Stability of functional differential equations of neutral type
Marianito A. Cruz,Jack K. Hale +1 more
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In this paper, the authors give sufficient conditions for the stability and instability of solutions of a large class of equations (1.1) in terms of functions similar to those occurring in the application of the second method of Liapunov to ordinary and functional differential equations of retarded type.About:
This article is published in Journal of Differential Equations.The article was published on 1970-03-01 and is currently open access. It has received 147 citations till now. The article focuses on the topics: Differential equation & Stochastic partial differential equation.read more
Citations
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Journal ArticleDOI
Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)
Journal ArticleDOI
Self-Sustained Oscillations in a Ring Array of Coupled Lossless Transmission Lines
Jianhong Wu,Huaxing Xia +1 more
TL;DR: In this paper, the authors derived a neutral difference-differential system with diffusion which arises from a ring array of coupled lossless transmission lines and applied a global Hopf bifurcation theorem to establish the existence of multiple large amplitude phase-locked periodic solutions in the corresponding neutral system.
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Brief paper: Lyapunov-Krasovskii functional for uniform stability of coupled differential-functional equations
TL;DR: The Lyapunov-Krasovskii functional approach for the stability problem of coupled differential-functional equations, which includes, as special cases, many types of time-delay systems, including the lossless propagation model, some neutral time- Delay systems and singular time- delay systems.
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Small gain problem in coupled differential‐difference equations, time‐varying delays, and direct Lyapunov method
TL;DR: In this paper, a Lyapunov-Krasovskii formulation of scaled small gain problem for systems described by coupled differential-difference equations is presented, where a discretization may be applied to reduce the conditions into linear matrix inequalities.
References
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Book
Differential-Difference Equations
Richard Bellman,Kenneth L. Cooke +1 more
TL;DR: In this paper, the authors introduce the study of differential difference equations and discuss some of the main features of the theory, and discuss the asymptotic behavior of solutions and the problem of stability.
Journal ArticleDOI
Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)
Journal ArticleDOI
Dynamical systems and stability
TL;DR: Topologies introduced on state space for differential equations to obtain dynamical systems were introduced in this article, where the state space was used to obtain the dynamical system topology of dynamical networks.
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Existence, uniqueness and continuous dependence for hereditary systems
TL;DR: In this article, a class of hereditary systems which includes functional differential equations of retarded type and many equations of neulral type as well as Volterra integral equations are studied.