Related papers: Averaging method for quasi-periodic response solut…
We study the Kaczmarz methods for solving systems of quadratic equations, i.e., the generalized phase retrieval problem. The methods extend the Kaczmarz methods for solving systems of linear equations by integrating a phase selection…
A well-behaved adjoint sensitivity technique for chaotic dynamical systems is presented. The method arises from the specialisation of established variational techniques to the unstable periodic orbits of the system. On such trajectories,…
Nonlinear control-affine systems described by ordinary differential equations with bounded measurable input functions are considered. The solvability of general boundary value problems for these systems is formulated in the sense of…
A singularly perturbed linear system of second order ordinary differential equations of reaction-diffusion type with given boundary conditions is considered. The leading term of each equation is multiplied by a small positive parameter.…
In this paper we suggest a moment matching method for quadratic-bilinear dynamical systems. Most system-theoretic reduction methods for nonlinear systems rely on multivariate frequency representations. Our approach instead uses univariate…
In this paper, we propose a model averaging approach for addressing model uncertainty in the context of partial linear functional additive models. These models are designed to describe the relation between a response and mixed-types of…
Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some…
The problem of the effect of two-frequency quasi-periodic perturbations on systems close to arbitrary nonlinear two-dimensional Hamiltonian ones is studied in the case when the corresponding perturbed autonomous systems have a double limit…
In this paper, we propose quasilinearization methods that convert nonlocal fully-nonlinear parabolic systems into the nonlocal quasilinear parabolic systems. The nonlocal parabolic systems serve as important mathematical tools for modelling…
Response solutions are quasi-periodic ones with the same frequency as the forcing term. The present work is devoted to constructing response solutions for $d$-dimensional nonlinear plate models with nonlocal energy damping, which are…
This article describes a method for constructing approximations to periodic solutions of dynamic Lorenz system with classical values of the system parameters. The author obtained a system of nonlinear algebraic equations in general form…
We introduce a generalization of Glimm's random choice method, which provides us with an approximation of entropy solutions to quasilinear hyperbolic system of balance laws. The flux-function and the source term of the equations may depend…
Quasinormal modes describe the ringdown of compact objects deformed by small perturbations. In generic theories of gravity that extend General Relativity, the linearized dynamics of these perturbations is described by a system of coupled…
This paper concerns the existence of multiple rotating quasi-periodic solutions for second order Hamiltonian systems with sub-quadratic potential. Such solutions have the form $x(t+T)=Qx(t)$ for some orthogonal matrix $Q$. To deal with such…
We examine the influence of quasi-periodic boundary conditions on the phenomenon of revivals in linear dispersive PDEs. We show that, in general, quasi-periodic problems do not support the revival effect at rational times. Our method is…
In the modelling of stochastic phenomena, such as quasi-reaction systems, parameter estimation of kinetic rates can be challenging, particularly when the time gap between consecutive measurements is large. Local linear approximation…
We consider existence and stability of an almost periodic solution of the quasilinear system of differential equations with piecewise constant argument of generalized type. The associated linear homogeneous system satisfies exponential…
We consider several models of nonlinear wave equations subject to very strong damping and quasi-periodic external forcing. This is a singular perturbation, since the damping is not the highest order term. We study the existence of response…
The main aim of this work is to present two different methodologies for configuration averaging in disordered systems. The Recursion method is suitable for the calculation of spatial or self-averaging, while the Augmented space formalism…
The Kaczmarz method for solving linear systems of equations is an iterative algorithm that has found many applications ranging from computer tomography to digital signal processing. Despite the popularity of this method, useful theoretical…