Scheda di dettaglio – i prodotti della ricerca
| Dato | Valore |
|---|---|
| Title | A Critical Case for the Spiral Stability for 2 × 2 Discontinuous Systems and an Application to Recursive Neural Networks |
| Abstract | We consider a piecewise smooth 2 × 2 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. |
| Source | Mediterranean journal of mathematics (Print) 13, pp. 4829–4844 |
| Keywords | Piecewise smooth systemsneural networksgenetic regulatory networksspiral motionstability |
| Journal | Mediterranean journal of mathematics (Print) |
| Editor | Birkhäuser,, Basel [etc.], Svizzera |
| Year | 2016 |
| Type | Articolo in rivista |
| DOI | 10.1007/s00009-016-0778-5 |
| Authors | Berardi M.; D'Abbicco M. |
| Text | 379335 2016 10.1007/s00009 016 0778 5 Scopus 2 s2.0 84982994347 ISI Web of Science WOS WOS 000387090000064 Piecewise smooth systems neural networks genetic regulatory networks spiral motion stability A Critical Case for the Spiral Stability for 2 × 2 Discontinuous Systems and an Application to Recursive Neural Networks Berardi M.; D Abbicco M. Istituto di Ricerca sulle Acque, Consiglio Nazionale delle Ricerche, Viale F. de Blasio, 5, Bari, 70132, Italy; Departamento de Computação e Matematica, Universidade de São Paulo USP , FFCLRP, Av. dos Bandeirantes, 3900, Ribeirão Preto, SP, CEP 14040 901, , Brazil We consider a piecewise smooth 2 × 2 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. 13 Published version http //www.scopus.com/record/display.url eid=2 s2.0 84982994347 origin=inward A Critical Case for the Spiral Stability for 2×2 Discontinuous Systems and an Application to Recursive Neural Networks MedJM_Berardi_DAbbicco_2016.pdf Articolo in rivista Birkhauser, 1660 5446 Mediterranean journal of mathematics Print Mediterranean journal of mathematics Print Mediterr. j. math. Print Mediterranean journal of mathematics Print MedJM Print marco.berardi BERARDI MARCO |