Exponential Stability of Discrete Neural Networks With Non-Instantaneous Impulses, Delays and Variable Connection Weights With Computer Simulation

Abstract

The exponential stability concept for nonlinear non-instantaneous impulsive difference equations with a single delay is studied and some criteria are derived. These results are also applied for a neural networks with switching topology at certain moments and long time lasting impulses. It is considered the general case of time varying connection weights. The equilibrium is defined and exponential stability is studied. The obtained results are illustrated on examples.

Stability and Anti-Chaos Control of Discrete Quadratic Maps

“…Figure(9). For the considered parameter values, the quadratic map (1) is stable in the spiral inwards form, as shown in Figure (9A).…”

“…For this study, it is necessary, but highly nontrivial, to detect the fixed point of the discrete dynamical systems and analyze the stability and bifurcation of each fixed point. The discrete dynamical systems have been studied in several areas of physics, biology, neural networks, and many other [3,9,13,15,17,20]. The stability analysis and chaos of the discrete ecological systems were studied by various authors [8,10,11,17,14].…”