scholarly journals Electronic Circuit Emuling a First-order Time-delay Differential Equation

2021 ◽  
Vol 19 (1 Jan-Jun) ◽  
Author(s):  
César Jiménez ◽  
I. Campos-Canton ◽  
L. J. Ontañón-García
Keyword(s):  
Differential Equation ◽  
Time Delay ◽  
Phase Shift ◽  
Electronic Circuit ◽  
Linear Time ◽  
Electrical Circuit ◽  
First Order ◽  
Simulation Results ◽  
Delay Differential ◽  
Theoretical Results

This article provides undergraduates a useful tool for a better understanding of the time delay eect on a electronic circuit. The time delay eect is analyzed on this paper in a rst order dierential equation. This linear time delay is associated with the amplitude of a first-order dierential equation and is responsible of three responses: one of the responses is an dierential equation type in first-order without delay, another one of the responses is a dierential equation type in second-order and nally we have the response of a harmonic oscillator.The proposed circuit is an emulator that develop the three different responses mentioned above. Simulink-Matlab software was used to implement the time delay and simulate the dierential equation. This simulation results coincide with the theoretical results. In the same manner, the experimental results match those of the theory. The electronical circuits suggested consist of three blocks: an integrator block, a phase shift block and a gain block. The electrical circuit is composed of resistors, capacitors and operational ampliers.

MULTISCROLL CHAOTIC ATTRACTORS FROM A HYSTERESIS BASED TIME-DELAY DIFFERENTIAL EQUATION

2010 ◽  
Vol 20 (10) ◽  
pp. 3275-3281 ◽  
Author(s):  
SELÇUK KILINÇ ◽  
MÜŞTAK E. YALÇIN ◽  
SERDAR ÖZOGUZ
Keyword(s):  
Differential Equation ◽  
Time Delay ◽  
Delay Differential Equation ◽  
Order Differential Equation ◽  
Chaotic Attractors ◽  
Nonlinear Characteristic ◽  
Circuit Implementation ◽  
First Order ◽  
State Variable ◽  
Delay Differential

In this paper, the generation of multiscroll chaotic attractors derived from a time-delay differential equation is presented. The proposed system is represented by only one first-order differential equation including time-delayed state variable, and employs hysteresis function as the nonlinear characteristic. The generalization of the introduced system is based on adding multihysteresis nonlinear characteristic which leads to n-scroll chaotic attractors. The circuit implementation of the proposed system and some experimental results referring to two-, three-, four-, and five-scroll chaotic attractors are reported.

scholarly journals A Convergent Collocation Approach for Generalized Fractional Integro-Differential Equations Using Jacobi Poly-Fractonomials

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 979
Author(s):  
Sandeep Kumar ◽  
Rajesh K. Pandey ◽  
H. M. Srivastava ◽  
G. N. Singh
Keyword(s):  
Differential Equation ◽  
Fractional Derivative ◽  
Collocation Method ◽  
Caputo Fractional Derivative ◽  
Fractional Derivatives ◽  
Special Cases ◽  
Collocation Approach ◽  
Linear And Nonlinear ◽  
Simulation Results ◽  
Theoretical Results

In this paper, we present a convergent collocation method with which to find the numerical solution of a generalized fractional integro-differential equation (GFIDE). The presented approach is based on the collocation method using Jacobi poly-fractonomials. The GFIDE is defined in terms of the B-operator introduced recently, and it reduces to Caputo fractional derivative and other fractional derivatives in special cases. The convergence and error analysis of the proposed method are also established. Linear and nonlinear cases of the considered GFIDEs are numerically solved and simulation results are presented to validate the theoretical results.

scholarly journals Oscillatory Behaviour of a First-Order Neutral Differential Equation in relation to an Old Open Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
K. C. Panda ◽  
R. N. Rath ◽  
S. K. Rath
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Oscillatory Behaviour ◽  
Neutral Delay ◽  
First Order ◽  
Neutral Delay Differential Equation ◽  
Delay Differential ◽  
Oscillation And Nonoscillation

In this paper, we obtain sufficient conditions for oscillation and nonoscillation of the solutions of the neutral delay differential equation yt−∑j=1kpjtyrjt′+qtGygt−utHyht=ft, where pj and rj for each j and q,u,G,H,g,h, and f are all continuous functions and q≥0,u≥0,ht<t,gt<t, and rjt<t for each j. Further, each rjt, gt, and ht⟶∞ as t⟶∞. This paper improves and generalizes some known results.

scholarly journals Exponential Stability of Stochastic Differential Equation with Mixed Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Wenli Zhu ◽  
Jiexiang Huang ◽  
Xinfeng Ruan ◽  
Zhao Zhao
Keyword(s):  
Differential Equation ◽  
Time Delay ◽  
Stochastic Differential Equation ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Martingale Inequality ◽  
Mixed Delay ◽  
Exponentially Stable ◽  
Theoretical Results

This paper focuses on a class of stochastic differential equations with mixed delay based on Lyapunov stability theory, Itô formula, stochastic analysis, and inequality technique. A sufficient condition for existence and uniqueness of the adapted solution to such systems is established by employing fixed point theorem. Some sufficient conditions of exponential stability and corollaries for such systems are obtained by using Lyapunov function. By utilizing Doob’s martingale inequality and Borel-Cantelli lemma, it is shown that the exponentially stable in the mean square of such systems implies the almost surely exponentially stable. In particular, our theoretical results show that if stochastic differential equation is exponentially stable and the time delay is sufficiently small, then the corresponding stochastic differential equation with mixed delay will remain exponentially stable. Moreover, time delay upper limit is solved by using our theoretical results when the system is exponentially stable, and they are more easily verified and applied in practice.

A Simultaneous Phase Shift Interferometry Used to Pulse Laser Pump-Probe Approach

2011 ◽  
Vol 346 ◽  
pp. 670-674 ◽  
Author(s):  
Hai Ying Song ◽  
Xue Peng He ◽  
Shi Bing Liu ◽  
Tao Chen
Keyword(s):  
Time Delay ◽  
Phase Shift ◽  
Pulse Laser ◽  
Laser Wavelength ◽  
Interference Channels ◽  
Phase Lag ◽  
Pump Probe ◽  
Laser Pump ◽  
Light Interference ◽  
Theoretical Results

A simultaneous phase shift interferometry was proposed to determine the time delay accurately in the pulse laser pump-probe detecting. The relevant optical system formed by four light interference channels was designed and optimized based on Jones theory. The light intensity distribution of interference pattern associated with the phase lag from these four light interference channels was derived by Jones matrix. The possible errors that exist in the applications were calculated. The theoretical results show that the minimum resolution of the time delay can be achieved to attosecond level for 800nm laser wavelength.

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