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Collective dynamics in heterogeneous networks of neuronal cellular automata

Author

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  • Manchanda, Kaustubh
  • Bose, Amitabha
  • Ramaswamy, Ramakrishna

Abstract

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.

Suggested Citation

  • Manchanda, Kaustubh & Bose, Amitabha & Ramaswamy, Ramakrishna, 2017. "Collective dynamics in heterogeneous networks of neuronal cellular automata," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 487(C), pages 111-124.
    • Handle: RePEc:eee:phsmap:v:487:y:2017:i:c:p:111-124
    DOI: 10.1016/j.physa.2017.06.021
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    References listed on IDEAS

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    1. H. Jeong & B. Tombor & R. Albert & Z. N. Oltvai & A.-L. Barabási, 2000. "The large-scale organization of metabolic networks," Nature, Nature, vol. 407(6804), pages 651-654, October.
    2. Burstedde, C & Klauck, K & Schadschneider, A & Zittartz, J, 2001. "Simulation of pedestrian dynamics using a two-dimensional cellular automaton," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(3), pages 507-525.
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