4 research outputs found
Sharp estimates for the global attractor of scalar reaction-diffusion equations with a Wentzell boundary condition
In this paper, we derive optimal upper and lower bounds on the dimension of
the attractor AW for scalar reaction-diffusion equations with a Wentzell
(dynamic) boundary condition. We are also interested in obtaining explicit
bounds about the constants involved in our asymptotic estimates, and to compare
these bounds to previously known estimates for the dimension of the global
attractor AK; K \in {D;N; P}, of reactiondiffusion equations subject to
Dirichlet, Neumann and periodic boundary conditions. The explicit estimates we
obtain show that the dimension of the global attractor AW is of different order
than the dimension of AK; for each K \in {D;N; P} ; in all space dimensions
that are greater or equal than three.Comment: to appear in J. Nonlinear Scienc
Multi-almost periodicity and invariant basins of general neural networks under almost periodic stimuli
In this paper, we investigate convergence dynamics of almost periodic
encoded patterns of general neural networks (GNNs) subjected to external almost
periodic stimuli, including almost periodic delays. Invariant regions are
established for the existence of almost periodic encoded patterns under
two classes of activation functions. By employing the property of
-cone and inequality technique, attracting basins are estimated
and some criteria are derived for the networks to converge exponentially toward
almost periodic encoded patterns. The obtained results are new, they
extend and generalize the corresponding results existing in previous
literature.Comment: 28 pages, 4 figure