相关论文: Stability of Localized Patterns in Neural Fields
Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay differential equation \begin{equation*} D^\alpha x(t)=\delta…
We transpose work by K.Yajima and by T.Mizumachi to prove dispersive and smoothing estimates for dispersive solutions of the linearization at a ground state of a Nonlinear Schr\"odinger equation (NLS) in 2D. As an application we extend to…
The computational capabilities of a neural network are widely assumed to be determined by its static architecture. Here we challenge this view by establishing that a fixed neural structure can operate in fundamentally different…
We address the problem of stability of motor actions implemented by the central nervous system based on simple algorithms potentially reflecting physical (including physiological) processes within the body. A number of conceptually simple…
The Davey-Stewartson (DS) equations with a perturbation term are presented by taking a fluid system as an example on an uneven bottom. Stability of dromions, solutions of the DS equations with localized structures, against the perturbation…
Localised radial patterns have been observed in the vegetation of semi-arid ecosystems, often as localised patches of vegetation or in the form of `fairy circles'. We consider stationary localised radial solutions to a reduced model for…
Deep predictive models of neuronal activity have recently enabled several new discoveries about the selectivity and invariance of neurons in the visual cortex. These models learn a shared set of nonlinear basis functions, which are linearly…
A particular type of random dynamical processes is considered, in which the stochasticity is introduced through randomly fluctuating parameters. A method of local multipliers is developed for treating the local stability of such dynamical…
The dynamics of two-level systems in an external periodic field are investigated in general. The necessary conditions of localization are obtained through analysing the time-evolving matrix. It is found that localization is possible if not…
We study the existence and stability of localized states in the two-dimensional (2D) nonlinear Schrodinger (NLS)/Gross-Pitaevskii equation with a symmetric four-well potential. Using a fourmode approximation, we are able to trace the…
A common problem to all applications of linear finite dynamical systems is analyzing the dynamics without enumerating every possible state transition. Of particular interest is the long term dynamical behaviour. In this paper, we study the…
Deep neural networks have become invaluable tools for supervised machine learning, e.g., classification of text or images. While often offering superior results over traditional techniques and successfully expressing complicated patterns in…
In this paper, we study the asymptotic behavior of solutions to a scalar fractional delay differential equations around the equilibrium points. More precise, we provide conditions on the coefficients under which a linear fractional delay…
We discuss the properties of equilibrium states in an autoassociative memory model storing hierarchically correlated patterns (hereafter, hierarchical patterns). We will show that symmetric mixed states (hereafter, mixed states) are…
Localized patterns in singularly perturbed reaction-diffusion equations typically consist of slow parts -- in which the associated solution follows an orbit on a slow manifold in a reduced spatial dynamical system -- alternated by fast…
The analysis on stability and bifurcations in the macroscopic dynamics exhibited by the system of two coupled large populations comprised of $N$ stochastic excitable units each is performed by studying an approximate system, obtained by…
This paper uses the notion of algorithmic stability to derive novel generalization bounds for several families of transductive regression algorithms, both by using convexity and closed-form solutions. Our analysis helps compare the…
Stability is a key property of both forward models and inverse problems, and depends on the norms considered in the relevant function spaces. For instance, stability estimates for hyperbolic partial differential equations are often based on…
Neuronal systems maintain stable functions despite large variability in their physiological components. Ion channel expression, in particular, is highly variable in neurons exhibiting similar electrophysiological phenotypes, which poses…
The aim of this paper is to study the stability of soliton-like static solutions via non-linear simulations in the context of a special class of massive tensor-multi-scalar-theories of gravity whose target space metric admits Killing…