The Hopf bifurcation analysis on a time-delayed recurrent neural network in the frequency domain

Authors:
Amirhossein Hajihosseini;Gholam Reza Rokni Lamooki;Babak Beheshti;Farzaneh Maleki
Affiliations:
Center of Excellence in Biomathematics, School of Mathematics, Statistics and Computer Science, University of Tehran, Tehran 14176-14411, Iran;Center of Excellence in Biomathematics, School of Mathematics, Statistics and Computer Science, University of Tehran, Tehran 14176-14411, Iran and College of Science, School of Mathematics, Statis ...;Center of Excellence in Biomathematics, School of Mathematics, Statistics and Computer Science, University of Tehran, Tehran 14176-14411, Iran;Center of Excellence in Biomathematics, School of Mathematics, Statistics and Computer Science, University of Tehran, Tehran 14176-14411, Iran
Venue:
Neurocomputing
Year:
2010

Citing 10
Cited 3

Elements of applied bifurcation theory (2nd ed.)

Elements of applied bifurcation theory (2nd ed.)
Bifurcation analysis on a two-neuron system with distributed delays

Physica D
Modern Control Engineering

Modern Control Engineering
Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delays

Neural Networks
Bifurcation analysis on a two-neuron system with distributed delays

Neural Networks
Global exponential stability of generalized recurrent neural networks with discrete and distributed delays

Neural Networks
Global attraction and stability for Cohen-Grossberg neural networks with delays

Neural Networks
Global exponential periodicity and global exponential stability of a class of recurrent neural networks with various activation functions and time-varying delays

Neural Networks
Exponential stability of recurrent neural networks with both time-varying delays and general activation functions via LMI approach

Neurocomputing
Existence, learning, and replication of periodic motions in recurrent neural networks

IEEE Transactions on Neural Networks

The Bogdanov-Takens bifurcation analysis on a three dimensional recurrent neural network

Neurocomputing
Dynamical behavior in a four-dimensional neural network model with delay

Advances in Artificial Neural Systems
Frequency domain approach to computational analysis of bifurcation and periodic solution in a two-neuron network model with distributed delays and self-feedbacks

Neurocomputing

Quantified Score

Hi-index	0.01

Visualization

Abstract

In this paper, a class of recurrent neural networks with distributed delays and a strong kernel is studied. It is shown that the Hopf bifurcation occurs as the bifurcation parameter, the mean delay, passes a critical value where a family of periodic solutions emanates from the equilibrium. The existence and stability of such solutions are determined by the Hopf bifurcation theorem in the frequency domain and the generalized Nyquist stability criterion.