Dynamics of a continuous Hénon model

We study a continuous Hénon system obtained by considering the discrete original model in continuous time. While the dynamics of the continuous model is trivial, we are able to recover the complexity of the discrete model by the introduction of time delays. In particular high period limit cycles and chaotic attractors are observed. We illustrate the results with some numerical simulations.Ministerio de Economía y CompetitividadConsejería de Innovación, Ciencia y Empresa (Junta de Andalucía

On a predator prey model with nonlinear harvesting and distributed delay

A predator prey model with nonlinear harvesting (Holling type-II) with both constant and distributed delay is considered. The boundeness of solutions is proved and some sufficient conditions ensuring the persistence of the two populations are established. Also, a detailed study of the bifurcation of positive equilibria is provided. All the results are illustrated by some numerical simulations.Ministerio de Economía y CompetitividadFondo Europeo de Desarrollo RegionalConsejería de Innovación, Ciencia y Empresa (Junta de Andalucía

Bifurcation scenarios in an ordinary differential equation with constant and distributed delay: A case study

In this article we consider a model introduced by Ucar in order to simply describe chaotic behaviour with a one dimensional ODE containing a constant delay. We study the bifurcation problem of the equilibria and we obtain an approximation of the periodic orbits generated by the Hopf bifurcation. Moreover, we propose and analyse a more general model containing distributed time delay. Finally, we propose some ideas for further study. All the theoretical results are supported and illustrated by numerical simulations.Consejería de Economía, Innovación, Ciencia y Empleo, Junta de AndalucíaJunta de Andalucía 2010/FQM314Ministerio de Economía y Competitividad MTM2015-63723-P P12-FQM-1492Federación Española de Enfermedades Rara

Geomorphic influence on small glacier response to post Little Ice Age climate warming: Julian Alps, Europe

The evolution of glaciers and ice patches, as well as the equilibrium-line altitude (ELA) since the Little Ice Age (LIA) were investigated in the Julian Alps (south-eastern European Alps) including ice masses previously unreported. 23 permanent firn and ice bodies have been recognized in the 1853 km2 of this alpine sector, covering a total area in 2012 of 0.385 km2, about one-fifth of the area covered during the LIA (2.350 km2)… … The ice masses in the region are at the lowest elevations of any glaciers in the Alpine Chain, and are characterized by low dynamics. The ELAs of the two major LIA glaciers (Canin and Triglav) have been established at 2275 ± 10 m and 2486 ± 10 m, respectively, by… ... Changes in the ELA and glaciers extension indicate a decoupling from climate. This is most evident in the smallest avalanche-dominated ice bodies, which are currently controlled mainly by precipitation… … resilient to recent climate warming instead of rapidly disappearing as should be expected

Pullback attractor for a non-linear evolution equation in elasticity

We prove the existence of a pullback attractor for a non{autonomous fourth order evolution equation arising in the fi eld of phase transitions and elasticity theory. The existence of several families of bounded absorbing sets is first proved in several spaces, and owing to the compactness of some inclusions between Sobolev spaces, we can then ensure the existence of a family of compact absorbing sets in the pullback sense and, as a consequence, the existence of a pullback attractor

Effects of additive and multiplicative noise on the dynamics of a parabolic equation

We consider the effects of additive and multiplicative noise on the asymptotic behavior of a fourth order parabolic equation arising in the study of phase transitions. On account that the deterministic model presents three different time scales, in this paper we have established some conditions under which the third time scale, which encounter finite dimensional behavior of the system, is preserved under both additive and multiplicative linear noise. In particular we have proved the existence of a random attractor in both cases, and observed that the order of magnitude of the third time scale is also preserved

A comparison between random and stochastic modeling for a SIR model

In this article, a random and a stochastic version of a SIR nonautonomous model previously introduced in P. E. Kloeden and V. S. Kozyakin, The dynamics of epidemiological systems with nonautonomous and random coefficients, MESA: Mathematics in Engineering, Science and Aerospace, vol. 2, no. 2 (2011).is considered. In particular, the existence of a random attractor is proved for the random model and the persistence of the disease is analyzed as well. In the stochastic case, we consider some environmental effect on the model, in fact, we assume that one of the coefficients of the system is affected by some stochastic perturbation, and analyze the asymptotic behavior of the solutions. The paper is concluded with a comparison between the two different modeling strategies.Fondo Europeo de Desarrollo RegionalMinisterio de Economía y CompetitividadJunta de Andalucí

Semi-Kolmogorov models for predation with indirect effects in random environments

In this work we study semi-Kolmogorov models for predation with both the carrying capacities and the indirect effects varying with respect to randomly fluctuating environments. In particular, we consider one random semi-Kolmogorov system involving random and essentially bounded parameters, and one stochastic semi-Kolmogorov system involving white noise and stochastic parameters defined upon a continuous-time Markov chain. For both systems we investigate the existence and uniqueness of solutions, as well as positiveness and boundedness of solutions. For the random semi-Kolmogorov system we also obtain sufficient conditions for the existence of a global random attractor.Ministerio de Economía y CompetitividadFondo Europeo de Desarrollo RegionalUnión EuropeaConsejería de Innovación, Ciencia y Empresa (Junta de Andalucía

A qualitative description of microstructure formation and coarsening phenomena for an evolution equation

We provide a qualitative description of microstructure formation and coarsening phenomena for the solutions of a singularly perturbed fourth order evolution equation arising in the study of phase transitions. In particular we study stationary and traveling wave solutions and we construct a class of approximate solution which mimics the principle features of the dynamics. Finally we present several simulations in order to illustrate the results.Fondo Europeo de Desarrollo RegionalMinisterio de Economía y CompetitividadConsejería de Innovación, Ciencia y Empresa (Junta de Andalucía