| Full text | |
| Author(s): |
Berardi, Marco
;
D'Abbicco, Marcello
Total Authors: 2
|
| Document type: | Journal article |
| Source: | Mediterranean Journal of Mathematics; v. 13, n. 6, p. 4829-4844, DEC 2016. |
| Web of Science Citations: | 0 |
| Abstract | |
We consider a piecewise smooth system, whose solutions locally spirally move around an equilibrium point which lies at the intersection of two discontinuity surfaces. We find a sufficient condition for the stability of this point, in the limit case in which a first-order approximation theory does not give an answer. This condition, depending on the vector field and its Jacobian evaluated at the equilibrium point, is trivially satisfied for piecewise-linear systems, whose first-order part is a diagonal matrix with negative entries. We show how our stability results may be applied to discontinuous recursive neural networks for which the matrix of self-inhibitions of the neurons does not commute with the connection weight matrix. In particular, we find a nonstandard relation between the ratio of the self-inhibition speeds and the structure of the connection weight matrix, which determines the stability. (AU) | |
| FAPESP's process: | 13/15140-2 - Decay estimates for semilinear hyperbolic equations |
| Grantee: | Marcello Dabbicco |
| Support Opportunities: | Research Grants - Young Investigators Grants |
| FAPESP's process: | 14/02713-7 - Decay estimates for semilinear hyperbolic equations |
| Grantee: | Marcello Dabbicco |
| Support Opportunities: | Scholarships in Brazil - Young Researchers |