TY - JOUR
T1 - Collective dynamics in heterogeneous networks of neuronal cellular automata
AU - Manchanda, Kaustubh
AU - Bose, Amitabha
AU - Ramaswamy, Ramakrishna
N1 - Funding Information:
We thank the anonymous referee for critically reviewing our manuscript and providing valuable comments that improved this work. KM is supported by the University Grants Commission, India under the D.S. Kothari Postdoctoral Fellowship Scheme ( BSR/PH/13-14/0044). AB was supported, in part, by the National Science Foundation, USA under DMS-112291. RR acknowledges the support of the Department of Science and Technology, India under DST-SR/S2/JCB/2008.
Publisher Copyright:
© 2017 Elsevier B.V.
PY - 2017/12/1
Y1 - 2017/12/1
N2 - We examine the collective dynamics of heterogeneous random networks of model neuronal cellular automata. Each automaton has b active states, a single silent state and r−b−1 refractory states, and can show ‘spiking’ or ‘bursting’ behavior, depending on the values of b. We show that phase transitions that occur in the dynamical activity can be related to phase transitions in the structure of Erdõs–Rényi graphs as a function of edge probability. Different forms of heterogeneity allow distinct structural phase transitions to become relevant. We also show that the dynamics on the network can be described by a semi-annealed process and, as a result, can be related to the Boolean Lyapunov exponent.
AB - We examine the collective dynamics of heterogeneous random networks of model neuronal cellular automata. Each automaton has b active states, a single silent state and r−b−1 refractory states, and can show ‘spiking’ or ‘bursting’ behavior, depending on the values of b. We show that phase transitions that occur in the dynamical activity can be related to phase transitions in the structure of Erdõs–Rényi graphs as a function of edge probability. Different forms of heterogeneity allow distinct structural phase transitions to become relevant. We also show that the dynamics on the network can be described by a semi-annealed process and, as a result, can be related to the Boolean Lyapunov exponent.
KW - Binary mixtures
KW - Boolean Lyapunov exponent
KW - Discrete dynamics
KW - Network motif
KW - Periodic activity
KW - Semi-annealed approximation
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U2 - 10.1016/j.physa.2017.06.021
DO - 10.1016/j.physa.2017.06.021
M3 - Article
AN - SCOPUS:85022174828
SN - 0378-4371
VL - 487
SP - 111
EP - 124
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
ER -