Abstract
Conditions for the global asymptotic stability of delayed artificial neural network model of n (≥3) neurons have been derived. For bifurcation analysis with respect to delay we have considered the model with three neurons and used suitable transformation on multiple time delays to reduce it to a system with single delay. Bifurcation analysis is discussed with respect to single delay. Numerical simulations are presented to verify the analytical results. Using numerical simulation, the role of delay and neuronal gain parameter in changing the dynamics of the neural network model has been discussed.
Highlights
In recent years, neural networks have been applied successfully in many areas such as signal processing, pattern recognition, and associative memories
We studied the global stability of artificial neural network model of n-neurons with time delay and obtained the criteria of involving the synaptic weight and decay parameters, independent of delay
The system shows chaotic behavior without delay and introduction of delay plays a vital role in controlling chaos in the system
Summary
Neural networks (especially Hopfield type, cellular, bidirectional, and recurrent neural networks) have been applied successfully in many areas such as signal processing, pattern recognition, and associative memories. Aihara et al [6] introduced chaotic neural network models in order to simulate the chaotic behavior of biological neurons. Both the network and its component neuron are responsible for chaotic dynamics if suitable parameter values are chosen [6, 7]. Change of neuronal gain parameter causes a change of all connectivity weights and affects the dynamical behavior of the network [21] For this reason, we are motivated to study effectiveness of time delay as well as neuronal gain parameters in changing the dynamics of an artificial neural network model. Some concluding remarks have been drawn on the implication of our results in the context of related work mentioned above
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