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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…
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…
Frequency responses of multi-degree-of-freedom mechanical systems with weak forcing and damping can be studied as perturbations from their conservative limit. Specifically, recent results show how bifurcations near resonances can be…
We study the behaviour of one-dimensional strongly dissipative systems subject to a quasi-periodic force. In particular we are interested in the existence of response solutions, that is quasi-periodic solutions having the same frequency…
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…
This paper provides two results that are useful in the study of the existence and the stability properties of a periodic solution for a given dynamical system. The first result deals with scalar time-periodic systems and establishes the…
We prove Lr-estimates on periodic solutions of periodically-forced, linearly-damped mechanical systems with polynomially-bounded potentials. The estimates are applied to obtain a non-existence result of periodic solutions in bounded…
We consider quasi-periodically systems in the presence of dissipation and study the existence of response solutions, i.e. quasi-periodic solutions with the same frequency vector as the forcing term. When the dissipation is large enough and…
The numerical optimized shooting method for finding periodic orbits in nonlinear dynamical systems was employed to determine the existence of periodic orbits in the well-known R\"ossler system. By optimizing the period $T$ and the three…
Characterizing existence or not of periodic orbit is a classical problem and it has both theoretical importance and many real applications. Here, several new criterions on nonexistence of periodic orbits of the planar dynamical system $\dot…
We present sufficient conditions for the existence of forced oscillations in non-autonomous mechanical systems. Previously, similar results were obtained for systems with friction. Presented results hold both for systems with and without…
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…
In this paper, we study the existence and uniqueness of periodic solutions of the differential equation of the form . Here, we obtain some sufficient conditions which guarantee the existence of periodic solutions. This equation is a quite…
We study the problem of existence of response solutions for a real-analytic one-dimensional system, consisting of a rotator subjected to a small quasi-periodic forcing. We prove that at least one response solution always exists, without any…
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…
Consider a periodically forced nonlinear system which can be presented as a collection of smaller subsystems with pairwise interactions between them. Each subsystem is assumed to be a massive point moving with friction on a compact surface,…
We study semi-dynamical systems associated to delay differential equations. We give a simple criteria to obtain weak and strong persistence and provide sufficient conditions to guarantee uniform persistence. Moreover, we show the existence…
We present an illustrative application of the two famous mathematical theorems in differential topology in order to show the existence of periodic orbits with arbitrary given period for a class of hamiltonians .This result point out for a…
In this paper we provide conditions to ensure the existence, for $e>0$ sufficiently small, of periodic solutions of given period $T>0$ in a prescribed domain $U$ for a class of singularly perturbed first order differential systems. Here…
For controlling periodic orbits with delayed feedback methods the periodicity has to be known a priori. We propose a simple scheme, how to detect the period of orbits from properties of the control signal, at least if a periodic but…