Simulation of a Vibrant Membrane Using a 2-Dimensional Cellular Automaton

I. Huerta-Trujillo, J. C. Chimal-Eguía, L. Muñoz-Salazar, J. A. Martinez-Nuño

Research output: Contribution to journalArticlepeer-review

Abstract

© 2015 I. Huerta-Trujillo et al. This paper proposes a 2-dimensional cellular automaton (CA) model and how to derive the model evolution rule to simulate a two-dimensional vibrant membrane. The resulting model is compared with the analytical solution of a two-dimensional hyperbolic partial differential equation (PDE), linear and homogeneous. This models a vibrant membrane with specific conditions, initial and boundary. The frequency spectrum is analysed as well as the error between the data produced by the CA model. Then it is compared to the data provided by the solution evaluation to the differential equation. This shows how the CA obtains a behavior similar to the PDE. Moreover, it is possible to simulate nonclassical initial conditions for which there is no exact solution using PDE. Very interesting information could be obtained from the CA model such as the fundamental frequency.
Original languageAmerican English
JournalDiscrete Dynamics in Nature and Society
DOIs
StatePublished - 1 Jan 2015

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