相关论文: Parameter Identification Problem in the Hodgkin an…

Non-autonomous differential equations are crucial for modeling systems influenced by external signals, yet fitting these models to data becomes particularly challenging when the signals change abruptly. To address this problem, we propose a…

In this paper, the parameter estimation problem for a multi-timescale adaptive threshold (MAT) neuronal model is investigated. By manipulating the system dynamics, which comprise of a non-resetting leaky integrator coupled with an adaptive…

We consider a classical space-clamped Hodgkin-Huxley model neuron stimulated by synaptic excitation and inhibition with conductances represented by Ornstein-Uhlenbeck processes. Using numerical solutions of the stochastic model system…

The use of Hodgkin-Huxley (HH) equations abounds in the literature, but the identifiability of the HH model parameters has not been broadly considered. Identifiability analysis addresses the question of whether it is possible to estimate…

In a succession of articles published over 65 years ago, Sir Alan Lloyd Hodgkin and Sir Andrew Fielding Huxley established what now forms our physical understanding of excitation in nerve, and how the axon conducts the action potential.…

We consider Hodgkin-Huxley-type model that is a stiff ODE system with two fast and one slow variables. For the parameter ranges under consideration the original version of the model has unstable fixed point and the oscillating attractor…

Understanding the human brain is the biggest challenge for scientists in the twenty-first century. The Hodgkin-Huxley (HH) model is one of the most successful mathematical models for bio-realistic simulations of the brain. However, the…

In this paper, we introduce a novel concept for learning of the parameters in a neural network. Our idea is grounded on modeling a learning problem that addresses a trade-off between (i) satisfying local objectives at each node and (ii)…

In many biological processes heterogeneity within cell populations is an important issue. In this work we consider populations where the behavior of every single cell can be described by a system of ordinary differential equations.…

We propose a novel method to reconstruct phase dynamics equations from responses in macroscopic variables to weak inputs. Developing linear and nonlinear response theories in coupled phase-oscillators, we derive formulae which connect the…

The generation of spikes by neurons is energetically a costly process and the evaluation of the metabolic energy required to maintain the signalling activity of neurons a challenge of practical interest. Neuron models are frequently used to…

The initial version of the planned paper has gone through a major revision in 2025. First, the paper ended up growing a bit too long, and as a result of that, we decided to split it into two parts. The first part focuses on the model for…

We present a modified library-based method for simulating the Hodgkin-Huxley (HH) neuronal networks. By pre-computing a high resolution data library during the interval of an action potential (spike), we can avoid evolving the HH equations…

In this paper we propose a solution to the problem of parameter estimation of nonlinearly parameterized regressions--continuous or discrete time--and apply it for system identification and adaptive control. We restrict our attention to…

By means of the concept DE we analyze the responses of a HH neuron to two types of spike-train inputs. Two characteristic quantities can be extracted, which can reflect partially the dynamical process of a HH neuron.

One of the most celebrated successes in computational biology is the Hodgkin-Huxley framework for modeling electrically active cells. This framework, expressed through a set of differential equations, synthesizes the impact of ionic…

This paper introduces the Neural Network for Nonlinear Hawkes processes (NNNH), a non-parametric method based on neural networks to fit nonlinear Hawkes processes. Our method is suitable for analyzing large datasets in which events exhibit…

We present a new interpretation for encoding information of the period of input signals into spike-trains in individual sensory neuronal systems. The spike-train could be described as the waveform sample of the input signal which locks…

Recent experimental and theoretical studies show that energy efficiency, which measures the amount of information processed by a neuron with per unit of energy consumption, plays an important role in the evolution of neural systems. Here,…

We investigate the use of neural networks (NNs) for the estimation of hidden model parameters and uncertainty quantification from noisy observational data for inverse parameter estimation problems. We formulate the parameter estimation as a…