Least-energy solutions of a non-autonomous semilinear problem with a small diiusion coeecient are studied in this paper. We prove that the solutions will develop single peaks as the diiusion coeecient approaches 0. The location of the peaks is also considered in this paper. It turns out that the location of the peaks is determined by the non-autonomous term of the equation and the type of the b...

This work investigates the possibility of using audible broadband acoustic signals for the navigation of autonomous mobile robots in unprepared, unknown, silent, static, indoor environments. To this day, audible sound signals are not used for the navigation of autonomous mobile robots. Nonetheless, they are the second best information source for the blind (next to tactile signals) for navigatin...

The aim of this session is to offer an overview on recent results concerning the asymptotic behaviour of solutions of stochastic and deterministic partial and ordinary differential equations. Some of the main topics, but not the only ones, in this sessions are: asymptotic dynamics of dynamical systems, in particular, existence and properties of attractors for autonomous, non-autonomous and stoc...

We investigate the dynamics associated to nearly–integrable dissipative systems, with particular reference to some models of Celestial Mechanics which can be described in a weakly dissipative framework. We start by studying some paradigmatic models provided by the dissipative standard maps in 2 and 4 dimensions. The dynamical investigation is performed applying frequency analysis and computing ...

In this paper, several three dimensional (3-D) four-wing smooth quadratic autonomous chaotic systems are analyzed. It is shown that these systems have a number of similar features. A new 3-D continuous autonomous system is proposed based on these features. The new system can generate a four-wing chaotic attractor with less terms in the system equations. Several basic properties of the new syste...

It is shown that a given non-autonomous system of two first-order ordinary differential equations can be expressed in Hamiltonian form. The derivation presented here allow us to obtain previously known results such as the infinite number of Hamiltonians in the autonomous case and the Helmholtz condition for the existence of a Lagrangian. Se muestra que un sistema dado, no autónomo, de ecuacione...

We study an optimal control problem for a non-autonomous SEIRS model with incidence given by a general function of the infective, the susceptible and the total population, and with vaccination and treatment as control variables. We prove existence and uniqueness results for our problem and, for the case of mass-action incidence, we present some simulation results designed to compare an autonomo...

Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for stochastic ordinary differential equations is relatively mature. In this paper, we present a unified theory of invariant manifolds for infinite dimensional random ...

A non-autonomous discrete commensal symbiosis model with Beddington-DeAngelis functional response is proposed and studied in this paper. Sufficient conditions are obtained for the existence of positive periodic solution system.

We summarize known criteria for the non–existence, existence and on number of limit cycles autonomous real planar polynomial differential systems, also provide new results. give examples systems which realize maximum provided by each criterion. In particular we consider class form x ̇ = P n ( , y ) + m Q where are natural numbers with > ≥ 1 i quasi-homogeneous vector fields.