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This paper addresses the long-time behavior of gradient flows of non convex functionals in Hilbert spaces. Exploiting the notion of generalized semiflows by J. M. Ball, we provide some sufficient conditions for the existence of a global…
We study --both in theory and practice-- the use of momentum motions in classic iterative hard thresholding (IHT) methods. By simply modifying plain IHT, we investigate its convergence behavior on convex optimization criteria with…
We discuss the nonlinear phenomena of irreversible tipping for non-autonomous systems where time-varying inputs correspond to a smooth "parameter shift" from one asymptotic value to another. We express tipping in terms of pullback…
Many natural and technological systems fail to adapt to changing external conditions and move to a different state if the conditions vary too fast. Such "non-adiabatic" processes are ubiquitous, but little understood. We identify these…
We calculate rigorous bounds on the Hausdorff dimension of the attractor at the accumulation of the period-doubling cascade for families of maps with quadratic, cubic, and quartic critical point. To do this, we express the attractors as the…
In this paper, for nonautonomous dynamical systems, we give first general conditions ensuring that a pullback attractor is a forward attractor as well in both the single and multivalued frameworks. In particular, we consider asymptotically…
We give a detailed study of attractors for measure driven quintic damped wave equations with periodic boundary conditions. This includes uniform energy-to-Strichartz estimates, the existence of uniform attractors in a weak or strong…
This paper is devoted to the study of nonautonomous multivalued semiflows and their associated pullback attractors. For this kind of dynamical systems we are able to characterize the upper and lower bounds of the attractor as complete…
The inner structure of the attractor appearing when the Varley-Gradwell-Hassell population model bifurcates from regular to chaotic behaviour is studied. By algebraic and geometric arguments the coexistence of a continuum of neutrally…
The construction of attractors of a dissipative difference equation is usually based on compactness assumptions. In this paper, we replace them with contractivity assumptions under which the pullback and forward attractors are identical. As…
In this paper the attractors synthesis algorithm for a class of dissipative dynamical systems with hyperbolic equilibria, presented in [1], is applied to generate any attractor of the Rikitake system. By switching periodically, or even…
Consider a parameter dependent vector field on either Euclidean space or a compact Riemannian manifold. Suppose that it possesses a parameter dependent initial condition and a parameter dependent stable hyperbolic equilibrium point. It is…
A non-autonomous system is proposed to model the seasonal pattern of dengue fever. We found that an approximate threshold condition for infection persistence describes all possible behavior of the system. As far as we know, the kind of…
In the one-parameter family of power-law maps of the form $f_a(x)=-|x|^{\alpha}+a,$ $\alpha >1,$ we give examples of mutually related dynamically determined quantities, depending on the parameter $a$, such that one is a Pick function of the…
Under consideration is the damped semilinear wave equation \[ u_{tt}+u_t-\Delta u + u + f(u)=0 \] on a bounded domain $\Omega$ in $\mathbb{R}^3$ with a perturbation parameter $\varepsilon>0$ occurring in an acoustic boundary condition,…
We prove the existence and uniqueness of tempered random attractors for stochastic Reaction-Diffusion equations on unbounded domains with multiplicative noise and deterministic non-autonomous forcing. We establish the periodicity of the…
The fast basin of an attractor of an iterated function system (IFS) is the set of points in the domain of the IFS whose orbits under the associated semigroup intersect the attractor. Fast basins can have non-integer dimension and comprise a…
We consider B\'ezier curves with complex parameters, and we determine explicitly the affine iterated function system (IFS) corresponding to the de Casteljau subdivision algorithm, together with the complex parametric domain over which such…
The Kauffman model describes a system of randomly connected nodes with dynamics based on Boolean update functions. Though it is a simple model, it exhibits very complex behavior for "critical" parameter values at the boundary between a…
We establish properties of a new type of fractal which has partial self similarity at all scales. For any collection of iterated functions systems with an associated probability distribution and any positive integer V there is a…