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We consider a class of ordinary differential equations describing one-dimensional systems with a quasi-periodic forcing term and in the presence of large damping. We discuss the conditions to be assumed on the mechanical force and the…
We consider a class of singular ordinary differential equations describing analytic systems of arbitrary finite dimension, subject to a quasi-periodic forcing term and in the presence of dissipation. We study the existence of response…
This paper develops a characterisation of when solutions of forced second order linear differential equations converge to the zero solution of the asymptotically stable and unforced second order equation, or when the solution is bounded,…
In this article, we investigate the existence and properties of time-periodic solutions for damped evolutionary partial differential equations subject to periodic forcing. Particular emphasis is placed on configurations where the energy…
A typical system of k difference (or differential) equations can be compressed, or folded into a difference (or ordinary differential) equation of order k. Such foldings appear in control theory as the canonical forms of the controllability…
This paper considers random Hill's equations in the limit where the periodic forcing function becomes a Dirac delta function. For this class of equations, the forcing strength $q_k$, the oscillation frequency $\af_k$, and the period are…
This article concerns time-periodic solutions to a two-dimensional Sellers-type energy balance model coupled to the three-dimensional primitive equations via a dynamic boundary condition. It is shown that the underlying equations admit at…
We consider the graph dynamical systems known as k-reversible processes. In such processes, each vertex in the graph has one of two possible states at each discrete time step. Each vertex changes its state between the current time and the…
We study the propagation of energy in one-dimensional anharmonic chains subject to a periodic, localized forcing. For the purely harmonic case, forcing frequencies outside the linear spectrum produce exponentially localized responses,…
If time is described by a fundamental process rather than a coordinate, it interacts with any physical system that evolves in time. The resulting dynamics is shown here to be consistent provided the fundamental period of the time system is…
We consider a class of ordinary differential equations describing one-dimensional quasiperiodically forced systems in the presence of large damping. We give a fully constructive proof of the existence of response solutions, that is…
We study the dynamics of the positive solutions of a second-order, Ricker-type exponential difference equation with periodic parameters. We find that qualitatively different dynamics occur depending on whether the period p of the main…
In this Note, we describe the stationary equilibria and the asymptotic behaviour of an heterogeneous logistic reaction-diffusion equation under the influence of autonomous or time-periodic forcing terms. We show that the study of the…
We consider several models (including both multidimensional ordinary differential equations (ODEs) and partial differential equations (PDEs), possibly ill-posed), subject to very strong damping and quasi-periodic external forcing. We study…
The paper studies solutions of stochastic partial differential equations with random initial conditions. First, it overviews some of the known results on scaled solutions of such equations and provides several explicit motivating examples.…
We relate the convergence of time-changed processes driven by fractional equations to the convergence of corresponding Dirichlet forms. The fractional equations we dealt with are obtained by considering a general fractional operator in…
The influence of a time-periodic forcing on stochastic processes can essentially be emphasized in the large time behaviour of their paths. The statistics of transition in a simple Markov chain model permits to quantify this influence. In…
A functional limit theorem is established for the partial-sum process of a class of stationary sequences which exhibit both heavy tails and long-range dependence. The stationary sequence is constructed using multiple stochastic integrals…
The article studies the reiterated homogenization of linear elliptic variational inequalities arising in problems with unilateral constrains. We assume that the coefficients of the equations satisfy and abstract hypothesis covering on each…
We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation…