Related papers: Characteristic matrices for linear periodic delay …
In the paper Lax pairs for linear Hamiltonian systems of differential equations are constructed. In particular, Gr\"obner bases are used for the computations. It is proved that the maps which appear in the construction of Lax pairs are…
This work is the first attempt to treat partial differential equations with discrete (concentrated) state-dependent delay. The main idea is to approximate the discrete delay term by a sequence of distributed delay terms (all with…
We present initially the motivation, definition and basic properties of differential equations with proportional delay. In the last Section we present open problems.
The problem considered in the paper is exponential stability of linear equations and global attractivity of nonlinear non-autonomous equations which include a non-delay term and one or more delayed terms. First, we demonstrate that…
Answering a question of Frank Calegari, we extend some of our earlier results on dimension of fixed point spaces of elements in irreducible linear groups. We consider characteristic polynomials rather than just fixed spaces.
We develop the theory of linear evolution equations associated with the adjacency matrix of a graph, focusing in particular on infinite graphs of two kinds: uniformly locally finite graphs as well as locally finite line graphs. We discuss…
This work deals with a scalar nonlinear neutral delay differential equation issued from the study of wave propagation. A critical value of the coefficients is considered, where only few results are known. The difficulty follows from the…
We extend the definition of $n$-dimensional difference equations to complex order $\alpha\in \mathbb{C} $. We investigate the stability of linear systems defined by an $n$-dimensional matrix $A$ and derive conditions for the stability of…
Numerical computations involving rational matrices often benefit from preserving underlying matrix structures such as symmetry, Hermitian properties, or sparsity that reflect physical, geometric, or algebraic characteristics of the system.…
Real-world systems can be strongly influenced by time delays occurring in self-coupling interactions, due to unavoidable finite signal propagation velocities. When the delays become significantly long, complicated high-dimensional phenomena…
One considers certain degenerations of the generic symmetric matrix over a field $k$ of characteristic zero and the main structures related to the determinant $f$ of the matrix, such as the ideal generated by its partial derivatives, the…
We consider the class of two-lag linear delay differential equations and develop a series expansion to solve for the roots of the nonlinear characteristic equation. Supporting numerical results are presented along with application of our…
We develop a new generalized coupling approach to the study of stochastic delay equations with H\"older continuous coefficients, for which analytical PDE-based methods are not available. We prove that such equations possess unique weak…
Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topological conjugacy, which only requires qualitative similarity.…
There has been a long-standing and at times fractious debate whether complex and large systems can be stable. In ecology, the so-called `diversity-stability debate' arose because mathematical analyses of ecosystem stability were either…
Parabolic differential equations with discrete state-dependent delay are studied. The approach, based on an additional condition on the delay function introduced in [A.V. Rezounenko, Differential equations with discrete state-dependent…
Complex periodic structures inherit spectral properties from the constituent parts of their unit cells, chiefly their spectral band gaps. Exploiting this intuitive principle, which is made precise in this work, means spectral features of…
In this work, we shall consider the existence and uniqueness of stationary solutions to stochastic partial functional differential equations with additive noise in which a neutral type of delay is explicitly presented. We are especially…
The aim of this article is to show that systems of linear partial differential equations on filtered manifolds, which are of weighted finite type, can be canonically rewritten as first order systems of a certain type. This leads immediately…
The solvability of a delay differential equation arising in the construction of quadratic cost functionals, i.e. Lyapunov functionals, for a linear time-delay system with a constant and a distributed delay is investigated. We present a…