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.
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http://dx.doi.org/10.1006/jtbi.1996.0240 | DOI Listing |
Chaos
March 2025
Center for Complex Quantum Systems, University of Texas, Austin, Texas 6TX 78712, USA.
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 PDFEntropy (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 PDFPhys 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 PDFNeural 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 PDFChaos
January 2024
Department of Systems and Control Engineering, Tokyo Institute of Technology, Tokyo 152-8550, Japan.
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.
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