Geodesic
Existence and exponential stability of periodic solution for continuous-time and discrete-time generalized bidirectional neural networks
Electronic journal of differential equations, Tome 2006 (2006)
We study the existence and global exponential stability of positive periodic solutions for a class of continuous-time generalized bidirectional neural networks with variable coefficients and delays. Discrete-time analogues of the continuous-time networks are formulated and the existence and global exponential stability of positive periodic solutions are studied using the continuation theorem of coincidence degree theory and Lyapunov functionals. It is shown that the existence and global exponential stability of positive periodic solutions of the continuous-time networks are preserved by the discrete-time analogues under some restriction on the discretization step-size. An example is given to illustrate the results obtained.
Classification : 34K13, 34K25
Keywords: bidirectional neural networks, global exponential stability, periodic solution, Fredholm mapping, Lyapunov functionals, discrete-time analogues 
@article{EJDE_2006__2006__a168,
     author = {Li,  Yongkun},
     title = {Existence and exponential stability of periodic solution for continuous-time and discrete-time generalized bidirectional neural networks},
     journal = {Electronic journal of differential equations},
     year = {2006},
     volume = {2006},
     zbl = {1100.34056},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a168/}
}
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%A Li,  Yongkun
%T Existence and exponential stability of periodic solution for continuous-time and discrete-time generalized bidirectional neural networks
%J Electronic journal of differential equations
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Li,  Yongkun. Existence and exponential stability of periodic solution for continuous-time and discrete-time generalized bidirectional neural networks. Electronic journal of differential equations, Tome 2006 (2006). http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a168/