Related papers: Stability of Localized Patterns in Neural Fields
It has long been believed that the brain is highly modular both in terms of structure and function, although recent evidence has led some to question the extent of both types of modularity. We used artificial neural networks to test the…
Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the…
We consider the motion described by the Navier-Stokes equations in a box with periodic boundary conditions. First we prove the existence of global strong two-dimensional solutions. Next we show the existence of global strong…
The behavior of two-dimensional coupled map lattices is studied with respect to the global stabilization of unstable local fixed points without external control. It is numerically shown under which circumstances such inherent global…
Existing analyses of neural network training often operate under the unrealistic assumption of an extremely small learning rate. This lies in stark contrast to practical wisdom and empirical studies, such as the work of J. Cohen et al.…
We consider the existence of standing pulse solutions of a neural network integro-differential equation. These pulses are bistable with the zero state and may be an analogue for short term memory in the brain. The network consists of a…
Persistent activity in neuronal populations has been shown to represent the spatial position of remembered stimuli. Networks that support bump attractors are often used to model such persistent activity. Such models usually exhibit…
Relationship for dynamical properties in the vicinity of fixed points between two-dimensional continuous and its positivity-preserving discretized dynamical systems is studied. Based on linear stability analysis, we reveal the conditions…
In this work, we systematically investigate linear multi-step methods for differential equations with memory. In particular, we focus on the numerical stability for multi-step methods. According to this investigation, we give some…
In the present paper we are concerned with a numerical algorithm for the approximation of the two-dimensional neural field equation with delay. We consider three numerical examples that have been analysed before by other authors and are…
A system of stochastic differential equations for the velocity and density of a classical self-gravitating matter is investigated by means of the field theoretic renormalization group. The existence of two types of large-scale scaling…
We use the model of L. Randall et al to investigate the stability of allowed quantum field configurations. Firstly, we find that due to the topology of this 5 dimensional model, there are 2 possible configurations of the scalar field,…
Stability is a fundamental property of dynamical systems, yet to this date it has had little bearing on the practice of recurrent neural networks. In this work, we conduct a thorough investigation of stable recurrent models. Theoretically,…
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 work we study kinklike structures, which are localized solutions that appear in models described by real scalar fields. The model to be considered is characterized by two real scalar fields and includes a function of one of the two…
Exactly solvable neural network models with asymmetric weights are rare, and exact solutions are available only in some mean-field approaches. In this article we find exact analytical solutions of an asymmetric spin-glass-like model of…
Dynamic imaging is essential for analyzing various biological systems and behaviors but faces two main challenges: data incompleteness and computational burden. For many imaging systems, high frame rates and short acquisition times require…
Many organisms can remember locations they have previously visited during a search. Visual search experiments have shown exploration is guided away from these locations, reducing the overlap of the search path before finding a hidden…
In spite of the large amount of existing neural models in the literature, there is a lack of a systematic review of the possible effect of choosing different initial conditions on the dynamic evolution of neural systems. In this short…
We derive a sufficient condition for stability in probability of an equilibrium of a randomly perturbed map in ${\mathbb R}^d$. This condition can be used to stabilize weakly unstable equilibria by random forcing. Analytical results on…