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In this paper, instability at an interface between two miscible liquids with identical mechanical properties but different electrical conductivities is analyzed in the presence of an electric field that is perpendicular to the interface. A…
Linear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote…
We consider constrained partial differential equations of hyperbolic type with a small parameter $\varepsilon>0$, which turn parabolic in the limit case, i.e., for $\varepsilon=0$. The well-posedness of the resulting systems is discussed…
Various types of stabilizing controls lead to a deterministic difference equation with the following property: once the initial value is positive, the solution tends to the unique positive equilibrium. Introducing additive perturbations can…
New explicit conditions of asymptotic and exponential stability are obtained for the scalar nonautonomous linear delay differential equation $$ \dot{x}(t)+\sum_{k=1}^m a_k(t)x(h_k(t))=0 $$ with measurable delays and coefficients. These…
Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic…
We consider the stability of a system of equations which are a singular perturbation of the incompressible rigid-plastic flow equations used to model granular flow. A linear stability analysis shows that solutions of these equations are…
Necessary and sufficient conditions for the internal stability of formations whose dynamics are obtained is determined by linear differential equations.
We obtain sharp criteria for transverse stability and instability of line solitons in the discrete nonlinear Schr\"{o}dinger equations on one- and two-dimensional lattices near the anti-continuum limit. On a two-dimensional lattice, the…
For nonautonomous linear difference equations, we introduce the notion of the so-called nonuniform dichotomy spectrum and prove a spectral theorem. Moreover, we introduce the notion of weak kinematical similarity and prove a reducibility…
For a discrete dynamics defined by a sequence of bounded and not necessarily invertible linear operators, we give a complete characterization of exponential stability in terms of invertibility of a certain operator acting on suitable Banach…
The paper discusses linear fractional representations of parameter-dependent nonlinear systems with dynamics defined by real rational nonlinearities and a finite set of point delays. The global asymptotic stability is investigated via…
The paper deals with the problem of existence of a convergent "strong" normal form in the neighbourhood of an equilibrium, for a finite dimensional system of differential equations with analytic and time-dependent non-linear term. The…
We propose a definition of equilibrium and non-equilibrium states in dynamical systems on the basis of the time average. We show numerically that there exists a non-equilibrium non-stationary state in the coupled modified Bernoulli map…
We show that hyperbolicity is a necessary condition for the well posedness of the noncharacteristic Cauchy problem for nonlinear partial differential equations. We give conditions on the initial data which are necessary for the existence of…
In this paper we consider the global stability of solutions of an affine stochastic differential equation. The differential equation is a perturbed version of a globally stable linear autonomous equation with unique zero equilibrium where…
In this paper, we prove the partial linearization for n-dimensional nonautonomous differential equations. The conditions are formulated in terms of the dichotomy spectrum.
The stability analysis of a class of discontinuous discrete-time systems is studied in this paper. The system under study is modeled as a feedback interconnection of a linear system and a set-valued nonlinearity. An equivalent…
In this paper, we study the asymptotic behavior of solutions to a scalar fractional delay differential equations around the equilibrium points. More precise, we provide conditions on the coefficients under which a linear fractional delay…
A class of linear hyperbolic partial differential equations, sometimes called networks of waves, is considered. For this class of systems, necessary and sufficient conditions are formulated on the system matrices for the operator dynamics…