Two Types Of Stability Of Bidirectional Associative Memory Neural Network Analysis

The delayed neural networks exhibiting the rich and colorful dynamical behaviors are an important part of the delayed large systems. Due to their important applications in signal processing,image processing as well as optimizing problems, the stability issues of delayed BAM neural networks have attracted worldwide attention in recent years. The thesis mainly deal with the global exponential asymptotic stability problem of the equilibria for two types of delayed BAM neural networks. A series of significative results have been obtained. The main contents are as follows:1. The problem of global exponential stability for a class of BAM neural networks with time-varying delays.Consider the following neural networks described by:u(t)=-C₁u(t)+A₁W(v(t))+B₁W(v(t-τ(t)))+I,v(t)=-C₂v(t)+A₂H(u(t))+B₂H(u(t-τ(t)))+J,where u(t)=[u₁(t),u₂(t),…,u_n(t)]^T,v(t)=[v₁(t),v₂(t),…,v_m(t)]^T are the neuron statevectors. C₁, C₂ are the relaxation matrices, A₁, B₁, A₂, B₂ are the weighting matrices, I, J are the constant external input vectors,τ(t) is the differentiate time delay, W(v(t)), W(v(t-τ(t))), H(u(t)), H(u(t -τ(t))) are the activation functions of the delayed BAM neural networks.Some new and easily verified sufficient conditions for global exponential stability of BAM neural networks are established via constructing an appropriate Lyapunov- Krasovskii functional, and furthermore. The proposed algorithm is less conservatism than the reported results.2. The problem of robust global exponential stability for a class of uncertain BAM neural networks with time-varying delays. Consider the following neural networks systems:u(t)=-(A₁+△A₁)u(t)+(B₁+△B₁)W(v(t-τ(t)))+I,v(t)=-(A₂+△A₂)v(t)+(B₂+△B₂)H(u(t-σ(t)))+J,where u(t),v(t) are the neuron state vectors,A₁,B₁,A₂,B₂ are the weighting matrices,△A₁,△A₂,△B₁,△B₂ are the parameter perturbations of A₁, A₂, B₁, B₂,I, J are the constant external input vectors,τ(t),σ(t) are the differentiable time delay, W(v(t -τ(t))), H(u(t -τ(t))) are the activation functions.In this thesis, a novel global exponential stability criterion with less restriction is derived via transforming the original model into an equivalent descriptor system. Numerical example is given to demonstrate the reduced conservatism of the algorithm.Throughout this paper, we take some traditional assumptions on the activation functions: Assumption 1: There exist some positive constantsα_i (i = 1,2,…,m) andβ_j (j = 1,2,…,n) such that0≤W_i(x)-W_i(y)/x-y≤α_i,i=1,2,…,m0≤H_j(x)-H_j(y)/x-y≤β_j,j=1,2,…,nfor any x,y∈R,x≠y.Assumption 2: The activation functions are bounded, that is,|W_i(x)|≤M_i,|H_j(x)|≤N_j,i=1,2,…,m,j=1,2,…,nwhere M_i > 0 and N_j > 0 are some positive constant numbers.