Discrete-time versus continuous-time models of neural networks

Discrete-Time versus Continuous-Time Models of Neural Networks

In mathematical modeling, very often discrete-time (DT) models are taken from, or can be viewed as numerical discretizations of, certain continuous-time (CT) models. In this paper, a general criterion, the asymptotic consistency criterion, for these DT models to inherit the dynamical behavior of their CT counterparts is derived. Detailed instances of this criterion are established for several c...

FINITE-TIME PASSIVITY OF DISCRETE-TIME T-S FUZZY NEURAL NETWORKS WITH TIME-VARYING DELAYS

This paper focuses on the problem of finite-time boundedness and finite-time passivity of discrete-time T-S fuzzy neural networks with time-varying delays. A suitable Lyapunov--Krasovskii functional(LKF) is established to derive sufficient condition for finite-time passivity of discrete-time T-S fuzzy neural networks. The dynamical system is transformed into a T-S fuzzy model with uncertain par...

A Continuous-time Hoppeld Net Simulation of Discrete Neural Networks a Continuous-time Hoppeld Net Simulation of Discrete Neural Networks

We investigate the computational power of continuous-time symmetric Hoppeld nets. Since the dynamics of such networks are governed by Liapunov (energy) functions, they cannot generate innnite nondamping oscillations, and hence cannot simulate arbitrary (potentially divergent) discrete computations. Nevertheless, we prove that any conver-gent fully parallel computation by a network of n discrete...

A Continuous-time Hoppeld Net Simulation of Discrete Neural Networks

Hybrid discrete-time neural networks.

Hybrid dynamical systems combine evolution equations with state transitions. When the evolution equations are discrete-time (also called map-based), the result is a hybrid discrete-time system. A class of biological neural network models that has recently received some attention falls within this category: map-based neuron models connected by means of fast threshold modulation (FTM). FTM is a c...