Control the stability in chaotic circuit coupled by memristor in different branch circuits

2021 ◽  
pp. 154074
Author(s):  
Yitong Guo ◽  
Zhao Yao ◽  
Ying Xu ◽  
Jun Ma
Keyword(s):  
Chaotic Circuit ◽  
The Stability

scholarly journals Theory and applications of new fractional-order chaotic system under Caputo operator

2021 ◽  
Vol 12 (1) ◽  
pp. 20-38
Author(s):  
Ndolane Sene
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Caputo Derivative ◽  
Phase Portraits ◽  
Chaotic Circuit ◽  
Chaotic Model ◽  
The Stability ◽  
The Impact ◽  
Schematic Circuit ◽  
Good Agreement

This paper introduces the properties of a fractional-order chaotic system described by the Caputo derivative. The impact of the fractional-order derivative has been focused on. The phase portraits in different orders are obtained with the aids of the proposed numerical discretization, including the discretization of the Riemann-Liouville fractional integral. The stability analysis has been used to help us to delimit the chaotic region. In other words, the region where the order of the Caputo derivative involves and where the presented system in this paper is chaotic. The nature of the chaos has been established using the Lyapunov exponents in the fractional context. The schematic circuit of the proposed fractional-order chaotic system has been presented and simulated in via Mutltisim. The results obtained via Multisim simulation of the chaotic circuit are in good agreement with the results with Matlab simulations. That provided the fractional operators can be applied in real- worlds applications as modeling electrical circuits. The presence of coexisting attractors for particular values of the parameters of the presented fractional-order chaotic model has been studied.

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 A Novel Memductor-Based Chaotic System and Its Applications in Circuit Design and Experimental Validation

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Li Xiong ◽  
Yanjun Lu ◽  
Yongfang Zhang ◽  
Xinguo Zhang
Keyword(s):  
Chaotic System ◽  
Secure Communication ◽  
Experimental Validation ◽  
Control Method ◽  
Dynamical Behavior ◽  
Chaotic Circuit ◽  
Initial State ◽  
Error System ◽  
The Stability ◽  
The Mathematical Model

This paper is expected to introduce a novel memductor-based chaotic system. The local dynamical entities, such as the basic dynamical behavior, the divergence, the stability of equilibrium set, and the Lyapunov exponent, are all investigated analytically and numerically to reveal the dynamic characteristics of the new memductor-based chaotic system as the system parameters and the initial state of memristor change. Subsequently, an active control method is derived to study the synchronous stability of the novel memductor-based chaotic system through making the synchronization error system asymptotically stable at the origin. Further to these, a memductor-based chaotic circuit is designed, realized, and applied to construct a new memductor-based secure communication circuit by employing the basic electronic components and memristor. Furthermore, the design principle of the memductor-based chaotic circuit is thoroughly analyzed and the concept of “the memductor-based chaotic circuit defect quantification index” is proposed for the first time to verify whether the chaotic output is consistent with the mathematical model. A good qualitative agreement is shown between the simulations and the experimental validation results.

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.

Initial conditions-related dynamical behaviors in PI-type memristor emulator-based canonical Chua’s circuit

Circuit World ◽  
2018 ◽  
Vol 44 (4) ◽  
pp. 178-186 ◽  
Author(s):  
Bocheng Bao ◽  
Jiaoyan Luo ◽  
Han Bao ◽  
Quan Xu ◽  
Yihua Hu ◽  
...  
Keyword(s):  
Phase Plane ◽  
Initial Conditions ◽  
Chaotic Circuit ◽  
Content Type ◽  
Dynamical Behaviors ◽  
The Stability ◽  
Plane Orbit ◽  
Memristor Emulator ◽  
Line Equilibrium ◽  
Lyapunov Exponent Spectrum

Purpose The purpose of this paper is to construct a proportion-integral-type (PI-type) memristor, which is different from that of the previous memristor emulator, but the constructing memristive chaotic circuit possesses line equilibrium, leading to the emergence of the initial conditions-related dynamical behaviors. Design/methodology/approach This paper presents a PI-type memristor emulator-based canonical Chua’s chaotic circuit. With the established mathematical model, the stability region for the line equilibrium is derived, which mainly consists of stable and unstable regions, leading to the emergence of bi-stability because of the appearance of a memristor. Initial conditions-related dynamical behaviors are investigated by some numerically simulated methods, such as phase plane orbit, bifurcation diagram, Lyapunov exponent spectrum, basin of the attraction and 0-1 test. Additionally, PSIM circuit simulations are executed and the seized results validate complex dynamical behaviors in the proposed memristive circuit. Findings The system exhibits the bi-stability phenomenon and demonstrates complex initial conditions-related bifurcation behaviors with the variation of system parameters, which leads to the occurrence of the hyperchaos, chaos, quasi-periodic and period behaviors in the proposed circuit. Originality/value These memristor emulators are simple and easy to physically fabricate, which have been increasingly used for experimentally demonstrating some interesting and striking dynamical behaviors in the memristor-based circuits and systems.

scholarly journals Dynamic Behaviors and the Equivalent Realization of a Novel Fractional-Order Memristor-Based Chaotic Circuit

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Ningning Yang ◽  
Cheng Xu ◽  
Chaojun Wu ◽  
Rong Jia ◽  
Chongxin Liu
Keyword(s):  
Numerical Simulations ◽  
Dynamic Behavior ◽  
Fractional Order ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Great Influence ◽  
Equivalent Circuits ◽  
Chaotic Circuit ◽  
Undetermined Coefficient ◽  
The Stability

This paper proposed a novel fractional-order memristor-based chaotic circuit. A memristive diode bridge cascaded with a fractional-order RL filter constitutes the generalized fractional-order memristor. The mathematical model of the proposed fractional-order chaotic circuit is established by extending the nonlinear capacitor and inductor in the memristive chaotic circuit to the fractional order. Detailed theoretical analysis and numerical simulations are carried out on the dynamic behavior of the proposed circuit by investigating the stability of equilibrium points and the influence of circuit parameters on bifurcations. The results show that the order of the fractional-order circuit has a great influence on the dynamical behavior of the system. The system may exhibit complicated nonlinear dynamic behavior such as bifurcation and chaos with the change of the order. The equivalent circuits of the fractional-order inductor and capacitor are also given in the paper, and the parameters of the equivalent circuits are solved by an undetermined coefficient method. Circuit simulations of the equivalent fractional-order memristive chaotic circuit are carried out in order to validate the correctness of numerical simulations and the practicability of using the integer-order equivalent circuit to substitute the fractional-order element.

scholarly journals Dynamic Behaviors Analysis of a Novel Fractional-Order Chua’s Memristive Circuit

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Chaojun Wu ◽  
Qi Zhang ◽  
Zhang Liu ◽  
Ningning Yang
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Fractional Order ◽  
Chaotic Circuit ◽  
Bifurcation And Chaos ◽  
Chaotic Region ◽  
Equivalent Circuit Method ◽  
Memristive Circuit ◽  
Basic Characteristics ◽  
The Stability

This paper proposed a novel fractional-order Chua’s memristive circuit. Firstly, a fractional-order mathematical model of a diode bridge generalized memristor with RLC filter cascade is established, and simulations verify that the fractional-order generalized memristor satisfies the basic characteristics of a memristor. Secondly, the capacitor and inductor in Chua’s chaotic circuit are extended to the fractional order, and the fractional-order generalized memristor is used instead of Chua’s diode to establish the fractional-order mathematical model of chaotic circuit based on RLC generalized memristor. By studying the stability analysis of the equilibrium point and the influence of the circuit parameters on the system dynamics, the dynamic characteristics of the proposed chaotic circuit are theoretically analyzed and numerically simulated. The results show that the proposed fractional-order memristive chaotic circuit has gone through three states: period, bifurcation, and chaos, and a narrow period window appears in the chaotic region. Finally, the equivalent circuit method is adopted in PSpice to realize the construction of the fractional-order capacitance and inductance, and the simulation of the fractional-order memristive chaotic circuit is completed. The results further verify the correctness of the theoretical analysis.

Open discussion

1982 ◽  
Vol 99 ◽  
pp. 605-613
Author(s):  
P. S. Conti
Keyword(s):  
Buenos Aires ◽  
Large Mass ◽  
List Type ◽  
Common Phenomenon ◽  
Open Discussion ◽  
The Stability ◽  
Ring Nebulae

Conti: One of the main conclusions of the Wolf-Rayet symposium in Buenos Aires was that Wolf-Rayet stars are evolutionary products of massive objects. Some questions:–Do hot helium-rich stars, that are not Wolf-Rayet stars, exist?–What about the stability of helium rich stars of large mass? We know a helium rich star of ∼40 MO. Has the stability something to do with the wind?–Ring nebulae and bubbles : this seems to be a much more common phenomenon than we thought of some years age.–What is the origin of the subtypes? This is important to find a possible matching of scenarios to subtypes.

Symmetric Multistep Methods Revisited: II. Numerical Experiments

1999 ◽  
Vol 173 ◽  
pp. 309-314 ◽  
Author(s):  
T. Fukushima
Keyword(s):  
Multistep Methods ◽  
Computational Time ◽  
Integration Time ◽  
Implicit Methods ◽  
Symmetric Methods ◽  
Celestial Bodies ◽  
The Stability ◽  
Predictor Corrector ◽  
Symmetric Multistep Methods ◽  
Integration Errors

AbstractBy using the stability condition and general formulas developed by Fukushima (1998 = Paper I) we discovered that, just as in the case of the explicit symmetric multistep methods (Quinlan and Tremaine, 1990), when integrating orbital motions of celestial bodies, the implicit symmetric multistep methods used in the predictor-corrector manner lead to integration errors in position which grow linearly with the integration time if the stepsizes adopted are sufficiently small and if the number of corrections is sufficiently large, say two or three. We confirmed also that the symmetric methods (explicit or implicit) would produce the stepsize-dependent instabilities/resonances, which was discovered by A. Toomre in 1991 and confirmed by G.D. Quinlan for some high order explicit methods. Although the implicit methods require twice or more computational time for the same stepsize than the explicit symmetric ones do, they seem to be preferable since they reduce these undesirable features significantly.

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