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Stability Theory
Stability of solutions is an important qualitative property in linear as well as nonlinear systems. The objective of this chapter is to introduce...
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Spectral Theory, Stability and Continuation
We review concepts to describe stability and hyperbolicity of nonautonomous ordinary differential equations based on their linearisation, namely...
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Spectral Theory, Stability and Continuation
In the framework of nonautonomous difference equations, we review tools to describe stability and hyperbolicity based on their linearisation, namely...
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Introduction to Stability Theory with Applications to Mechanics
In this chapter we introduce the basics in the theory of Lyapunov stability, which was first formulated at the end of the nineteenth century.
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Linear Stability
This chapter is devoted to presenting the theory of linear stability for numerical methods solving ODEs. Characteristic properties occurring when the...
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Input-to-State Stability Theory and Applications
Input-to-State Stabilitypresents the dominating stability paradigm in nonlinear control theory that revolutionized our view on stabilization of...
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Time scale theory on stability of explicit and implicit discrete epidemic models: applications to Swine flu outbreak
Time scales theory has been in use since the 1980s with many applications. Only very recently, it has been used to describe within-host and...
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Matrix Inequalities in the Stability Theory: New Results Based on the Convolution Theorem
AbstractUsing Pyatnitskiy’s convolution theorem, the circle criterion of absolute stability for Lurie systems with several nonlinearities is obtained...
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A kinetic theory approach to modeling prey–predator ecosystems with expertise levels: analysis, simulations and stability considerations
In this paper a kinetic modeling approach for an ecological system is proposed, based on the prey–predator structure in terms of individuals...
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Mittag-Leffler stability and Lyapunov stability for a problem arising in porous media
A fractional order problem arising in porous media is considered. Well-posedness as well as stability are discussed. Mittag-Leffler stability is...
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Practical Semiglobal Uniform Exponential Stability Of Nonlinear Nonautonomous Systems
We solve the following twofold problem: In the first part, we deduce Lyapunov sufficient conditions for the practical uniform exponential stability...
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Strong well-posedness, stability and optimal control theory for a mathematical model for magneto-viscoelastic fluids
In this article, we study the strong well-posedness, stability and optimal control of an incompressible magneto-viscoelastic fluid model in two...
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Testability in group theory
This paper is a journal counterpart to [5], in which we initiate the study of property testing problems concerning a finite system of relations E ...
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On Using the Shell Theory in Stability Analysis of Fluid Flows in Compliant Pipes
AbstractThe linear stability of the Poiseuille flow in a compliant pipe of circular cross-section is numerically analyzed using two different wall...
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Stability conditions and Teichmüller space
We consider a 3-Calabi–Yau triangulated category associated to an ideal triangulation of a marked bordered surface. Using the theory of harmonic maps...
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Input-to-State Stability of Infinite Networks
Stability analysis and control of ODE systems remain the backbone of much of systems theory.
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Normal Forms and Stability of Hamiltonian Systems
This book introduces the reader to the study of Hamiltonian systems, focusing on the stability of autonomous and periodic systems and expanding to...
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Computation of the Evolution of Tollmien–Schlichting Waves Based on Global Stability Analysis
AbstractA computational methodology is presented for calculating the spatial evolution of Tollmien–Schlichting (T–S) waves and their amplitude...
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Global stability for a new predator–prey model with cross-dispersal among patches based on graph theory
In this paper, cross-dispersal is considered in a predator–prey model with a patchy environment. A new predator–prey model with cross-dispersal among...
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Partial Stability of Systems of Itô Linear Delay Differential Equations
AbstractWe study the moment stability of solutions in part of the variables with respect to the initial data for systems of Itô linear delay...