Bifurcation analysis of a class of neural networks with delays

Stability of Quasi-Periodic Orbits in Recurrent Neural Networks

“…References [10,12] and [27] complete the bifurcation results for two-neuron discrete-time Hopfield neural networks with time delay and only self-connections between the neurons (no interactions between them) [26]. In [4,5,23] and [24] the results are generalized to n-neuron Hopfield neural networks. In [17], the discrete-time dynamics of a two-neuron network with recurrent connectivity, known as "ring neural networks", are studied, showing the relationship between the dynamics and the evolution of its external outputs for specific parameter configurations.…”

Stability switches and double Hopf bifurcation in a two-neural network system with multiple delays

“…Many researchers tried to fill in some ''piece of the puzzle'' for the multiple delays problem (Li et al 1999). Considered the average/sum of time delays as the variable parameter and used the time-scale transformation, some multipledelayed neural network systems with simple architecture can be transformed to the equivalent models with one single delay (Cao and Xiao 2007;Mao and Hu 2008;Wei and Zhang 2008).…”

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

“…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].…”

“…For more information, one can see [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. In 1986 and 1987, Babcock and Westervelt [24,25] had analyzed the stability and dynamics of the following simple neural network model of two neurons with inertial coupling: 4 , dx 3 dt = −2ξx 3 …”

“…For a more detailed interpretation of the parameters, one can see [24,25]. In 1997, Lin and Li [26] made a detailed investigation on the bifurcation direction of periodic solution for system (1).…”