Global exponential stability and existence of periodic solution of Hopfield-type neural networks with impulses

• DOI: 10.1016/j.physleta.2004.09.083
• Publication Date: 2004-10-24T03:07:12Z
• Authors: Yongkun Li; Linghong Lu
• Keywords: Hopfield network

Abstract We use the continuation theorem of coincidence degree theory and Lyapunov functions to study the existence and global exponential stability of periodic solution for Hopfield-type model of neural network with impulses { d x i ( t ) d t = − a i ( t ) x i ( t ) + ∑ j = 1 m b i j ( t ) f j ( x j ( t ) ) + J i ( t ) , t > 0 , t ≠ t k , Δ x i ( t k ) = x i ( t k + ) − x i ( t k − ) = − γ i k x i ( t k ) , i = 1 , … , m , k = 1 , 2 , … , where a i ( t ) > 0 , b i j , J i : R → R , i , j = 1 , … , m , a i , b i j , J i ( i , j = 1 , … , m ) are functions of period ω > 0 , and there exists a positive integer q, such that t k + q = t k + ω , γ i ( k + q ) = γ i k > 0 . An illustrative example is given to demonstrate the effectiveness of the obtained results.