforms, simple and accurate expressions for these steady-state values and the monodromy matrix are derived and validated. The simple expression of the steady-state operation and the monodromy matrix allow to analytically predict the onset of instability in the system and the stability region in the parametric space is determined. Numerical simulations from the exact switched model validate the theoretical predictions.

STABILITY OF STEADY STATE AND TRAVELING WAVES SOLUTIONS IN COUPLED MAP LATTICES

2008 ◽  
Vol 18 (01) ◽  
pp. 219-225 ◽  
Author(s):  
DANIEL TURZÍK ◽  
MIROSLAVA DUBCOVÁ
Keyword(s):  
Steady State ◽  
Essential Spectrum ◽  
Traveling Waves ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Linear Operators ◽  
Coupled Map Lattices ◽  
Basic Tool ◽  
Wave Solutions ◽  
The Stability

We determine the essential spectrum of certain types of linear operators which arise in the study of the stability of steady state or traveling wave solutions in coupled map lattices. The basic tool is the Gelfand transformation which enables us to determine the essential spectrum completely.

The flow of a micropolar liquid layer down an inclined plane

1968 ◽  
Vol 64 (2) ◽  
pp. 513-526 ◽  
Author(s):  
A. J. Willson
Keyword(s):  
Thin Films ◽  
Steady State ◽  
Liquid Layer ◽  
Stability Criterion ◽  
Long Waves ◽  
Inclined Plane ◽  
The Stability ◽  
Micropolar Liquid

AbstractConsideration is given to the flow of a micropolar liquid down an inclined plane. The steady state is analysed and Yih's technique is employed in an investigation of the stability of this flow with respect to long waves. Detailed calculations are given for thin films and it is shown that the micropolar properties of the liquid play an important role in the stability criterion.

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