Results 151 to 160 of about 9,050,649 (204)
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Applicable Analysis, 1987
This paper discusses existence and nonexistence of C1 quasi-steady-states to singularly perturbed problems near a singular point. In contrast to the existence and uniqueness result well known for the same problem near a regular point, the answer depends on generic conditions involving both the differential and the transcendental equations of the system.
Patrick J. Rabier, Shiva Shankar
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This paper discusses existence and nonexistence of C1 quasi-steady-states to singularly perturbed problems near a singular point. In contrast to the existence and uniqueness result well known for the same problem near a regular point, the answer depends on generic conditions involving both the differential and the transcendental equations of the system.
Patrick J. Rabier, Shiva Shankar
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Scale-invariance in singularly perturbed systems
53rd IEEE Conference on Decision and Control, 2014The property termed scale-invariance, or fold-change detection, represents a phenomenon that is observed in a variety of biological systems, ranging from bacterial to eukaryotic signaling pathways. Mathematically, it represents invariance of the complete output trajectory with respect to a rescaling of input magnitudes.
Maja Skataric +2 more
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On hopf bifurcations in singularly perturbed systems
IEEE Transactions on Automatic Control, 2003It has been shown recently that, under some generic assumptions, there exists a Hopf curve /spl lambda/ = /spl lambda/ (/spl epsiv/) for singularly perturbed systems of the form x/spl dot/ = f (x, y, /spl lambda/), /spl epsiv/y/spl dot/ = g(x, y, /spl lambda/) near the singular surface defined by det g/sub v/ = 0.
L. Yang, Yun Tang, Dongyun Du
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1984
In this chapter we turn our attention to some vector boundary value problems which may be regarded as vector analogs of the scalar problems. However, as the reader will see, our results for vector problems are very incomplete, especially in comparison with the scalar theory.
K. W. Chang, F. A. Howes
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In this chapter we turn our attention to some vector boundary value problems which may be regarded as vector analogs of the scalar problems. However, as the reader will see, our results for vector problems are very incomplete, especially in comparison with the scalar theory.
K. W. Chang, F. A. Howes
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Dissipativity of Singularly Perturbed Lur’e Systems
IEEE Transactions on Circuits and Systems II: Express Briefs, 2019The problem of singularly perturbed Lur’e systems is investigated in this brief. Two new storage functions are constructed to explore the dynamics of both the fast and slow models, as well as their interaction more efficiently. By using the merit of the proposed storage functions, some new $\varepsilon $ -uniformly strict dissipativity criteria in
Yan-Wu Wang +3 more
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Singularly Perturbed Semilinear Systems
Studies in Applied Mathematics, 1979Solutions of a singularly perturbed vector boundary‐value problem are studied under the principal assumption that the trivial solution of the unperturbed equation is stable in certain senses. This is accomplished by constructing special invariant regions in which solutions display the kind of nonuniformity known as boundary‐layer behavior.
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Stabilization of Singularly Perturbed Fuzzy Systems
IEEE Transactions on Fuzzy Systems, 2004This paper presents some novel results for stabilizing singularly perturbed (SP) nonlinear systems with guaranteed control performance. By using Takagi-Sugeno fuzzy model, we construct the SP fuzzy (SPF) systems. The corresponding fuzzy slow and fast subsystems of the original SPF system are also obtained. Two fuzzy control designs are explored. In the
Tzuu-Hseng S. Li, Kuo-Jung Lin
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Discrete Approximations of Singularly Perturbed Systems
2007In the paper we study discrete approximations of singularly perturbed system in a finite dimensional space. When the right-hand side is almost upper semicontinuous with convex compact values and one-sided Lipschitz we show that the distance between the solution set of the original and the solution set of the discrete system is O(h1/2.
Tzanko Donchev, Vasile Lupulescu
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On parametric instability of singularly perturbed systems
Automation and Remote Control, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Anatoliy A. Martynyuk, A. S. Khoroshun
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Singularly Perturbed Systems of Volterra Equations
Journal of Applied Analysis, 2002This paper studies the behaviour of the solution \(u(t,\varepsilon)\) of the system of Volterra integral equations \[ \varepsilon u(t) = f(t) + \int_0^t A(t,s)u(s)\,ds, \quad 0 \leq t \leq T, \] as the positive parameter \(\epsilon\) tends to zero. Both \(f\) and \(A\) are continuous, and the eigenvalues of \(A(t,t)\) are supposed to be negative.
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