相关论文: Modeling the modulation of neuronal bursting: a si…

Neural networks exhibit a remarkable degree of representational convergence across diverse architectures, training objectives, and even data modalities. This convergence is predictive of alignment with brain representation. A recent…

A piecewise continuous map for modeling bursting and spiking behaviour of isolated neuron is proposed. The map was created from phenomenological viewpoint. The map demonstrates oscillations, which are qualitatively similar to oscillations…

A simple and general formalism for mode coupling by a spatial, temporal or spatiotemporal perturbation in dispersive materials is developed. This formalism can be used for studying various linear and non-linear optical interactions…

By controlling the state of neuronal populations, neuromodulators ultimately affect behaviour. A key neuromodulation mechanism is the alteration of neuronal excitability via the modulation of ion channel expression. This type of…

The growth of several biological tissues is known to be controlled in part by local geometrical features, such as the curvature of the tissue interface. This control leads to changes in tissue shape that in turn can affect the tissue's…

We report on the origin of synchronized bursting dynamics in various networks of neural spiking oscillators, when a certain threshold in coupling strength is exceeded. These ensembles synchronize at relatively low coupling strength and lose…

We study the dynamics of a low-dimensional system of coupled model neurons as a step towards understanding the vastly complex network of neurons in the brain. We analyze the bifurcation structure of a system of two model neurons with…

Understanding how biological constraints shape neural computation is a central goal of computational neuroscience. Spatially embedded recurrent neural networks provide a promising avenue to study how modelled constraints shape the combined…

We propose to control the orbits of the two-dimensional Rulkov model affected by bounded noise. For the correct parameter choice the phase space presents two chaotic regions separated by a transient chaotic region in between. One of the…

We propose a hierarchically modular, dynamical neural network model whose architecture minimizes a specifically designed energy function and defines its temporal characteristics. The model has an internal and an external space that are…

All higher order central nervous systems exhibit spontaneous neural activity, though the purpose and mechanistic origin of such activity remains poorly understood. We explore the ignition and spread of collective spontaneous…

We develop a generalization of the time-varying Drude model, treating carrier density, effective mass, and collision rate as explicit functions of time. We derive expressions for polarization, susceptibility, displacement, and permittivity…

Neurons in the brain are often finely tuned for specific task variables. Moreover, such disentangled representations are highly sought after in machine learning. Here we mathematically prove that simple biological constraints on neurons,…

Human learning is a complex phenomenon requiring flexibility to adapt existing brain function and precision in selecting new neurophysiological activities to drive desired behavior. These two attributes -- flexibility and selection -- must…

We investigate the collective dynamics of bursting neurons on clustered network. The clustered network is composed of subnetworks each presenting a small-world property, and in a given subnetwork each neuron has a probability to be…

Noise-induced population bursting has been widely identified to play important roles in the information process. We constructed a mathematical model for a random and sparse neural network where bursting can be induced from the resting state…

We propose a discrete time dynamical system (a map) as phenomenological model of excitable and spiking-bursting neurons. The model is a discontinuous two-dimensional map. We find condition under which this map has an invariant region on the…

A central goal of neuroscience is to understand the representations formed by brain activity patterns and their connection to behavior. The classical approach is to investigate how individual neurons encode the stimuli and how their tuning…

Predicting how the brain can be driven to specific states by means of internal or external control requires a fundamental understanding of the relationship between neural connectivity and activity. Network control theory is a powerful tool…

In a series of two papers, we investigate the mechanisms by which complex oscillations are generated in a class of nonlinear dynamical systems with resets modeling the voltage and adaptation of neurons. This first paper presents…