Author
Hongjiong Tian
Other affiliations: University of Manchester
Bio: Hongjiong Tian is an academic researcher from Shanghai Normal University. The author has contributed to research in topics: Numerical stability & Differential algebraic equation. The author has an hindex of 12, co-authored 31 publications receiving 495 citations. Previous affiliations of Hongjiong Tian include University of Manchester.
Papers
More filters
TL;DR: In this article, the asymptotic stability of theoretical solutions and numerical methods for systems of neutral differential equations is investigated, where A, B, and C are constant complex N × N matrices, and τ > 0.
Abstract: This paper deals with the asymptotic stability of theoretical solutions and numerical methods for systems of neutral differential equationsx′=Ax′(t−τ)+Bx(t)+Cx(t−τ), whereA, B, andC are constant complexN ×N matrices, and τ>0 A necessary and sufficient condition such that the differential equations are asymptotically stable is derived We also focus on the numerical stability properties of adaptations of one-parameter methods Further, we investigate carefully the characterization of the stability region
95 citations
TL;DR: In this paper, the exponential stability of singularly perturbed delay DDEs with a bounded (state-independent) lag was studied and a sufficient condition was provided to ensure that any solution of the DDE is exponentially stable uniformly for sufficiently small e > 0.
87 citations
TL;DR: A generalized Halanay inequality is derived, and a sufficient condition is presented to ensure that delay differential equations with a bounded variable lag are dissipative, and θ-method is applied.
Abstract: This paper focuses on the analytic and numerical dissipativity of θ-method for delay differential equations with a bounded variable lag. A generalized Halanay inequality is derived, and a sufficient condition is presented to ensure that delay differential equations with a bounded variable lag are dissipative. We then apply θ-method to such delay differential equations, and investigate the numerical dissipativity of the θ-method.
46 citations
TL;DR: In this article, the existence of almost periodic solutions of nonlinear discrete Volterra equations with unbounded delay is obtained by using stability properties of a bounded solution, which is the same as in this paper.
29 citations
TL;DR: In this article, a semi-explicit form of delay differential algebraic equations with after-effect is considered, and the complexity and obstacles that can arise when solving these problems are highlighted.
28 citations
Cited by
More filters
2,084 citations
Book•
06 May 1998
TL;DR: Orthogonal approximations in Sobolev spaces stability and convergence spectral methods and pseudospectral methods spectral methods for multi-dimensional and high order problems mixed spectral methods combined spectral methods spectral method on the spherical surface as discussed by the authors.
Abstract: Orthogonal approximations in Sobolev spaces stability and convergence spectral methods and pseudospectral methods spectral methods for multi-dimensional and high order problems mixed spectral methods combined spectral methods spectral methods on the spherical surface.
365 citations
TL;DR: In this article, a generalized model of neural networks involving time-varying delays and impulses is considered, and sufficient conditions for global exponential stability of impulsive delay model are obtained.
263 citations
TL;DR: In this article, the dissipativity of theoretical solutions to nonlinear Volterra functional differential equations (VFDEs) is studied. And the authors give some generalizations of Halanay's inequality which play an important role in study of dissipativity and stability of differential equations.
129 citations
Book•
01 Jan 1975
TL;DR: In this paper, Liapunov functions are used to define the boundary value problem in almost periodic systems, and the existence of almost periodic solutions is proved by the existence theorems for Periodic Solutions.
Abstract: I. Preliminaries.- 1. Liapunov Functions.- 2. Almost Periodic Functions.- 3. Asymptotically Almost Periodic Functions.- 4. Quasi-Periodic Functions.- 5. Boundary Value Problem.- II. Stability and Boundedness.- 6. Stability of a Solution.- 7. Asymptotic Stability of a Solution.- 8. Boundedness of Solutions.- 9. Asymptotic Stability in the Large.- 10. Asymptotic Behavior of Solutions.- 11. Converse Theorems.- 12. Total Stability.- 13. Inherited Properties in Almost Periodic Systems.- 14. Uniformly Asymptotic Stability in Almost Periodic Systems.- III. Existence Theorems for Periodic Solutions and Almost Periodic Solutions.- 15. Existence Theorems for Periodic Solutions.- 16. Existence Theorems for Almost Periodic Solutions.- 17. Separation Condition in Almost Periodic Systems.- 18. Uniform Stability and Existence of Almost Periodic Solutions.- 19. Existence of Almost Periodic Solutions by Liapunov Functions.- References.
127 citations