This paper presents a stability criterion for global asymptotic stability of the equilibrium point for Bidirectional Associative Memory (BAM) neural networks with fixed time delays. An approach combining the Lyapunov-Krasovskii functional with Linear Matrix Inequality (LMI) is taken to investigate the stability of the system. A delay-dependent LMI criterion is derived. Finally, a numerical exam...

Building on recent work on homogeneous cooperative systems, we extend results concerning stability of such systems to subhomogeneous systems. We also consider subhomogeneous cooperative systems with constant input, and relate the global asymptotic stability of the unforced system to the existence and stability of positive equilibria for the system with input.

A subset A of the state space is called uniformly globally weakly attractive if for any neighborhood S of A and any bounded subset B there is a uniform finite time τ so that any trajectory starting in B intersects S within the time not larger than τ . We show that practical uniform global asymptotic stability (pUGAS) is equivalent to the existence of a bounded uniformly globally weakly attracti...

It was conjectured that for every integer m 3 the unique equilibrium c = 1 of the generalized Putnam equation xn+1 = ∑m−2 i=0 xn−i + xn−m+1xn−m xnxn−1 + ∑m i=2 xn−i , n= 0,1,2, . . . , with positive initial conditions is globally asymptotically stable. In this paper, we prove this conjecture. © 2005 Elsevier Inc. All rights reserved.

Conditions for Global Asymptotic Stability (GAS) of a nonlinear relaxation process realized by a Recurrent Neural Network (RNN) are provided. Existence. convergence, and robustness of such a process are analyzed. This is undertaken based upon the Contraction Mapping Theorein (CMT) and the corresponding Fixed Point Iteration (FPI). Upper bounds for such a process are shown to be the conditions o...

In this paper, we study the global stability of the difference equation

We study the difference equation xn = [( f × g1 + g2 +h)/(g1 + f × g2 +h)](xn−1, . . . ,xn−r), n = 1,2, . . . , x1−r , . . . ,x0 > 0, where f ,g1,g2 : (R+) → R+ and h : (R+) → [0,+∞) are all continuous functions, and min1≤i≤r{ui,1/ui} ≤ f (u1, . . . ,ur) ≤ max1≤i≤r{ui,1/ui}, (u1, . . . ,ur) T ∈ (R+) . We prove that this difference equation admits c = 1 as the globally asymptotically stable equi...