arXiv subjects

Ana M. Sanz

Publications and source records attributed to Ana M. Sanz.

10 recordsLinked to original sources

arXiv2026

A new class of generalized ordinary differential equations with applications

The space of parametric b-measures endowed with appropriate topologies is introduced to define a new class of generalized ODEs given by parametric b-measures. This framework offers a new approach for dealing with precompact families of Carathéodory ODEs using nonautonomous dynamical systems techniques. An application to the study of the dynamics of the fast variables of a slow-fast system of ODEs, where the fast motion is determined by a Carathéodory vector field with equicontinuous $m$-bounds and bounded $l$-bounds, is given.

math.DS↗

arXiv2025

Nonautonomous modelling in Energy Balance Models of climate. Limitations of averaging and climate sensitivity

Starting from a classical Budyko-Sellers-Ghil energy balance model for the average surface temperature of the Earth, a nonautonomous version is designed by allowing the solar irradiance and the cloud cover coefficients to vary with time in a fast timescale, and to exhibit chaos in a precise sense. The dynamics of this model is described in terms of three existing nonautonomous equilibria, the upper one being attracting and representing the present temperature profile. The theory of averaging is used to compare the nonautonomous model and its time-averaged version. We analyse the influence of the qualitative properties of the time-dependent coefficients and develop physically significant error estimates close to the upper attracting solution. Furthermore, previous concepts of two-point response and sensitivity functions are adapted to the nonautonomous context and used to value the increase in temperature when a forcing caused by CO2 and other emissions intervenes.

physics.ao-ph↗

arXiv2024

Tracking nonautonomous attractors in singularly perturbed systems of ODEs with dependence on the fast time

New results on the behaviour of the fast motion in slow-fast systems of ODEs with dependence on the fast time are given in terms of tracking of nonautonomous attractors. Under quite general assumptions, including the uniform ultimate boundedness of the solutions of the layer problems, inflated pullback attractors are considered. In general, one cannot disregard the inflated version of the pullback attractor, but it is possible under the continuity of the fiber projection map of the attractor. %In particular this happens when the attractors of the layer problems are copies of the base, which is the counterpart of an asymptotically stable equilibrium point in the autonomous case. The problem of the limit of the solutions of the slow-fast system at each fixed positive value of the slow time is also treated and in this formulation the critical set is given by the union of the fibers of the pullback attractors. The results can be seen as extensions of the classical Tikhonov theorem to the nonautonomous setting.

math.DS↗

arXiv2023

Attractors In Almost Periodic Nicholson Systems And Some Numerical Simulations

The existence of a global attractor is proved for the skew-product semiflow induced by almost periodic Nicholson systems and new conditions are given for the existence of a unique almost periodic positive solution which exponentially attracts every other positive solution. Besides, some numerical simulations are included to illustrate our results in some concrete Nicholson systems.

math.DS↗

arXiv2022

The exponential ordering for non-autonomous delay systems with applications to compartmental Nycholson systems

The exponential ordering is exploited in the context of non-auto\-no\-mous delay systems, inducing monotone skew-product semiflows under less restrictive conditions than usual. Some dynamical concepts linked to the order, such as semiequilibria, are considered for the exponential ordering, with implications for the determination of the presence of uniform persistence or the existence of global attractors. Also, some important conclusions on the long-term dynamics and attraction are obtained for monotone and sublinear delay systems for this ordering. The results are then applied to almost periodic Nicholson systems and new conditions are given for the existence of a unique almost periodic positive solution which asymptotically attracts every other positive solution.

math.DS↗

arXiv2022

Topologies of continuity for Carathéodory parabolic PDEs from a dynamical perspective

Systems of non-autonomous parabolic partial differential equations over a bounded domain with nonlinear term of Carathéodory type are considered. Appropriate topologies on sets of Lipschitz Carathéodory maps are defined in order to have a continuous dependence of the mild solutions with respect to the variation of both the nonlinear term and the initial conditions, under different assumptions on the bound-maps of the nonlinearities.

math.DS↗

arXiv2018

Persistence in nonautonomous quasimonotone parabolic partial functional differential equations with delay

This paper provides a dynamical frame to study non-autonomous parabolic partial differential equations with finite delay. Assuming monotonicity of the linearized semiflow, conditions for the existence of a continuous separation of type II over a minimal set are given. Then, practical criteria for the uniform or strict persistence of the systems above a minimal set are obtained.

math.DS↗

arXiv2018

Asymptotic behaviour for a class of non-monotone delay differential systems with applications

The paper concerns a class of $n$-dimensional non-autonomous delay differential equations obtained by adding a non-monotone delayed perturbation to a linear homogeneous cooperative system of ordinary differential equations. This family covers a wide set of models used in structured population dynamics. By exploiting the stability and the monotone character of the linear ODE, we establish sufficient conditions for both the extinction of all the populations and the permanence of the system. In the case of DDEs with autonomous coefficients (but possible time-varying delays), sharp results are obtained, even in the case of a reducible community matrix. As a sub-product, our results improve some criteria for autonomous systems published in recent literature. As an important illustration, the extinction, persistence and permanence of a non-autonomous Nicholson system with patch structure and multiple time-dependent delays are analysed.

math.CA↗

arXiv2017

Global an cocycle atractor for non-utonomous reaction-difussion equations . The case of null upper Lyapunov exponente

In this paper we obtain a detailed description of the global and cocycle attractors for the skew-product semiflows induced by the mild solutions of a family of scalar linear-dissipative parabolic problems over a minimal and uniquely ergodic flow. We consider the case of null upper Lyapunov exponent for the linear part of the problem. Then, two different types of attractors can appear, depending on whether the linear equations have a bounded or an unbounded associated real cocycle. In the first case (e.g.~in periodic equations), the structure of the attractor is simple, whereas in the second case (which occurs in aperiodic equations), the attractor is a pinched set with a complicated structure. We describe situations when the attractor is chaotic in measure in the sense of Li-Yorke. Besides, we obtain a non-autonomous discontinuous pitchfork bifurcation scenario for concave equations, applicable for instance to a linear-dissipative version of the Chafee-Infante equation.

math.DS↗

arXiv2017

Is uniform persisitence a robust property in almost periodic models? A well-behaved family: almost periodic Nicholson systems

Using techniques of non-autonomous dynamical systems, we completely characterize the persistence properties of an almost periodic Nicholson system in terms of some numerically computable exponents. Although similar results hold for a class of cooperative and sublinear models, in the general non-autonomous setting one has to consider persistence as a collective property of the family of systems over the hull: the reason is that uniform persistence is not a robust property in models given by almost periodic differential equations.

math.DS↗