Hopf bifurcating periodic orbits in a ring of neurons with delays

Dynamical Behavior in a Four-Dimensional Neural Network Model with Delay

“…The object of this section is to investigate the stability of the equilibrium and the existence of local Hopf bifurcations for system (2). It is easy to see that if the following condition:…”

“…The interest in the periodic orbits of a delay neural networks has increased strongly in recent years and substantial efforts have been made in neural network models, for example, Wei and Zhang [1] studied the stability and bifurcation of a class of n-dimensional neural networks with delays, Guo and Huang [2] investigated the Hopf bifurcation behavior of a ring of neurons with delays, Yan [3] discussed the stability and bifurcation of a delayed trineuron network model, Hajihosseini et al [4] made a discussion on the Hopf bifurcation of a delayed recurrent neural network in the frequency domain, and Liao et al [5] did a theoretical and empirical investigation of a two-neuron system with distributed delays in the frequency domain. For more information, one can see [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23].…”

“…When delays are incorporated into the network models, stability, and Hopf bifurcation analysis become much complex. To obtain a deep and clear understanding of dynamics of neural network model with delays, we will make a investigation on system (2), that is, we study the stability, the local Hopf bifurcation for system (2). The remainder of the paper is organized as follows.…”

Equivariant Hopf bifurcation for neutral functional differential equations

“…It is easy to see that system (3.1) is D n -equivariant (see [8,12]). Let A(c) be the infinitesimal generator of the linear operator generated by the linearization of (3.1) about the trivial solution u = 0.…”

Existence and exponentially stability of anti-periodic solutions for neutral BAM neural networks with time-varying delays in the leakage terms

“…In the last three decades, considerable attention has been paid to BAM neural networks as well as various generalizations for their essential applications in classification, pattern recognition, optimization, signal and image processing, parallel computation, associative memory and nonlinear optimization problems and so on [1,2,7,9,11,13,15,17,21,25,28,29,30,33,34,37,38,39,40,41,42]. Recently, Li and Li [16] studied the following neutral delay BAM neural networks with time-varying delays in leakage terms…”