For autonomous Lotka-Volterra systems of differential equations modelling the dynamics of n competing species, new criteria are established for the existence of a single point global attractor. Under the conditions of these criteria, some of the species will survive and stabilise at a steady state whereas the others, if any, will die out.

We study the Kolmogorov ε-entropy and the fractal dimension of global attractors for autonomous and nonautonomous equations of mathematical physics. We prove upper estimates for the ε-entropy and fractal dimension of the global attractors of nonlinear dissipative wave equations. Andrey Nikolaevich Kolmogorov discovered applications of notions of information theory in the theory of dynamical sys...

In this paper, we address the model of global attractor formulated in form evolution differential inclusions with second order Banach spaces. Firstly, based on fixed point theorem, existence result mild solutions is deduced. Then, by implementing measure noncompactness, associated m -semiflow validated. Finally, a concre...

The existence of a global attractor in the natural energy space is proved for the semilinear wave equation utt + βut − ∆u + f(u) = 0 on a bounded domain Ω ⊂ R with Dirichlet boundary conditions. The nonlinear term f is supposed to satisfy an exponential growth condition for n = 2, and for n ≥ 3 the growth condition |f(u)| ≤ c0(|u|γ + 1), where 1 ≤ γ ≤ n n−2 . No Lipschitz condition on f is assu...