Tikhonov theorem for differential equations with singular impulses

Download
index.pdf
2018-01-01
Akhmet, Marat
Show full item record
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
36
views
0
downloads
The paper considers impulsive systems with singularities. The main novelty of the present research is that impulses (impulsive functions) are singular. This is beside singularity of differential equations. The Lyapunov second method is applied to proof the main theorems. Illustrative examples with simulations are given to support the theoretical results.
Singular differential equations, Tikhonov theorem, Singular impulsive functions, Lyapunov second method
https://hdl.handle.net/11511/38719
Discontinuity, Nonlinearity, and Complexity
Department of Mathematics, Article

Suggestions

Discrete linear Hamiltonian systems: Lyapunov type inequalities, stability and disconjugacy criteria
Zafer, Ağacık (2012-12-15)
In this paper, we first establish new Lyapunov type inequalities for discrete planar linear Hamiltonian systems. Next, by making use of the inequalities, we derive stability and disconjugacy criteria. Stability criteria are obtained with the help of the Floquet theory, so the system is assumed to be periodic in that case.
Periodic solutions and stability of linear impulsive delay differential equations
ALZabut, Jehad; Ağacık, Zafer; Department of Mathematics (2004)
In this thesis, we investigate impulsive differential systems with delays of the form And more generally of the form The dissertation consists of five chapters. The first chapter serves as introduction, contains preliminary considerations and assertions that will be encountered in the sequel. In chapter 2, we construct the adjoint systems and obtain the variation of parameters formulas of the solutions in terms of fundamental matrices. The asymptotic behavior of solutions of systems satisfying the Perron co...
Boundary value problems for higher order linear impulsive differential equations
Uğur, Ömür; Akhmet, Marat; Taşeli, Hasan; Department of Mathematics (2003)
The theory of impulsive di®erential equations has become an important area of research in recent years. Linear equations, meanwhile, are fundamental in most branches of applied mathematics, science, and technology. The theory of higher order linear impulsive equations, however, has not been studied as much as the cor- responding theory of ordinary di®erential equations. In this work, higher order linear impulsive equations at xed moments of impulses together with certain boundary conditions are investigated...
Global exponential stability of neural networks with non-smooth and impact activations
Akhmet, Marat (2012-10-01)
In this paper, we consider a model of impulsive recurrent neural networks with piecewise constant argument. The dynamics are presented by differential equations with discontinuities such as impulses at fixed moments and piecewise constant argument of generalized type. Sufficient conditions ensuring the existence, uniqueness and global exponential stability of the equilibrium point are obtained. By employing Green's function we derive new result of existence of the periodic solution. The global exponential s...
Morphing of transient sounds based on shift invariant discrete wavelet transform and singular value decomposition
Ahmad, Wasim; Hacıhabiboğlu, Hüseyin; kondoz, ahmet (2009-04-19)
In this paper, a new morphing algorithm for transient sounds is introduced. Input sounds are first projected onto orthogonal bases from which intermediate or novel sounds can be generated. The proposed algorithm uses a shift invariant version of discrete wavelet transform and the singular value decomposition (SVD) to represent the input sound signals over a set of orthogonal bases. Interpolation is carried out between the weight vectors from the SVD to produce a new weight vector used for synthesising a new...
Citation Formats
M. Akhmet, “Tikhonov theorem for differential equations with singular impulses,” Discontinuity, Nonlinearity, and Complexity, pp. 291–303, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/38719.
METU IIS - Integrated Information Service open@metu.edu.tr