Chaos in weakly-coupled pacemaker cells.

J Theor Biol

Department of Physics, Norwegian University of Science and Technology, Trondheim, Norway.

Published: January 1997

A model of the rabbit sinoatrial action potential is introduced, based on a model by Morris & Lecar. One cell is described by two nonlinear first-order ordinary differential equations, with ten constant parameters. The model is much simpler than most other models in use, but can reproduce perfectly experimentally recorded action potentials. The dynamics of two coupled cells, with and without the presence of periodic acetylcholine pulses, shows examples of bifurcations and strange attractors, mathematical phenomena characterizing chaotic motion. It remains to be clarified whether such dynamics is actually observed, for example in the small irregular variations of the normal heart rate.

Download full-text PDF

Source
http://dx.doi.org/10.1006/jtbi.1996.0240DOI Listing

Publication Analysis

Top Keywords

chaos weakly-coupled
4
weakly-coupled pacemaker
4
pacemaker cells
4
cells model
4
model rabbit
4
rabbit sinoatrial
4
sinoatrial action
4
action potential
4
potential introduced
4
introduced based
4

Similar Publications

We perform analytical and quantitative analyses of the motion of a non-integrable pendulum with two degrees of freedom, in which an integrable nonlinear pendulum and a harmonic oscillator are weakly coupled through a non-integrable perturbative interaction, based on the eigenvalue problem of the Liouvillian, which is the generator of time evolution in classical mechanics. The eigenfunctions belonging to the zero eigenvalue of the Liouvillian correspond to the invariants of the motion. The zero eigenvalue of the integrable unperturbed Liouvillian is infinitely degenerate at the resonance point.

View Article and Find Full Text PDF

Nonlinear Charge Transport and Excitable Phenomena in Semiconductor Superlattices.

Entropy (Basel)

August 2024

Gregorio Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain.

Semiconductor superlattices are periodic nanostructures consisting of epitaxially grown quantum wells and barriers. For thick barriers, the quantum wells are weakly coupled and the main transport mechanism is a sequential resonant tunneling of electrons between wells. We review quantum transport in these materials, and the rate equations for electron densities, currents, and the self-consistent electric potential or field.

View Article and Find Full Text PDF

Quantum diffusion induced by small quantum chaos.

Phys Rev E

June 2024

College of Science and Engineering, Ritsumeikan University, Noji-higashi 1-1-1, Kusatsu 525-8577, Japan.

It is demonstrated that quantum systems classically exhibiting strong and homogeneous chaos in a bounded region of the phase space can induce a global quantum diffusion. As an ideal model system, a small quantum chaos with finite Hilbert space dimension N weakly coupled with M additional degrees of freedom which is approximated by linear systems is proposed. By twinning the system the diffusion process in the additional modes can be numerically investigated without taking the unbounded diffusion space into account explicitly.

View Article and Find Full Text PDF

Fading memory as inductive bias in residual recurrent networks.

Neural Netw

May 2024

Ernst Strüngmann Institute, Deutschordenstraße 46, Frankfurt am Main, 60528, Germany. Electronic address:

Residual connections have been proposed as an architecture-based inductive bias to mitigate the problem of exploding and vanishing gradients and increased task performance in both feed-forward and recurrent networks (RNNs) when trained with the backpropagation algorithm. Yet, little is known about how residual connections in RNNs influence their dynamics and fading memory properties. Here, we introduce weakly coupled residual recurrent networks (WCRNNs) in which residual connections result in well-defined Lyapunov exponents and allow for studying properties of fading memory.

View Article and Find Full Text PDF

We analyze the simplest model of identical coupled phase oscillators subject to two-body and three-body interactions with permutation symmetry and phase lags. This model is derived from an ensemble of weakly coupled nonlinear oscillators by phase reduction, where the first and second harmonic interactions with phase lags naturally appear. Our study indicates that the higher-order interactions induce anomalous transitions to synchrony.

View Article and Find Full Text PDF

Want AI Summaries of new PubMed Abstracts delivered to your In-box?

Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!