Continuous attractors and oculomotor control
Neural Networks - Special issue on neural control and robotics: biology and technology
Analysis of Cyclic Dynamics for Networks of Linear Threshold Neurons
Neural Computation
Analysis of continuous attractors for 2-D linear threshold neural networks
IEEE Transactions on Neural Networks
Dynamics of Winner-Take-All Competition in Recurrent Neural Networks With Lateral Inhibition
IEEE Transactions on Neural Networks
Boolean Factor Analysis by Attractor Neural Network
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
Local and Global Stability Analysis of an Unsupervised Competitive Neural Network
IEEE Transactions on Neural Networks
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Attractor dynamics is a crucial problem for attractor neural networks, as it is the underling computational mechanism for memory storage and retrieval in neural systems. This brief studies a class of attractor network consisting of linearized threshold neurons, and analyzes global attractors based on a parameterized 2-D model. On the basis of previous results on nondegenerate and degenerate equilibria in mathematics, we further elucidate all possible nontrivial global attractors. Our theoretical result provides precise descriptions on how the changes of network parameters affect the attractors' distribution and landscape, and it may give a feasible solution towards specifying attractors by specifying weights. Simulations are presented to illustrate the theoretical results.