The relation between the complexity of a time-switched dynamics and the complexity of its control sequence depends critically on the concept of a non-autonomous pullback attractor. For instance, the switched dynamics associated with scalar dissipative affine maps has a pullback attractor consisting of singleton component sets. This entails that the complexity of the control sequence and switche...

This work is concerned about the asymptotic behavior of solutions two and three dimensional stochastic convective Brinkman-Forchheimer (SCBF) equations driven by white noise with nonlinear diffusion terms. We prove existence uniqueness weak pullback mean random attractors for 2D SCBF (for $r\geq1$) as well 3D $r>3$, any $\mu,\beta>0$ $r=3$, $2\mu\beta\geq1$) in Bochner spaces, when terms are Li...

<p style='text-indent:20px;'>Consider the second order nonautonomous lattice systemswith singular perturbations</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} \epsilon \ddot{u}_{m}+\dot{u}_{m}+(Au)_{m}+\lambda_{m}u_{m}+f_{m}(u_{j}|j\in I_{mq}) = g_{m}(t),\; \; m\in \mathbb{Z}^{k},\; \epsilon&amp...

The asymptotic behavior of continuous dissipative systems and dissipative numerical integrators with fixed time-stepping can be fully investigated by Lyapunov-type theorem on continuous and discrete dynamical systems, respectively. However, once adaptive time-stepping is involved, such theories cease to work, and usually the dynamics should be investigated in a backward way, such as in terms of...

There is a vast body of literature devoted to the study of bifurcation phenomena in autonomous systems of differential equations. However, there is currently no well-developed theory that treats similar questions for the non-autonomous case. Inspired in part by the theory of pullback attractors, we discuss generalizations of various autonomous concepts of stability, instability, and invariance....