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In this work, we propose and study the stability of nerve impulse propagation as electrical and mechanical signals through linear approximation. We present a potential energy stored in the biomembrane due to the deformation, bending, and…

Pattern Formation and Solitons · Physics 2021-08-20 F. M. Moukam Kakmeni , B. Njinabo Akoni

Neuronal avalanches are a novel mode of activity in neuronal networks, experimentally found in vitro and in vivo, and exhibit a robust critical behaviour: These avalanches are characterized by a power law distribution for the size and…

Neurons and Cognition · Quantitative Biology 2012-04-02 Lucilla de Arcangelis , Hans J. Herrmann

Most models of neurons incorporate a capacitor to account for the marked capacitive behavior exhibited by the cell membrane. However, such capacitance is widely considered constant, thereby neglecting the possible effects of time-dependent…

Neurons and Cognition · Quantitative Biology 2025-12-29 Matías Courdurier , Leonel E. Medina , Esteban Paduro

Hopfield models, originally developed to study memory retrieval in neural networks, have become versatile tools for modeling diverse biological systems in which function emerges from collective dynamics. In this review, we provide a…

Biological Physics · Physics 2025-06-17 Maria Yampolskaya , Pankaj Mehta

We propose a dynamical neural network model with a hierarchical and modular structure. The network architecture can be derived by minimizing an energy function that is originally designed based on two kinds of neurons with quite different…

Neurons and Cognition · Quantitative Biology 2026-04-14 Kazuyoshi Tsutsumi , Ernst Niebur

We introduce and study a new model of interacting neural networks, incorporating the spatial dimension (e.g. position of neurons across the cortex) and some learning processes. The dynamic of each neural network is described via the elapsed…

Analysis of PDEs · Mathematics 2020-09-03 Delphine Salort , Nicolas Torres

In view of ever-changing conditions both in the external world and in intrinsic brain states, maintaining the robustness of computations poses a challenge, adequate solutions to which we are only beginning to understand. At the level of…

Neurons and Cognition · Quantitative Biology 2022-03-29 Nelson Niemeyer , Jan-Hendrik Schleimer , Susanne Schreiber

We examine the dynamical evolution of the state of a neurone, with particular care to the non-equilibrium nature of the forces influencing its movement in state space. We combine non-equilibrium statistical mechanics and dynamical systems…

Neurons and Cognition · Quantitative Biology 2021-02-19 Dalton A R Sakthivadivel

The human brain is one of the most complex and intriguing scientific topics. The most established theory on neuronal communication is a pure electrical model based on the propagation of intracell cationic charges along the neurons. Here we…

Neurons and Cognition · Quantitative Biology 2024-03-26 Francisco Meseguer , Fernando Ramiro-Manzano

Neuronal network dynamics depends on network structure. In this paper we study how network topology underpins the emergence of different dynamical behaviors in neuronal networks. In particular, we consider neuronal network dynamics on…

Neurons and Cognition · Quantitative Biology 2019-02-13 Marinho A. Lopes , Alexander V. Goltsev

Fluid pumping and the generation of electric current by living tissues are required during morphogenetic processes and for maintainance of homeostasis. How these flows emerge from active and passive ion transport in cells has been well…

Biological Physics · Physics 2022-11-15 Marko Popović , Jacques Prost , Frank Jülicher

The structure of continuous Hopfield networks is revisited from a system-theoretic point of view. After adopting a novel electrical network interpretation involving nonlinear capacitors, it is shown that Hopfield networks admit a…

Optimization and Control · Mathematics 2026-01-07 Arjan van der Schaft

Cortical activity in-vivo displays relaxational time scales much longer than the membrane time constant of the neurons or the deactivation time of ionotropic synaptic conductances. The mechanisms responsible for such slow dynamics are not…

Disordered Systems and Neural Networks · Physics 2025-08-07 Ferdinand Tixidre , Gianluigi Mongillo , Alessandro Torcini

We investigate the dynamics of a network consisting of an array of identical cortical units with nearest neighbor interactions under periodic arousal. Each unit consists of two interconnected populations of neurons tuned to a state in which…

Neurons and Cognition · Quantitative Biology 2019-02-12 Leandro M. Alonso

The integration and transmission of information in the brain are dependent on the interplay between structural and dynamical properties. Implicit in any pursuit aimed at understanding neural dynamics from appropriate sets of mathematically…

Neurons and Cognition · Quantitative Biology 2020-06-30 Joshua M. Roldan , Sebastian Pardo G. , Vivek Kurien George , Gabriel A. Silva

Early recordings of nervous conduction revealed a notable thermal signature associated with the electrical signal. The observed production and subsequent absorption of heat arise from physicochemical processes that occur at the cell…

Biological Physics · Physics 2020-02-19 Aymar C. L. de Lichtervelde , J. Pedro de Souza , Martin Z. Bazant

Mounting evidence in neuroscience suggests the possibility of neuronal representations that individual neurons serve as the substrates of different mental representations in a point-to-point way. Combined with associationism, it can…

Neurons and Cognition · Quantitative Biology 2021-09-06 Chiyin Zheng

The origin of nonlinear responses in cells has been suggested to be crucial for various cell functions including the propagation of the nervous impulse. In physics nonlinear behavior often originates from phase transitions. Evidence for…

Biological Physics · Physics 2022-11-23 Carina S. Fedosejevs , Matthias F. Schneider

The present work investigates electron transport and heating mechanisms using an (r, z) particle-in-cell (PIC) simulation of a typical rf-driven axisymmetric magnetron discharge with a conducting target. It is shown that for the considered…

Information flow is central to contemporary accounts of cognition, yet its physical basis in living neural matter remains poorly specified. Here, we develop a multiscale resource-theoretical framework motivated by the \textit{thermocoherent…

Neurons and Cognition · Quantitative Biology 2026-04-14 Onur Pusuluk