On the P-critical dynamics analysis of projection recurrent neural networks

Dynamics research of recurrent neural networks is very meaningful in both theoretical importance and practical significance. Recently, the study on the critical dynamics behaviors of such networks has drawn especial attention because of its application requirements. In this paper, new criteria are found to ascertain the global convergence and asymptotic stability of recurrent neural networks under the generally P  -critical conditions, i.e., a discriminant matrix M(L,Γ)+PM(L,Γ)+P is nonnegative definite, where M(L,Γ)M(L,Γ) is a matrix related with the network and P   is an arbitrary nonnegative definite matrix. The analysis results given in this paper improve substantially upon the existing relevant convergence and stability results in literature, including both the non-critical conclusions, i.e., the dynamics analysis under the conditions that M(L,Γ)M(L,Γ) is positive definite, and the special critical discuss when M(L,Γ)M(L,Γ) is nonnegative definite.