Related papers: Minimal Random Attractors
We state necessary and sufficient conditions for the existence of $T$-discrete exponential attractors for semigroups in complete metric spaces. These conditions are formulated in terms of a covering condition for iterates of the absorbing…
We study from a statistical mechanics viewpoint some of the simplest mathematical objects, finite pure sets. Starting from the empty set, new generations are produced step by step, sets of the next generation being those whose elements are…
The structure of the graph defined by the interactions in a Boolean network can determine properties of the asymptotic dynamics. For instance, considering the asynchronous dynamics, the absence of positive cycles guarantees the existence of…
This paper refined and introduced some notations (namely attractors, physical attractors, proper attractors, topologically exact and topologically mixing) within the context of relations. We establish necessary and sufficient conditions,…
We characterize the dynamical systems consisting of the set of 5-adic integers and polynomial maps which consist of only one minimal component.
In an earlier paper, we discussed the probability that the determinant of a matrix undergoes the least change upon perturbation of one of its elements, provided that most or all of the elements of the matrix are chosen at random and that…
In this paper, we consider the 2D periodic stochastic Nernst-Planck-Navier-Stokes equations with body forces perturbed by multiplicative white noise. We first transform the stochastic Nernst-Planck-Navier-Stokes system into the…
In this paper we introduce a notion of an attractor for local semiflows on topological spaces, which in some cases seems to be more suitable than the existing ones in the literature. Based on this notion we develop a basic attractor theory…
We study generic holomorphic families of dynamical systems presenting problems of small divisors with fixed arithmetic. We prove that we have convergence for all parameter values or divergence everywhere except for an exceptional set in the…
Let $\Lambda$ be a complete metric space, and let $\{S_\lambda(\cdot):\ \lambda\in\Lambda\}$ be a parametrised family of semigroups with global attractors ${\mathscr A}_\lambda$. We assume that there exists a fixed bounded set $D$ such that…
In this paper we investigate how many periodic attractors maps in a small neighbourhood of a given map can have. For this purpose we develop new tools which help to make uniform cross-ratio distortion estimates in a neighbourhood of a map…
Attractor dynamics are a hallmark of many complex systems, including the brain. Understanding how such self-organizing dynamics emerge from first principles is crucial for advancing our understanding of neuronal computations and the design…
This paper concerns the dynamical behavior of weakly reversible, deterministically modeled population processes near the facets (codimension-one faces) of their invariant manifolds and proves that the facets of such systems are "repelling."…
Selecting a few available actuators to ensure the controllability of a linear system is a fundamental problem in control theory. Previous works either focus on optimal performance, simplifying the controllability issue, or make the system…
We study the dynamics of the periodically-forced May-Leonard system. We extend previous results on the field and we identify different dynamical regimes depending on the strength of attraction $\delta$ of the network and the frequency…
Let $f:T\longrightarrow T$ be a mapping and $\Omega$ be a subset of $T$ which intersects every (positive) orbit of $f$. Assume that there are given a second dynamical system $\lambda:Y\longrightarrow Y$ and a mapping…
We study the behaviour of discrete dynamical systems generated by a continuous map $f$ of a compact real interval into itself where at randomly chosen times a function different from $f$ - so called impulse function is applied. We show that…
Two one-parametric bifurcation problems for scalar nonautonomous ordinary differential equations are analyzed assuming the coercivity of the time-dependent function determining the equation and the concavity of its derivative with respect…
We study the long-term behavior of the distribution of the solution process to the non-autonomous McKean-Vlasov stochastic delay lattice system defined on the integer set $\mathbb{Z}$. Specifically, we first establish the well-posedness of…
Habituation - a phenomenon in which a dynamical system exhibits a diminishing response to repeated stimulations that eventually recovers when the stimulus is withheld - is universally observed in living systems from animals to unicellular…