Related papers: On the Stability of Multilinear Dynamical Systems
We investigate the stability properties of discrete and hybrid stochastic nonlinear dynamical systems. More precisely, we extend the stochastic contraction theorems (which were formulated for continuous systems) to the case of discrete and…
The stability radius for finitely many interconnected linear exponentially stable well-posed systems with respect to static perturbations is studied. If the output space of each system is finite-dimensional, then a lower bound for the…
Many nonlinear dynamical systems can be written as Lure systems, which are described by a linear time-invariant system interconnected with a diagonal static sector-bounded nonlinearity. Sufficient conditions are derived for the global…
A model of nonlinear elastic medium with internal structure is considered. The medium is assumed to contain cavities, microcracks or blotches of substances that differ sharply in physical properties from the base material. To describe the…
In this paper, Van der pol equation has been analyzed for stability and bifurcation phenomena with and without forcing component. Analytical solution of the Van der pol equation using Method of Multiple Scales (MMS) is compared with…
General asymptotic approach to the stability problem of multi-parameter solitons in Hamiltonian systems $i\partial E_n/\partial z=\delta H/\delta E_n^*$ has been developed. It has been shown that asymptotic study of the soliton stability…
Learning stable dynamics from observed time-series data is an essential problem in robotics, physical modeling, and systems biology. Many of these dynamics are represented as an inputs-output system to communicate with the external…
Dynamical networks with time delays can pose a considerable challenge for mathematical analysis. Here, we extend the approach of generalized modeling to investigate the stability of large networks of delay-coupled delay oscillators. When…
Reaction-diffusion equations coupled to ordinary differential equations (ODEs) may exhibit spatially low-regular stationary solutions. This work provides a comprehensive theory of asymptotic stability of bounded, discontinuous or…
The existence and stability of stable bright solitons in one-dimensional (1D) media with a spatially periodical modulated Kerr nonlinearity are demonstrated by means of the linear-stability analysis and in direct numerical simulations. The…
Peixoto's structural stability and density theorems represent milestones in the modern theory of dynamical systems and their applications. Despite the importance of these theorems, they are often treated rather superficially, if at all, in…
This paper investigates oscillation-free stability conditions of numerical methods for linear parabolic partial differential equations with some example extrapolations to nonlinear equations. Not clearly understood, numerical oscillations…
This paper develops a new approach to the estimation of the degree of boundedness or stability of multidimensional nonlinear systems with time-dependent nonperiodic coefficients-an essential task in various engineering and natural science…
In this work, we study continuity and topological structural stability of attractors for nonautonomous random differential equations obtained by small bounded random perturbations of autonomous semilinear problems. First, we study existence…
We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…
We carry out a comprehensive linear stability analysis of active Brownian particle systems around a constant homogeneous state. These scalar models, being important prototypes for the continuous description of active matter, are…
This article is focused on two related topics within the study of partial differential equations (PDEs) that illustrate a beautiful connection between dynamics, topology, and analysis: stability and spatial dynamics. The first is a property…
This paper deals with the global stability of time-delayed dynamical networks. We show that for a time-delayed dynamical network with non-distributed delays the network and the corresponding non-delayed network are both either globally…
Finding separable certificates of stability is important for tractability of analysis methods for large-scale networked systems. In this paper we consider the question of when a nonlinear system which is contracting, i.e. all solutions are…
A nonlinear Schr\"odinger equation with repulsive (defocusing) nonlinearity is considered. As an example, a system with a spatially varying coefficient of the nonlinear term is studied. The nonlinearity is chosen to be repelling except on a…