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On the Periods of Parallel Dynamical Systems

Author

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  • Juan A. Aledo
  • Luis G. Diaz
  • Silvia Martinez
  • Jose C. Valverde

Abstract

In this work, we provide conditions to obtain fixed point theorems for parallel dynamical systems over graphs with (Boolean) maxterms and minterms as global evolution operators. In order to do that, we previously prove that periodic orbits of different periods cannot coexist, which implies that Sharkovsky’s order is not valid for this kind of dynamical systems.

Suggested Citation

  • Juan A. Aledo & Luis G. Diaz & Silvia Martinez & Jose C. Valverde, 2017. "On the Periods of Parallel Dynamical Systems," Complexity, Hindawi, vol. 2017, pages 1-6, January.
    • Handle: RePEc:hin:complx:7209762
    DOI: 10.1155/2017/7209762
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    References listed on IDEAS

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    1. Juan A. Aledo & Silvia Martinez & Jose C. Valverde, 2015. "Parallel Dynamical Systems over Graphs and Related Topics: A Survey," Journal of Applied Mathematics, Hindawi, vol. 2015, pages 1-14, March.
    2. G. Chiaselotti & G. Marino & P. A. Oliverio & D. Petrassi, 2013. "A Discrete Dynamical Model of Signed Partitions," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-10, April.
    3. Barrett, Chris L & Chen, William Y.C & Zheng, Michelle J, 2004. "Discrete dynamical systems on graphs and Boolean functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 66(6), pages 487-497.
    4. Chiaselotti, G. & Gentile, T. & Oliverio, P.A., 2014. "Parallel and sequential dynamics of two discrete models of signed integer partitions," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 1249-1261.
    5. Toroczkai, Zoltán & Guclu, Hasan, 2007. "Proximity networks and epidemics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 378(1), pages 68-75.
    6. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
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    1. Aledo, Juan A. & Diaz, Luis G. & Martinez, Silvia & Valverde, Jose C., 2019. "Dynamical attraction in parallel network models," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 874-888.
    2. Juan A. Aledo & Luis G. Diaz & Silvia Martinez & Jose C. Valverde, 2019. "Predecessors Existence Problems and Gardens of Eden in Sequential Dynamical Systems," Complexity, Hindawi, vol. 2019, pages 1-10, March.
    3. Juan A. Aledo & Ali Barzanouni & Ghazaleh Malekbala & Leila Sharifan & Jose C. Valverde, 2020. "On the Periodic Structure of Parallel Dynamical Systems on Generalized Independent Boolean Functions," Mathematics, MDPI, vol. 8(7), pages 1-14, July.
    4. Juan A. Aledo & Luis G. Diaz & Silvia Martinez & Jose C. Valverde, 2020. "Coexistence of Periods in Parallel and Sequential Boolean Graph Dynamical Systems over Directed Graphs," Mathematics, MDPI, vol. 8(10), pages 1-14, October.

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