Chua Corsage Memristor Oscillator via Hopf Bifurcation

2016 ◽  
Vol 26 (04) ◽  
pp. 1630009 ◽  
Author(s):  
Zubaer Ibna Mannan ◽  
Hyuncheol Choi ◽  
Hyongsuk Kim
Keyword(s):  
Hopf Bifurcation ◽  
Equivalent Circuit ◽  
Series Expansion ◽  
Taylor Series ◽  
Taylor Series Expansion ◽  
Operating Point ◽  
Small Signal ◽  
Local Activity ◽  
Edge Of Chaos ◽  
In Series

This paper demonstrates that the Chua Corsage Memristor, when connected in series with an inductor and a battery, oscillates about a locally-active operating point located on the memristor’s DC [Formula: see text]–[Formula: see text] curve. On the operating point, a small-signal equivalent circuit is derived via a Taylor series expansion. The small-signal admittance [Formula: see text] is derived from the small-signal equivalent circuit and the value of inductance is determined at a frequency where the real part of the admittance [Formula: see text] of the small-signal equivalent circuit of Chua Corsage Memristor is zero. Oscillation of the circuit is analyzed via an in-depth application of the theory of Local Activity, Edge of Chaos and the Hopf-bifurcation.

Design of a Low-Frequency Oscillator with PTC Memristor and an Inductor

2016 ◽  
Vol 26 (08) ◽  
pp. 1630021 ◽  
Author(s):  
Vetriveeran Rajamani ◽  
Changju Yang ◽  
Hyongsuk Kim ◽  
Leon Chua
Keyword(s):  
Hopf Bifurcation ◽  
Active Region ◽  
Equivalent Circuit ◽  
Low Frequency ◽  
Negative Resistance ◽  
Small Signal ◽  
Sinusoidal Oscillation ◽  
Frequency Oscillator ◽  
In Series ◽  
Electronic Oscillator

An electronic oscillator circuit is designed by connecting an inductor in series with a locally-active PTC Memristor and a battery. The PTC Memristor is locally active on the negative resistance region of its DC [Formula: see text]–[Formula: see text] curve. A DC operating point [Formula: see text] is chosen on the locally-active region of the PTC Memristor and a small-signal equivalent circuit at [Formula: see text] is derived via Taylor series. The small-signal admittance [Formula: see text] of the composite one-port in Fig. 1 is derived using the small-signal equivalent circuit at [Formula: see text], in series with an inductor whose value is chosen such that [Formula: see text] at some [Formula: see text]. The sinusoidal oscillation computed numerically from this circuit is shown to emerge from a supercritical Hopf bifurcation.

Full-Scale Bounds Estimation for the Nonlinear Transient Heat Transfer Problems with Interval Uncertainties

2021 ◽  
pp. 2150026
Author(s):  
Ruifei Peng ◽  
Haitian Yang ◽  
Yanni Xue
Keyword(s):  
Heat Transfer ◽  
Series Expansion ◽  
Taylor Series ◽  
Taylor Series Expansion ◽  
Transient Heat Transfer ◽  
High Fidelity ◽  
Interval Scale ◽  
Nonlinear Transient ◽  
Transfer Problems ◽  
Derivatives Of

A package solution is presented for the full-scale bounds estimation of temperature in the nonlinear transient heat transfer problems with small or large uncertainties. When the interval scale is relatively small, an efficient Taylor series expansion-based bounds estimation of temperature is stressed on the acquirement of first and second-order derivatives of temperature with high fidelity. When the interval scale is relatively large, an optimization-based approach in conjunction with a dimension-adaptive sparse grid (DSG) surrogate is developed for the bounds estimation of temperature, and the heavy computational burden of repeated deterministic solutions of nonlinear transient heat transfer problems can be efficiently alleviated by the DSG surrogate. A temporally piecewise adaptive algorithm with high fidelity is employed to gain the deterministic solution of temperature, and is further developed for recursive adaptive computing of the first and second-order derivatives of temperature. Therefore, the implementation of Taylor series expansion and the construction of DSG surrogate are underpinned by a reliable numerical platform. The parallelization is utilized for the construction of DSG surrogate for further acceleration. The accuracy and efficiency of the proposed approaches are demonstrated by two numerical examples.

scholarly journals Weighted Measurement Fusion Particle Filter for Nonlinear Systems with Correlated Noises

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3242 ◽  
Author(s):  
Ke Wei Zhang ◽  
Gang Hao ◽  
Shu Li Sun
Keyword(s):  
Nonlinear Systems ◽  
Particle Filter ◽  
Series Expansion ◽  
Taylor Series ◽  
Asymptotic Optimality ◽  
Taylor Series Expansion ◽  
Full Rank ◽  
Expansion Method ◽  
Least Square ◽  
Correlated Noises

The multi-sensor information fusion particle filter (PF) has been put forward for nonlinear systems with correlated noises. The proposed algorithm uses the Taylor series expansion method, which makes the nonlinear measurement functions have a linear relationship by the intermediary function. A weighted measurement fusion PF (WMF-PF) was put forward for systems with correlated noises by applying the full rank decomposition and the weighted least square theory. Compared with the augmented optimal centralized fusion particle filter (CF-PF), it could greatly reduce the amount of calculation. Moreover, it showed asymptotic optimality as the Taylor series expansion increased. The simulation examples illustrate the effectiveness and correctness of the proposed algorithm.

scholarly journals Bounds on the Third Order Hankel Determinant for Certain Subclasses of Analytic Functions

2017 ◽  
Vol 25 (3) ◽  
pp. 199-214
Author(s):  
S.P. Vijayalakshmi ◽  
T.V. Sudharsan ◽  
Daniel Breaz ◽  
K.G. Subramanian
Keyword(s):  
Series Expansion ◽  
Taylor Series ◽  
Analytic Functions ◽  
Unit Disc ◽  
Taylor Series Expansion ◽  
Upper Bounds ◽  
Hankel Determinant ◽  
Third Order ◽  
The Third

Abstract Let A be the class of analytic functions f(z) in the unit disc ∆ = {z ∈ C : |z| < 1g with the Taylor series expansion about the origin given by f(z) = z+ ∑n=2∞ anzn, z ∈∆ : The focus of this paper is on deriving upper bounds for the third order Hankel determinant H3(1) for two new subclasses of A.

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