Differential equations and dynamical systems
Differential equations and dynamical systems
Continuous attractors and oculomotor control
Neural Networks - Special issue on neural control and robotics: biology and technology
Selectively grouping neurons in recurrent networks of lateral inhibition
Neural Computation
Permitted and forbidden sets in symmetric threshold-linear networks
Neural Computation
A Competitive-Layer Model for Feature Binding and Sensory Segmentation
Neural Computation
A Winner-Take-All Neural Networks of N Linear Threshold Neurons without Self-Excitatory Connections
Neural Processing Letters
Discrete-time recurrent neural networks with complex-valued linear threshold neurons
IEEE Transactions on Circuits and Systems II: Express Briefs
Analysis of continuous attractors for 2-D linear threshold neural networks
IEEE Transactions on Neural Networks
Nontrivial global attractors in 2-D multistable attractor neural networks
IEEE Transactions on Neural Networks
Memory dynamics in attractor networks with saliency weights
Neural Computation
Continuous attractors of a class of neural networks with a large number of neurons
Computers & Mathematics with Applications
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The network of neurons with linear threshold (LT) transfer functions is a prominent model to emulate the behavior of cortical neurons. The analysis of dynamic properties for LT networks has attracted growing interest, such as multistability and boundedness. However, not much is known about how the connection strength and external inputs are related to oscillatory behaviors. Periodic oscillation is an important characteristic that relates to nondivergence, which shows that the network is still bounded although unstable modes exist. By concentrating on a general parameterized two-cell network, theoretical results for geometrical properties and existence of periodic orbits are presented. Although it is restricted to two-dimensional systems, the analysis can provide a useful contribution to analyze cyclic dynamics of some specific LT networks of high dimension. As an application, it is extended to an important class of biologically motivated networks of large scale: the winner-take-all model using local excitation and global inhibition.