Displaying similar documents to “Permanence and global exponential stability of Nicholson-type delay systems”

On exponential stability of second order delay differential equations

Ravi P. Agarwal, Alexander Domoshnitsky, Abraham Maghakyan (2015)

Czechoslovak Mathematical Journal

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We propose a new method for studying stability of second order delay differential equations. Results we obtained are of the form: the exponential stability of ordinary differential equation implies the exponential stability of the corresponding delay differential equation if the delays are small enough. We estimate this smallness through the coefficients of this delay equation. Examples demonstrate that our tests of the exponential stability are essentially better than the known ones....

On Exponential Stability of Volterra Difference Equations with Infinite Delay

Pham Huu Anh Ngoc, Le Trung Hieu (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

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General nonlinear Volterra difference equations with infinite delay are considered. A new explicit criterion for global exponential stability is given. Furthermore, we present a stability bound for equations subject to nonlinear perturbations. Two examples are given to illustrate the results obtained.

Boundedness and stability in third order nonlinear differential equations with multiple deviating arguments

Moussadek Remili, Lynda D. Oudjedi (2016)

Archivum Mathematicum

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In this paper, we establish some new sufficient conditions which guarantee the stability and boundedness of solutions of certain nonlinear and non autonomous differential equations of third order with delay. By defining appropriate Lyapunov function, we obtain some new results on the subject. By this work, we extend and improve some stability and boundedness results in the literature.

Uniform Stability In Nonlinear Infinite Delay Volterra Integro-differential Equations Using Lyapunov Functionals

Youssef Raffoul, Habib Rai (2016)

Nonautonomous Dynamical Systems

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In [10] the first author used Lyapunov functionals and studied the exponential stability of the zero solution of finite delay Volterra Integro-differential equation. In this paper, we use modified version of the Lyapunov functional that were used in [10] to obtain criterion for the stability of the zero solution of the infinite delay nonlinear Volterra integro-differential equation [...]

Stability and Boundedness of Solutions of Some Third-order Nonlinear Vector Delay Differential Equation

Larbi Fatmi, Moussadek Remili (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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This paper investigates the stability of the zero solution and uniformly boundedness and uniformly ultimately boundedness of all solutions of a certain vector differential equation of the third order with delay. Using the Lyapunov–Krasovskiĭ functional approach, we obtain a new result on the topic and give an example for the related illustrations.

Stabilization of solutions to a differential-delay equation in a Banach space

J. J. Koliha, Ivan Straškraba (1997)

Annales Polonici Mathematici

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A parameter dependent nonlinear differential-delay equation in a Banach space is investigated. It is shown that if at the critical value of the parameter the problem satisfies a condition of linearized stability then the problem exhibits a stability which is uniform with respect to the whole range of the parameter values. The general theorem is applied to a diffusion system with applications in biology.

On delay-dependent robust stability under model transformation of some neutral systems

Salvador A. Rodríguez, Luc Dugard, Jean-Michel Dion, Jesús de León (2009)

Kybernetika

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This paper focuses on the delay-dependent robust stability of linear neutral delay systems. The systems under consideration are described by functional differential equations, with norm bounded time varying nonlinear uncertainties in the "state" and norm bounded time varying quasi-linear uncertainties in the delayed "state" and in the difference operator. The stability analysis is performed via the Lyapunov-Krasovskii functional approach. Sufficient delay dependent conditions for robust...

Delays induced in population dynamics

Eva Sánchez (2003)

Banach Center Publications

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This paper provides an introduction to delay differential equations together with a short survey on state-dependent delay differential equations arising in population dynamics. Our main goal is to examine how the delays emerge from inner mechanisms in the model, how they induce oscillations and stability switches in the system and how the qualitative behaviour of a biological model depends on the form of the delay.

On delay-dependent stability for neutral delay-differential systems

Qing-Long Han (2001)

International Journal of Applied Mathematics and Computer Science

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This paper deals with the stability problem for a class of linear neutral delay-differential systems. The time delay is assumed constant and known. Delay-dependent criteria are derived. The criteria are given in the form of linear matrix inequalities which are easy to use when checking the stability of the systems considered. Numerical examples indicate significant improvements over some existing results.

New qualitative methods for stability of delay systems

Erik I. Verriest (2001)

Kybernetika

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A qualitative method is explored for analyzing the stability of systems. The approach is a generalization of the celebrated Lyapunov method. Whereas classically, the Lyapunov method is based on the simple comparison theorem, deriving suitable candidate Lyapunov functions remains mostly an art. As a result, in the realm of delay equations, such Lyapunov methods can be quite conservative. The generalization is here in using the comparison theorem directly with a different scalar equation...