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Information transmission is a key element for information processing in the brain. A number of mechanisms have been proposed for transferring volleys of spikes between layers of a feedforward neural circuit. Many of these mechanisms use…
Attractor dynamics are a fundamental computational motif in neural circuits, supporting diverse cognitive functions through stable, self-sustaining patterns of neural activity. In these lecture notes, we review four key examples that…
Neural circuits in the brain perform a variety of essential functions, including input classification, pattern completion, and the generation of rhythms and oscillations that support processes such as breathing and locomotion. There is also…
Classical autoassociative memory models have been central to understanding emergent computations in recurrent neural circuits across diverse biological contexts. However, they typically neglect neuromodulatory agents that are known to…
Phasor Agents are dynamical systems whose internal state is a Phasor Graph: a weighted graph of coupled Stuart-Landau oscillators. A Stuart-Landau oscillator is a minimal stable "rhythm generator" (the normal form near a Hopf bifurcation);…
It is shown that the time-averaged dynamics of memristors and their networks periodically driven by alternating-polarity pulses may converge to fixed-point attractors. Starting with a general memristive system model, we derive basic…
The asymptotic attractors of a nonlinear dynamical system play a key role in the long-term physically observable behaviors of the system. The study of attractors and the search for distinct types of attractor have been a central task in…
Recordings of increasingly large neural populations have revealed that the firing of individual neurons is highly coordinated. When viewed in the space of all possible patterns, the collective activity forms non-linear structures called…
Bump attractors are wandering localised patterns observed in in vivo experiments of spatially-extended neurobiological networks. They are important for the brain's navigational system and specific memory tasks. A bump attractor is…
Recent evidence suggests that neural information is encoded in packets and may be flexibly routed from region to region. We have hypothesized that neural circuits are split into sub-circuits where one sub-circuit controls information…
Self-sustained, elevated neuronal activity persisting on time scales of ten seconds or longer is thought to be vital for aspects of working memory, including brain representations of real space. Continuous-attractor neural networks, one of…
In this review, we describe the singular success of attractor neural network models in describing how the brain maintains persistent activity states for working memory, error-corrects, and integrates noisy cues. We consider the mechanisms…
Neural oscillations can enhance feature recognition, modulate interactions between neurons, and improve learning and memory. Simulational studies have shown that coherent oscillations give rise to windows in time during which information…
In a first step towards the comprehension of neural activity, one should focus on the stability of the various dynamical states. Even the characterization of idealized regimes, such as a perfectly periodic spiking activity, reveals…
Understanding how the dynamics of a neural network is shaped by the network structure, and consequently how the network structure facilitates the functions implemented by the neural system, is at the core of using mathematical models to…
Anatomical studies demonstrate that brain reformats input information to generate reliable responses for performing computations. However, it remains unclear how neural circuits encode complex spatio-temporal patterns. We show that neural…
While spiking neural networks (SNNs) provide a biologically inspired and energy-efficient computational framework, their robustness and the dynamic advantages inherent to biological neurons remain significantly underutilized owing to…
Combinatorial threshold-linear networks (CTLNs) are a special class of inhibition-dominated TLNs defined from directed graphs. Like more general TLNs, they display a wide variety of nonlinear dynamics including multistability, limit cycles,…
Coherent neural spiking and local field potentials are believed to be signatures of the binding and transfer of information in the brain. Coherent activity has now been measured experimentally in many regions of mammalian cortex. Synfire…
Recent experimental and computational evidence suggests that several dynamical properties may characterize the operating point of functioning neural networks: critical branching, neutral stability, and production of a wide range of firing…