Analog simulator of integro-differential equations with classical memristors
Abstract
An analog computer makes use of continuously changeable quantities of a system, such as its electrical, mechanical, or hydraulic properties, to solve a given problem. While these devices are usually computationally more powerful than their digital counterparts, they suffer from analog noise which does not allow for error control. We will focus on analog computers based on active electrical networks comprised of resistors, capacitors, and operational amplifiers which are capable of simulating any linear ordinary differential equation. However, the class of nonlinear dynamics they can solve is limited. In this work, by adding memristors to the electrical network, we show that the analog computer can simulate a large variety of linear and nonlinear integro-differential equations by carefully choosing the conductance and the dynamics of the memristor state variable. We study the performance of these analog computers by simulating integro-diferential models related to fluid dynamics, nonlinear Volterra equations for population growth, and quantum models describing non-Markovian memory effects, among others. Finally, we perform stability tests by considering imperfect analog components, obtaining robust solutions with up to 13% relative error for relevant timescales.
- Authors:
-
[1];
[3];
- Universidad de Santiago de Chile (USACH) (Chile). Dept. de Fisica; Center for the Development of Nanoscience and Nanotechnology, Santiago (Chile); Shanghai Univ. (China). Dept. of Physics. International Center of Quantum Articificial Intelligence for Science and Technology (QuArtists)
- Universidad de Santiago de Chile (USACH) (Chile). Dept. de Fisica; Center for the Development of Nanoscience and Nanotechnology, Santiago (Chile)
- Shanghai Univ. (China). Dept. of Physics. International Center of Quantum Articificial Intelligence for Science and Technology (QuArtists); Univ. of the Basque Country UPV/EHU, Bilbao (Spain). Dept. of Physical Chemistry; Basque Foundation for Science, Bilboa (Spain). IKERBASQUE
- Univ. of the Basque Country UPV/EHU, Bilbao (Spain). Dept. of Physical Chemistry
- Publication Date:
- Research Org.:
- Universidad de Santiago de Chile (USACH) (Chile)
- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
- OSTI Identifier:
- 1624487
- Grant/Contract Number:
- FG02-00ER41132
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Scientific Reports
- Additional Journal Information:
- Journal Volume: 9; Journal Issue: 1; Journal ID: ISSN 2045-2322
- Publisher:
- Nature Publishing Group
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING; Science & Technology - Other Topics
Citation Formats
Barrios, G. Alvarado, Retamal, J. C., Solano, E., and Sanz, M. Analog simulator of integro-differential equations with classical memristors. United States: N. p., 2019.
Web. doi:10.1038/s41598-019-49204-y.
Barrios, G. Alvarado, Retamal, J. C., Solano, E., & Sanz, M. Analog simulator of integro-differential equations with classical memristors. United States. https://doi.org/10.1038/s41598-019-49204-y
Barrios, G. Alvarado, Retamal, J. C., Solano, E., and Sanz, M. Tue .
"Analog simulator of integro-differential equations with classical memristors". United States. https://doi.org/10.1038/s41598-019-49204-y. https://www.osti.gov/servlets/purl/1624487.
@article{osti_1624487,
title = {Analog simulator of integro-differential equations with classical memristors},
author = {Barrios, G. Alvarado and Retamal, J. C. and Solano, E. and Sanz, M.},
abstractNote = {An analog computer makes use of continuously changeable quantities of a system, such as its electrical, mechanical, or hydraulic properties, to solve a given problem. While these devices are usually computationally more powerful than their digital counterparts, they suffer from analog noise which does not allow for error control. We will focus on analog computers based on active electrical networks comprised of resistors, capacitors, and operational amplifiers which are capable of simulating any linear ordinary differential equation. However, the class of nonlinear dynamics they can solve is limited. In this work, by adding memristors to the electrical network, we show that the analog computer can simulate a large variety of linear and nonlinear integro-differential equations by carefully choosing the conductance and the dynamics of the memristor state variable. We study the performance of these analog computers by simulating integro-diferential models related to fluid dynamics, nonlinear Volterra equations for population growth, and quantum models describing non-Markovian memory effects, among others. Finally, we perform stability tests by considering imperfect analog components, obtaining robust solutions with up to 13% relative error for relevant timescales.},
doi = {10.1038/s41598-019-49204-y},
journal = {Scientific Reports},
number = 1,
volume = 9,
place = {United States},
year = {Tue Sep 10 00:00:00 EDT 2019},
month = {Tue Sep 10 00:00:00 EDT 2019}
}
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Works referencing / citing this record:
Quantized Three-Ion-Channel Neuron Model for Neural Action Potentials
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