Chaotic Oscillator Based on Mathematical Model of Multiple-Valued Memory Cell

In this paper, a new electro-mechanical chaotic oscillator is presented. The system is based on the motion of the metal tip of a beam in a double-well potential generated by two magnets, and works thanks to the vibrations generated in the flexible mechanical structure by two rotating coils that produce noise-like signals. As the source of vibration is internal, the system may be considered an autonomous oscillator. Chaotic motion is experimentally observed and verified with a mathematical model of the phenomenon.

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Chaotic Oscillator Based on Fractional Order Memcapacitor

Journal of Circuits System and Computers ◽

10.1142/s0218126619502396 ◽

2019 ◽

Vol 28 (14) ◽

pp. 1950239 ◽

Cited By ~ 5

Author(s):

Akif Akgul

Keyword(s):

Mathematical Model ◽

Lyapunov Exponents ◽

Fractional Order ◽

Nonlinear Oscillator ◽

Equilibrium Points ◽

Dynamical Behavior ◽

Chaotic Oscillator ◽

State Equations ◽

Chaotic Oscillators ◽

Eigen Values

Many literatures have discussed fractional order memristor and memcapacitor-based chaotic oscillators but the entire oscillator model is considered to be of fractional order. My interest is to propose a nonlinear oscillator with considering only the memcapacitor element of fractional order. Hence, I propose a fractional order memcapacitor (FMC)-based novel chaotic oscillator. The complete mathematical model for the proposed oscillator is derived and presented in this paper. The dimensionless state equations are then analyzed by using the equilibrium points and their stability, Eigen values, Kaplan–Yorke dimensions and Lyapunov exponents. To understand the complete dynamical behavior, bifurcation graphs are obtained and presented. Finally, the proposed fractional memcapacitor oscillator is implemented by using the shelf components.

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Colpitts Chaotic Oscillator Coupling with a Generalized Memristor

Mathematical Problems in Engineering ◽

10.1155/2015/249102 ◽

2015 ◽

Vol 2015 ◽

pp. 1-9 ◽

Cited By ~ 7

Author(s):

Ling Lu ◽

Changdi Li ◽

Zicheng Zhao ◽

Bocheng Bao ◽

Quan Xu

Keyword(s):

Mathematical Model ◽

Equilibrium Point ◽

Fourth Order ◽

Chaotic Attractors ◽

Chaotic Oscillator ◽

Nonlinear Phenomena ◽

Unique Equilibrium ◽

First Order ◽

The Mathematical Model ◽

Order Parallel

By introducing a generalized memristor into a fourth-order Colpitts chaotic oscillator, a new memristive Colpitts chaotic oscillator is proposed in this paper. The generalized memristor is equivalent to a diode bridge cascaded with a first-order parallel RC filter. Chaotic attractors of the oscillator are numerically revealed from the mathematical model and experimentally captured from the physical circuit. The dynamics of the memristive Colpitts chaotic oscillator is investigated both theoretically and numerically, from which it can be found that the oscillator has a unique equilibrium point and displays complex nonlinear phenomena.

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New Chaotic Oscillator Derived from Class C Single Transistor-Based Amplifier

Mathematical Problems in Engineering ◽

10.1155/2020/2640629 ◽

2020 ◽

Vol 2020 ◽

pp. 1-18

Author(s):

Jiri Petrzela

Keyword(s):

Dynamical System ◽

Mathematical Model ◽

High Frequency ◽

Piecewise Linear ◽

Chaotic Oscillator ◽

Chaotic Dynamical System ◽

Transient Behaviour ◽

Local Polynomial ◽

Good Accordance ◽

Class C

This paper describes a new autonomous deterministic chaotic dynamical system having a single unstable saddle-spiral fixed point. A mathematical model originates in the fundamental structure of the class C amplifier. Evolution of robust strange attractors is conditioned by a bilateral nature of bipolar transistor with local polynomial or piecewise linear feedforward transconductance and high frequency of operation. Numerical analysis is supported by experimental verification and both results prove that chaos is neither a numerical artifact nor a long transient behaviour. Also, good accordance between theory and measurement has been observed.

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Mathematical model for efficient design of a plated-wire memory cell

IEEE Transactions on Magnetics ◽

10.1109/tmag.1971.1067191 ◽

1971 ◽

Vol 7 (3) ◽

pp. 622-625

Author(s):

R. McCary ◽

W. Barber

Keyword(s):

Mathematical Model ◽

Memory Cell ◽

Efficient Design

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A Chaotic Oscillator Based on Meminductor, Memcapacitor, and Memristor

Complexity ◽

10.1155/2021/7223557 ◽

2021 ◽

Vol 2021 ◽

pp. 1-16

Author(s):

Xingce Liu ◽

Xiuguo Bi ◽

Huizhen Yan ◽

Jun Mou

Keyword(s):

Numerical Simulation ◽

Mathematical Model ◽

State Transition ◽

State Equation ◽

Chaotic Oscillator ◽

Hyperchaotic System ◽

Analysis Method ◽

Numerical Simulation Result ◽

Dynamical Characteristics ◽

The Stability

In this paper, a hyperchaotic circuit consisting of a series memristor, meminductor, and memcapacitor is proposed. The dimensionless mathematical model of the system is established by the state equation of the circuit. The stability of equilibrium point of the system is analyzed by using the traditional dynamic analysis method. Then, the dynamical characteristics of the chaotic system with parameters are analyzed in detail. In addition, the system also has some particular phenomena such as attractor coexistence and state transition. Finally, the circuit is realized by DSP, and the result is consistent with that of numerical simulation. This proves the accuracy of the theoretical analysis. Numerical simulation result shows which hyperchaotic system has very abundant dynamical characteristics.

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Optimizing the Kaplan–Yorke Dimension of Chaotic Oscillators Applying DE and PSO

Technologies ◽

10.3390/technologies7020038 ◽

2019 ◽

Vol 7 (2) ◽

pp. 38 ◽

Cited By ~ 7

Author(s):

Alejandro Silva-Juarez ◽

Gustavo Rodriguez-Gomez ◽

Luis Gerardo de la Fraga ◽

Omar Guillen-Fernandez ◽

Esteban Tlelo-Cuautle

Keyword(s):

Mathematical Model ◽

Time Series ◽

Color Image ◽

Equilibrium Points ◽

Computing Time ◽

Chaotic Oscillator ◽

State Variables ◽

Huge Number ◽

Chaotic Oscillators ◽

Swarm Optimization

When a new chaotic oscillator is introduced, it must accomplish characteristics like guaranteeing the existence of a positive Lyapunov exponent and a high Kaplan–Yorke dimension. In some cases, the coefficients of a mathematical model can be varied to increase the values of those characteristics but it is not a trivial task because a very huge number of combinations arise and the required computing time can be unreachable. In this manner, we introduced the optimization of the Kaplan–Yorke dimension of chaotic oscillators by applying metaheuristics, e.g., differential evolution (DE) and particle swarm optimization (PSO) algorithms. We showed the equilibrium points and eigenvalues of three chaotic oscillators that are simulated applying ODE45, and the Kaplan–Yorke dimension was evaluated by Wolf’s method. The chaotic time series of the state variables associated to the highest Kaplan–Yorke dimension provided by DE and PSO are used to encrypt a color image to demonstrate that they are useful in implementing a secure chaotic communication system. Finally, the very low correlation between the chaotic channel and the original color image confirmed the usefulness of optimizing Kaplan–Yorke dimension for cryptographic applications.

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