Forced synchronization of autonomous dynamical Boolean networks.
We present the design of an autonomous time-delay Boolean network realized with readily available electronic components. Through simulations and experiments that account for the detailed nonlinear response of each circuit element, we demonstrate that a network with five Boolean nodes displays complex behavior. Furthermore, we show that the dynamics of two identical networks display near-instantaneous synchronization to a periodic state when forced by a common periodic Boolean signal. A theoretical analysis of the network reveals the conditions under which complex behavior is expected in an individual network and the occurrence of synchronization in the forced networks. This research will enable future experiments on autonomous time-delay networks using readily available electronic components with dynamics on a slow enough time-scale so that inexpensive data collection systems can faithfully record the dynamics.
División de Matemáticas Aplicadas, Instituto Potosino de Investigación Científica y Tecnológica A. C., Camino a la Presa San José 2055, Col. Lomas 4 Sección, C.P. 78216, San Luis Potosí, S.L.P., Mexico.
R R
RR
Rivera-Durón
División de Matemáticas Aplicadas, Instituto Potosino de Investigación Científica y Tecnológica A. C., Camino a la Presa San José 2055, Col. Lomas 4 Sección, C.P. 78216, San Luis Potosí, S.L.P., Mexico.
E
E
Campos-Cantón
Facultad de Ciencias, Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, C.P. 78000, San Luis Potosí, S.L.P., Mexico.
I
I
Campos-Cantón
Department of Physics and Center for Nonlinear and Complex Systems, Duke University, Box 90305, Durham, North Carolina 27708, USA.
Daniel J
DJ
Gauthier
D000465:Algorithms; D008962:Models, Theoretical; D013997:Time Factors