Exponential stability and periodic oscillatory of bi-directional associative memory neural network involving delays

In this paper, bidirectional associative memory (BAM) neural network with delays is considered. By employing the inequality bm+1∏k=1mbkqk⩽1/r∑k=1mqkbkr+(1/r)bm+1r(bm+1⩾0,bk⩾0,qk>0(bm+1⩾0,bk⩾0,qk>0 with 1+∑k=1mqk=r,k=1,…,m), applying homotopic mapping and constructing a new Lyapunov functional method, we present some new criteria ensuring globally exponential stability and the existence of periodic oscillatory solution. These results are helpful to design globally exponential stability and periodic oscillatory for BAM neural network with delays.