Search

Abstract: The global exponential stability of cellular neural networks (CNNs) with time-varying delays is analyzed. Two new sufficient conditions ensuring global exponential stability for delayed CNNs are obtained. The conditions presented here are related to the size of delay. The stability results improve the earlier publications. Two examples are given to demonstrate the effectiveness of the obtained results. [Copyright &y& Elsevier]

A new subalgebra G of the Lie algebra A2 is first constructed. Then two loop algebra G1, G2 are presented in terms of different definitions of gradations. Using G1, G2 designs two isospectral problems, respectively. Again utilizing Tu-pattern obtains two types of various integrable Hamiltonian hierarchies of evolution equations. As reduction cases, the well-known Schro¨dinger equation and MKdV equation are obtained. At last, we turn the subalgebras G1, G2 of the loop algebra A2 into equivalent subalgebras of the loop algebra A1 by making a suitable linear transformation so that the two types of 5-dimensional loop algebras are constructed. Two kinds of integrable couplings of the obtained hierarchies are showed. Specially, the integrable couplings of Schro¨dinger equation and MKdV equation are obtained, respectively. [Copyright &y& Elsevier]