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Encyclopedia of Theoretical Ecology, 2019
where x t ( ) x (t ) and 0. Observe that xt ( ) with 0 represents a portion of the solution trajectory in a recent past. Here, f is a functional operator that takes a time input and a continuous function xt ( ) with 0 and generates a real number (dx (t )/
Y. Kuang
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where x t ( ) x (t ) and 0. Observe that xt ( ) with 0 represents a portion of the solution trajectory in a recent past. Here, f is a functional operator that takes a time input and a continuous function xt ( ) with 0 and generates a real number (dx (t )/
Y. Kuang
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Mathematische Nachrichten, 2020
New oscillation criteria for the second‐order Emden–Fowler delay differential equation with a sublinear neutral term are presented. An essential feature of our results is that oscillation of the studied equation is ensured via only one condition ...
J. Džurina +3 more
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New oscillation criteria for the second‐order Emden–Fowler delay differential equation with a sublinear neutral term are presented. An essential feature of our results is that oscillation of the studied equation is ensured via only one condition ...
J. Džurina +3 more
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Physica Scripta, 2021
In this paper, we modified the Predictor-Corrector scheme to simulate the delay differential equations in new generalised Caputo-type non-classical derivatives sense. We provided some numerical illustrations to exhibit availability of the algorithm. From
Z. Odibat +3 more
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In this paper, we modified the Predictor-Corrector scheme to simulate the delay differential equations in new generalised Caputo-type non-classical derivatives sense. We provided some numerical illustrations to exhibit availability of the algorithm. From
Z. Odibat +3 more
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A Novel Approach to Mean Square Exponential Stability of Stochastic Delay Differential Equations
IEEE Transactions on Automatic Control, 2021We present a novel approach to the mean square exponential stability of stochastic delay differential equations. Consequently, some new explicit criteria for the mean square exponential stability of general nonlinear stochastic delay differential ...
P. H. A. Ngoc, Le Trung Hieu
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2010
Dynamical systems with delay (which we simply designate hereafter as delay dynamical systems or delay systems) are abundant in nature. They occur in a wide variety of physical, chemical, engineering, economic and biological systems and their networks. One can cite many examples where delay plays an important role.
M. Lakshmanan, D.V. Senthilkumar
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Dynamical systems with delay (which we simply designate hereafter as delay dynamical systems or delay systems) are abundant in nature. They occur in a wide variety of physical, chemical, engineering, economic and biological systems and their networks. One can cite many examples where delay plays an important role.
M. Lakshmanan, D.V. Senthilkumar
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Complex Delay-Differential Equations
2021Kai Liu, Ilpo Laine, Lianzhong Yang
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2012
In this chapter we study general non-autonomous delay differential equations of the form $$\dot{x}(t) = F(t,x(t),x(t - \rho (t))).$$ Our intention is to demonstrate how pullback attractors can be used to investigate the behaviour of such models.
Alexandre N. Carvalho +2 more
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In this chapter we study general non-autonomous delay differential equations of the form $$\dot{x}(t) = F(t,x(t),x(t - \rho (t))).$$ Our intention is to demonstrate how pullback attractors can be used to investigate the behaviour of such models.
Alexandre N. Carvalho +2 more
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Mathematical methods in the applied sciences, 2020
In this paper, we consider a Cauchy problem for a Caputo‐type time delay linear system of fractional differential equations with permutable matrices.
Ismail T. Huseynov, N. Mahmudov
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In this paper, we consider a Cauchy problem for a Caputo‐type time delay linear system of fractional differential equations with permutable matrices.
Ismail T. Huseynov, N. Mahmudov
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Sharp oscillation criteria for second‐order neutral delay differential equations
Mathematical methods in the applied sciences, 2020This paper is a continuation of a recent work by the authors on the oscillatory properties of second‐order half‐linear neutral delay differential equations.
M. Bohner, S. Grace, I. Jadlovská
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