Coexistence of domains of attraction of nonautonomous neural networks with time-varying delays

This paper presents new dynamical behavior, i.e., the coexistence of 2^N domains of attraction of N-dimensional nonautonomous neural networks with time-varying delays. By imposing some new assumptions on activation functions and system parameters, we construct 2^N invariant basins for neural system and derive some criteria on the boundedness and exponential attractivity for each invariant basin. Particularly, when neural system degenerates into periodic case, we not only attain the coexistence of 2^N periodic orbits in bounded invariant basins but also give their domains of attraction. Moreover, our results are suitable for autonomous neural systems. Our new results improve and generalize former ones. Finally, computer simulation is performed to illustrate the feasibility of our results.