An analytical solution for a nonlinear time-delay model in biology

Khan, Hamid; Liao, Shijun; Mohapatra, R. N.; Vajravelu, K.

doi:10.1016/j.cnsns.2008.11.003

Cited by 39 publications

(23 citation statements)

References 14 publications

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“…where Λ is a general Lagrange multiplier, which can be identified optimally via variational theory, the subscript n indexes the order of approximation andx n is considered as restricted variations [16], that is, δx n (t) = 0, δx n (t − τ j ) = 0, j = 1, . .…”

Section: Variational Iteration Methodsmentioning

confidence: 99%

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Solution of linear time-varying multi-delay systems via variational iteration method

Mirhosseini-Alizamini¹,

Effati²,

Heydari³

2016

J. Math. Computer Sci.

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This work presents an approximate solution method for the linear time-varying multi-delay systems and time delay logistic equation using variational iteration method. The method is based on the use of Lagrange multiplier for identification of optimal value of a parameter in a functional. This procedure is a powerful tool for solving large amount of problems. Also, it provides a sequence which converges to the solution of the problem without discretization of the variables. In this study, an idea is proposed that accelerates the convergence of the sequence which results from the variational iteration formula for solving systems of delay differential equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

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Section: Variational Iteration Methodsmentioning

confidence: 99%

“…Properties of Eq. (4.2) were studied very extensively by various authors [12,16]. Now, according to the VIM (3.6), its correction functional of Eq.…”

Section: Application Of the Vim For Nonlinear Time-delay Systemmentioning

confidence: 99%

Solution of linear time-varying multi-delay systems via variational iteration method

Mirhosseini-Alizamini¹,

Effati²,

Heydari³

2016

J. Math. Computer Sci.

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“…Recently authors of [39] applied the homotopy analysis method to develop an analytic approach for nonlinear differential equations with time delay. In [39] a new discontinuous function is defined so as to express the piecewise continuous solutions of time-delay differential equations in a convenient way for symbolic computation.…”

Section: Introductionmentioning

confidence: 99%

“…In [39] a new discontinuous function is defined so as to express the piecewise continuous solutions of time-delay differential equations in a convenient way for symbolic computation.…”

Section: Introductionmentioning

confidence: 99%

Solution of a nonlinear time-delay model in biology via semi-analytical approaches

Dehghan

Salehi

2010

Computer Physics Communications

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“…Perturbation approaches, such as the method of multiple scales and the method of harmonic balance, are widely used to reveal the complex dynamics of nonlinear systems [29][30][31][32][33][34][35][36]. Khan et al [37] investigated a nonlinear model in biology by means of the HAM. A new discontinuous function is defined so as to express the piecewise continuous solutions of timedelay differential equations.…”

Section: Introductionmentioning

confidence: 99%

Analytical approximations for the periodic motion of the Duffing system with delayed feedback

You

2010

Numer Algor

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In this study, the homotopy analysis method is developed to give periodic solutions of delayed differential equations that describe time-delayed position feedback on the Duffing system. With this technique, some approximate analytical solutions of high accuracy for some possible solutions are captured, which agree well with the numerical solutions in the whole time domain. Two examples of dynamic systems are considered, focusing on the periodic motions near a Hopf bifurcation of an equilibrium point. It is found that the current technique leads to higher accurate prediction on the local dynamics of time-delayed systems near a Hopf bifurcation than the energy analysis method or the traditional method of multiple scales.

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An analytical solution for a nonlinear time-delay model in biology

Cited by 39 publications

References 14 publications

Solution of linear time-varying multi-delay systems via variational iteration method

Solution of linear time-varying multi-delay systems via variational iteration method

Solution of a nonlinear time-delay model in biology via semi-analytical approaches

Analytical approximations for the periodic motion of the Duffing system with delayed feedback

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