Topological stabilization for synchronized dynamics on networks

A general scheme is proposed and tested to control the symmetry breaking instability of a homogeneous solution of a spatially extended multispecies model, defined on a network. The inherent discreteness of the space makes it possible to act on the topology of the inter-nodes contacts to achieve the desired degree of stabilization, without altering the dynamical parameters of the model. Both symmetric and asymmetric couplings are considered. In this latter setting the web of contacts is assumed to be balanced, for the homogeneous equilibrium to exist. The performance of the proposed method are assessed, assuming the Complex Ginzburg-Landau equation as a reference model. In this case, the implemented control allows one to stabilize the synchronous limit cycle, hence time-dependent, uniform solution. A system of coupled real Ginzburg-Landau equations is also investigated to obtain the topological stabilization of a homogeneous and constant fixed point.     

Complex Dynamics in a ODE Model Related to Phase Transition

Motivated by some recent studies on the Allen–Cahn phase transition model with a periodic nonautonomous term, we prove the existence of complex dynamics for the second order equation

$$\begin{aligned} -\ddot{x} + \left( 1 + \varepsilon ^{-1} A(t)\right) G'(x) = 0, \end{aligned}$$

where A(t) is a nonnegative T-periodic function and \(\varepsilon > 0\) is sufficiently small. More precisely, we find a full symbolic dynamics made by solutions which oscillate between any two different strict local minima \(x_0\) and \(x_1\) of G(x). Such solutions stay close to \(x_0\) or \(x_1\) in some fixed intervals, according to any prescribed coin tossing sequence. For convenience in the exposition we consider (without loss of generality) the case \(x_0 =0\) and \(x_1 = 1\).

     

A regularity criterion for the Navier-Stokes equations in terms of the pressure gradient

The incompressible three-dimensional Navier-Stokes equations are considered. A new regularity criterion for weak solutions is established in terms of the pressure gradient.     

Asymptotic behavior of a semilinear problem in heat conduction with memory

This paper is devoted to existence, uniqueness and asymptotic behavior, as time tends to infinity, of the solutions of an integro-partial differential equation arising from the theory of heat conduction with memory, in presence of a temperature-dependent heat supply. A linearized heat flux law involving positive instantaneous conductivity is matched with the energy balance, to generate an autonomous semilinear system subject to initial history and Dirichlet boundary conditions. Existence and uniqueness of solution is provided. Moreover, under proper assumptions on the heat flux memory kernel, the existence of absorbing sets in suitable function spaces is achieved. Received March 23, 1997 - Revised version received November 12, 1997     

A convergence–divergence test for series of nonnegative terms

We present a convergence–divergence test for series of nonnegative terms. Our proof is elementary, and yet we show examples of application to some apparently difficult cases.     

Uniform estimates of Gronwall type

We discuss a Gronwall-type lemma depending on a small parameter ε>0, based on an integral inequality that predicts blow-up in finite time of the involved unknown function for any fixed ε. The result permits to establish uniform estimates even if the function itself depends on ε.     

Selenated and Sulfurated Analogues of Triacyl Glycerols: Selective Synthesis and Structural Characterization

The synthesis of sulfur- and selenium-containing isosters of triacyl glycerols is herein described. Regioselective fluoride-induced ring-opening reaction of suitable substituted thiiranes with bis(trimethyl)silyl selenide, followed by in situ S- and Se-acylation with fatty acid acyl chlorides, enables the one pot synthesis of mixed chalcogeno esters in good yield. The key step of this methodology is the functionalization of S−Si and Se−Si bonds of silyl chalcogenides, generated in situ under mild conditions. A related procedure for the synthesis of functionalized selenides, bearing two thiol ester and two ester moieties, was also developed through a fine tuning of the reaction conditions. The physico-chemical properties of these novel fatty acid chalcogeno esters have been investigated through DSC, SAXS, WAXS, FTIR and polarized optical microscopy, and compared to those of the common triglycerides in order to highlight the effect of the replacement of oxygen with other chalcogen elements in the polar head of the lipid.     

On the exponential stability of linear thermoelasticity

Received March 28, 2000     

Stability properties of an abstract system with applications to linear thermoelastic plates

This paper deals with an abstract version of the evolution system $$\left\{\begin{array}{ll}u_{tt}-\omega \Delta u_{tt}+\Delta (\Delta u + \theta)=0 \\\theta_t - \Delta \theta -\Delta u_t=0\end{array}\right.$$ with ω ≥  0, ruling the dynamics of linear thermoelastic plates. In particular, we will consider a more general coupling term depending on a real parameter σ. The (exponential and polynomial) decay properties of the related solution semigroup are investigated in dependence of the values of σ.     

The Theory of Individual Based Discrete-Time Processes

A general theory is developed to study individual based models which are discrete in time. We begin by constructing a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are hence intrinsic to the system and can induce qualitative changes to the dynamics predicted from the deterministic map. From the Chapman–Kolmogorov equation for the discrete-time Markov process, we derive the analogues of the Fokker–Planck equation and the Langevin equation, which are routinely employed for continuous time processes. In particular, a stochastic difference equation is derived which accurately reproduces the results found from the Markov chain model. Stochastic corrections to the deterministic map can be quantified by linearizing the fluctuations around the attractor of the map. The proposed scheme is tested on stochastic models which have the logistic and Ricker maps as their deterministic limits.