An Improved Approach to Nonlinear Dynamical System Identification using PID Neural Networks

Li, Shouju; Liu, Yingxi

doi:10.1515/ijnsns.2006.7.2.177

Cited by 47 publications

(19 citation statements)

References 10 publications

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“…problems and reported the efficiency of the HPM for handling nonlinear engineering problems [31][32][33][34]. This method is a combination of Homotopy in topology and classic perturbation techniques.…”

Section: A New Approach To Homotopy Perturbation Methods and Its Advanmentioning

confidence: 99%

Theoretical Analysis of an Amperometric Biosensor Based on Parallel Substrates Conversion

Praveen¹,

Rajendran²

2014

ISRN Electrochemistry

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The behaviour of an amperometric biosensor based on parallel substrates conversion for steady-state condition has been discussed. This analysis contains a nonlinear term related to enzyme kinetics. Simple and closed form of analytical expressions of concentrations and of biosensor current is derived. This model was originally reported by Vytautas Aseris and his team (2012). Concentrations of substrate and product are expressed in terms of single dimensionless parameter. A new approach to Homotopy perturbation method (HPM) is employed to solve the system of nonlinear reaction diffusion equations. Furthermore, in this work, the numerical solution of the problem is also reported using Matlab program. The analytical results are compared with the numerical results. The analytical result provided is reliable and efficient to understand the behavior of the system.

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Section: A New Approach To Homotopy Perturbation Methods and Its Advanmentioning

confidence: 99%

Theoretical Analysis of an Amperometric Biosensor Based on Parallel Substrates Conversion

Praveen¹,

Rajendran²

2014

ISRN Electrochemistry

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“…In addition, several groups demonstrated the efficiency and suitability of the HPM for solving nonlinear equations and other electrochemical problems [26][27][28][29]. He [30] used HPM to solve the Lighthill equation, the Duffing equation [31], and the Blasius equation [32].…”

Section: For Small and Medium Values Of The Saturation Parameter α Anmentioning

confidence: 99%

Approximate Analytical Solution of Nonlinear Reaction’s Diffusion Equation at Conducting Polymer Ultramicroelectrodes

Anitha¹,

Alwarappan

Rajendran³

2012

ISRN Physical Chemistry

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A theoretical model of reaction/diffusion within conducting polymer microelectrodes is discussed. The model is based on the steady-state diffusion equation containing a nonlinear term related to the Michaelis-Menten kinetic of the enzymatic reaction. An analytical expression pertaining to the concentration of substrate and current is obtained using homotopy perturbation method for all values of diffusion and the saturation parameter. The substrate concentration profile and current response can be used in a large range of concentrations including the non-linear contributions. These approximate analytical results were found to be in good agreement with the previously reported limiting case results.

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“…Nonlinear phenomena play a crucial role in applied to Equations (15)- (17) [11][12][13][14]. This method is a combination of topology and classic perturbation techniques.…”

Section: Analytical Expressions Of Concentrationsmentioning

confidence: 99%

Analytical Solutions of System of Non-Linear Differential Equations in the Single-Enzyme, Single-Substrate Reaction with Non-Mechanism-Based Enzyme Inactivation

Varadharajan¹,

Rajendran²

2011

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A closed form of an analytical expression of concentration in the single-enzyme, single-substrate system for the full range of enzyme activities has been derived. The time dependent analytical solution for substrate, enzyme-substrate complex and product concentrations are presented by solving system of non-linear differential equation. We employ He's Homotopy perturbation method to solve the coupled non-linear differential equations containing a non-linear term related to basic enzymatic reaction. The time dependent simple analytical expressions for substrate, enzyme-substrate and free enzyme concentrations have been derived in terms of dimensionless reaction diffusion parameters

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An Improved Approach to Nonlinear Dynamical System Identification using PID Neural Networks

Cited by 47 publications

References 10 publications

Theoretical Analysis of an Amperometric Biosensor Based on Parallel Substrates Conversion

Theoretical Analysis of an Amperometric Biosensor Based on Parallel Substrates Conversion

Approximate Analytical Solution of Nonlinear Reaction’s Diffusion Equation at Conducting Polymer Ultramicroelectrodes

Analytical Solutions of System of Non-Linear Differential Equations in the Single-Enzyme, Single-Substrate Reaction with Non-Mechanism-Based Enzyme Inactivation

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