Alternative perspectives on the maintenance of biodiversity and the assembly of ecological
communities suggest that both processes cannot be investigated simultaneously. In this …

Brain dynamics depicts an extremely complex energy landscape that changes over time,
and its characterisation is a central unsolved problem in neuroscience. We approximate the …

The large time behavior of deterministic and stochastic three dimensional convective
Brinkman-Forchheimer (CBF) equations ∂ _t u-μ Δ u+(u ⋅ ∇) u+ α u+ β| u|^ r-1 u+ ∇ p …

Finite-dimensional attractors play an important role in finite-dimensional reduction of PDEs
in mathematical modelization and numerical simulations. For non-autonomous random …

The self-organising global dynamics underlying brain states emerge from complex recursive
nonlinear interactions between interconnected brain regions. Until now, most efforts of …

This paper investigates the well-posedness of global solutions, the existence of global and
exponential attractors and their continuity for an extensible beam equation with rotational …

This article is concerned with the asymptotically autonomous robustness (almost surely and
in probability) of random attractors for stochastic version of 3D convective Brinkman …

In this paper we study the dynamics of Chafee-Infante equations under Lipschitz
perturbations of the domain and equation. First, we describe the geometric equivalence …

Bifurcation theory is a major topic in dynamical systems theory with profound applications.
However, in contrast to autonomous dynamical systems, it is not clear what a bifurcation of a …

Non-autonomous differential equations exhibit highly intricate dynamics, and various
concepts have been introduced to describe their qualitative behavior. In general, it is rare to …