Sequences of neural activity arise in many brain areas, including cortex, hippocampus, and
central pattern generator circuits that underlie rhythmic behaviors like locomotion. While …

There is enormous interest--both mathematically and in diverse applications--in
understanding the dynamics of coupled oscillator networks. The real-world motivation of …

Threshold-linear networks consist of simple units interacting in the presence of a threshold
nonlinearity. Competitive threshold-linear networks have long been known to exhibit …

Neurons in the brain are constantly flickering with activity, which can be spontaneous or in
response to stimuli [LBH09]. Because of positive feedback loops and the potential for …

Threshold-linear networks consist of simple units interacting in the presence of a threshold
nonlinearity. Competitive threshold-linear networks have long been known to exhibit …

Oscillatory activity is highly prevalent in the brain. Oscillations with specific characteristics
are associated with a variety of healthy and diseased brain functions. This letter considers …

Nonlinear network dynamics are notoriously difficult to understand. Here we study a class of
recurrent neural networks called combinatorial threshold-linear networks (CTLNs) whose …

Neurons in the brain are constantly flickering with activity, which can be spontaneous or in
response to stimuli LBH09. Because of positive feedback loops and the potential for …

This paper is concerned with global dynamics, especially periodicity, for a piecewise smooth
system incorporating a new control strategy. The switches take place at discrete times and …

Oscillations arise in many real-world systems and are associated with both functional and
dysfunctional states. Whether a network can oscillate can be estimated if we know the …