1,721,044 research outputs found
Special solutions for an equation arising in sand ripple dynamics
Get PDFWe study a nonlinear fourth order evolution equation arising in the context of sand ripple dynamics. We analyse the set of stationary solutions and travelling waves in order to recover the observed phenomenology such as different wavelengths ripples, travelling waves, coarsening and time scales. Moreover, we construct an approximate solution which describes the early stages of the dynamics and which suggests the existence of coarsening and of time scales with different dynamical behaviour
Coexistence in a One-Predator, Two-Prey System with Indirect Effects
Get PDFWe study the dynamics of a one-predator, two-prey system in which the predator has an indirect effect on the preys. We show that, in presence of the indirect effect term, the system admits coexistence of the three populations while, if we disregard it, at least one of the populations goes to extinction
Solitary waves for an equation related to a problem of microstructure formation
No full textWe prove the non existence of solitary wave solutions for an evolution equation related to a problem of microstructure formation. Moreover, we analyze in detail the ODEs system describing traveling waves and characterize bounded and unbounded solutions. Finally we construct an oscillating approximate solution and provide numerical simulations in order to illustrate the theoretical results
Analysis of microstructure of a non-convex functional with penalization term
No full textAbstractWe study the properties of the minimizers of a singularly perturbed non-convex functional with a penalization term Fε,μ(v,u;I)=12ε2∫Ivxx2dx+12∫IW(vx)dx+μ2ε2∫I(v−u)2dx, where I=(0,1), 0<ε≪1 and μ>0 are parameters, u is a given function and W(p)=(p2−1)2. We analyze the phenomenon of microstructure formation and show the dependence on μ and u
Existence of global and blowup solutions for a singular second-order ODE
No full textWe study the existence of global solutions of a singular ordinary differential
equation arising in the construction of self similar solution for a
backward-forward parabolic equation. Also we present several numerical
simulations and obtain an upper bound for the blowup time
A comparison between random and stochastic modeling for a SIR model
Get PDFn this article, a random and a stochastic version of a SIR nonautonomous model previously introduced in [19] 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
Asymptotic behavior of a fourth order evolution equation
No full textWe study the asymptotic behavior of a singularly perturbed fourth order evolution equation related to the regularization of an ill posed equation encountering forward and backward diffusion. In particular we prove the existence of an exponential attractor and give an estimate of its dimension
Recurrence analysis on Julia sets of semigroups of complex polynomials
No full textWe introduce a recurrence function in order to analyze the dynamics of semigroups of complex polynomials. We show that under a regularity hypothesis, the recurrence function is continuous in the complex plane. This is a new notion even for the case of a semigroup with just one generator
Semi-Kolmogorov models for predation with indirect effects in random environments
No full textIn 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
Predation with indirect effects in fluctuating environments
No full textWe investigate the long-term dynamics for a predation model of Plankton community with indirect effects, under fluctuating environments. A random version and a stochastic version with multiplicative noise of the model are discussed and compared. We prove that the solutions to both versions are nonnegative and bounded given any nonnegative positive initial conditions. We also prove that both the random system and the stochastic system possess a unique random attractor under the same set of assumptions, by using the classical theory of random dynamical systems. In addition, we provide conditions under which coexistence of species exists for the random system
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