Related papers: Controlling chaos in diluted networks with continu…
We provide an empirical study of the stability of recurrent neural networks trained to recognize regular languages. When a small amount of noise is introduced into the activation function, the neurons in the recurrent layer tend to saturate…
This paper is concerned with the study of synchronization and consensus phenomena in complex networks of diffusively-coupled nodes subject to external disturbances. Specifically, we make use of stochastic Lyapunov functions to provide…
Biological neural networks operate in the presence of task disruptions as they guide organisms toward goals. A familiar stream of stimulus-response causations can be disrupted by subtask streams imposed by the environment. For example,…
Synaptic connections between neurons in the brain are dynamic because of continuously ongoing spine dynamics, axonal sprouting, and other processes. In fact, it was recently shown that the spontaneous synapse-autonomous component of spine…
The paper considers a stabilizing stochastic control which can be applied to a variety of unstable and even chaotic maps. Compared to previous methods introducing control by noise, we relax assumptions on the class of maps, as well as…
Oscillatory activities are widely observed in specific frequency bands of recorded field potentials in different brain regions, and play critical roles in processing neural information. Understanding the structure of these oscillatory…
Given a population of interconnected input-output agents repeatedly exposed to independent random inputs, we talk of correlated variability when agents' outputs are variable (i.e., they change randomly at each input repetition) but…
Synaptic connections in neuronal circuits are modulated by pre- and post-synaptic spiking activity. Heuristic models of this process of synaptic plasticity can provide excellent fits to results from in-vitro experiments in which pre- and…
This paper studies how complicated and irregular behavior, known as chaos, can arise in a simple mathematical model that includes time delays. The model is a delay differential equation in which the present rate of change depends not only…
Many studies have shown that the excitation and inhibition received by cortical neurons remain roughly balanced across many conditions. A key question for understanding the dynamical regime of cortex is the nature of this balancing.…
The dynamics of activation waves in excitable media can give rise to spiral turbulence, the resulting spatiotemporal chaos being associated with empirical biological phenomena such as life-threatening disturbances in the natural rhythm of…
We study the spike statistics of neurons in a network with dynamically balanced excitation and inhibition. Our model, intended to represent a generic cortical column, comprises randomly connected excitatory and inhibitory leaky…
Recurrent Neural Network models have elucidated the interplay between structure and dynamics in biological neural networks, particularly the emergence of irregular and rhythmic activities in cortex. However, most studies have focused on…
Cortical networks can maintain memories for decades despite the short lifetime of synaptic strength. Can a neural network store long-lasting memories in unstable synapses? Here, we study the effects of random noise on the stability of…
Neural-network models of high-level brain functions such as memory recall and reasoning often rely on the presence of stochasticity. The majority of these models assumes that each neuron in the functional network is equipped with its own…
Understanding how the brain learns to compute functions reliably, efficiently and robustly with noisy spiking activity is a fundamental challenge in neuroscience. Most sensory and motor tasks can be described as dynamical systems and could…
Previous work showed that the collective activity of large neuronal networks can be tamed to remain near its critical point by a feedback control that maximizes the temporal correlations of the mean-field fluctuations. Since such…
A complete self-control mechanism is proposed in the dynamics of neural networks through the introduction of a time-dependent threshold, determined in function of both the noise and the pattern activity in the network. Especially for…
The effects of disorder in external forces on the dynamical behavior of coupled nonlinear oscillator networks are studied. When driven synchronously, i.e., all driving forces have the same phase, the networks display chaotic dynamics. We…
The dynamics and the stationary states of an exactly solvable three-state layered feed-forward neural network model with asymmetric synaptic connections, finite dilution and low pattern activity are studied in extension of a recent work on…