Mathematical theory of neural learning
New Generation Computing - Selected papers from the international workshop on algorithmic learning theory,1990
Neural networks and fuzzy systems: a dynamical systems approach to machine intelligence
Neural networks and fuzzy systems: a dynamical systems approach to machine intelligence
Recursive neural networks for associative memory
Recursive neural networks for associative memory
Exponential stability of Cohen-Grossberg neural networks
Neural Networks
Convergence of a Subclass of Cohen–Grossberg Neural Networks via the Łojasiewicz Inequality
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Existence, learning, and replication of periodic motions in recurrent neural networks
IEEE Transactions on Neural Networks
Existence and learning of oscillations in recurrent neural networks
IEEE Transactions on Neural Networks
Time delays and stimulus-dependent pattern formation in periodic environments in isolated neurons
IEEE Transactions on Neural Networks
High-order neural network structures for identification of dynamical systems
IEEE Transactions on Neural Networks
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In this paper, we study the dynamical behavior of an adaptive higher-order Cohen-Grossberg model and choose a biologically plausible rule specifying how the connection weights will vary in time, i.e., we incorporate an unsupervised Hebbian-type learning rule with a higher-order Cohen-Grossberg model. By constructing several Lyapunov functions, some sufficient conditions for the asymptotic and exponential stability of the equilibrium are derived. Furthermore, we also study how a temporally varying, in particular, a periodic environment, can influence on the dynamics of this model, i.e., the neuronal parameters, synaptic weights, and gains can either be temporally uniform or be periodic with same period as that of the stimulus. Sufficient condition for the existence of a globally attractive periodic solution associated with a given periodic external stimulus is also derived. Some numerical examples are employed to illustrate our theoretical results.