Convergent activation dynamics in continuous time networks
Neural Networks
Associative dynamics in a chaotic neural network
Neural Networks
Elements of applied bifurcation theory (2nd ed.)
Elements of applied bifurcation theory (2nd ed.)
Dynamics of a class of discete-time neural networks and their comtinuous-time counterparts
Mathematics and Computers in Simulation
Stability and bifurcation analysis on a discrete-time neural network
Journal of Computational and Applied Mathematics
SIAM Journal on Scientific Computing
SO(2)-networks as neural oscillators
IWANN'03 Proceedings of the Artificial and natural neural networks 7th international conference on Computational methods in neural modeling - Volume 1
How delays affect neural dynamics and learning
IEEE Transactions on Neural Networks
Bifurcation of a discrete-time cohen-grossberg-type BAM neural network with delays
ISNN'13 Proceedings of the 10th international conference on Advances in Neural Networks - Volume Part I
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This paper is devoted to the analysis of a discrete-time-delayed Hopfield-type neural network of p neurons with ring architecture. The stability domain of the null solution is found, the values of the characteristic parameter for which bifurcations occur at the origin are identified and the existence of Fold/Cusp, Neimark-Sacker and Flip bifurcations is proved. These bifurcations are analyzed by applying the center manifold theorem and the normal form theory. It is proved that resonant 1:3 and 1:4 bifurcations may also be present. It is shown that the dynamics in a neighborhood of the null solution become more and more complex as the characteristic parameter grows in magnitude and passes through the bifurcation values. A theoretical proof is given for the occurrence of Marotto's chaotic behavior, if the magnitudes of the interconnection coefficients are large enough and at least one of the activation functions has two simple real roots.