Glossary
- Deterministic cellular automata:
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Discrete systems, defined on a lattice or on a graph, that evolve following the application of a deterministic function in parallel to all sites/nodes. They may constitute the discrete equivalent of partial differential equations.
- Probabilistic cellular automata:
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Extensions of deterministic cellular automata, where the evolution rule is defined (at least partially) in probabilistic terms. They may be considered as the discrete analogous of stochastic partial differential equations.
- Boolean derivatives:
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The extension of the derivative to Boolean functions. The derivative is one if the function varies when the variable does, and zero otherwise.
- Master-slave synchronization:
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A kind of synchronization mechanism among replicas of a dynamical system. One replica (the master) evolves freely in time and the other (the slave) is (partially) forced to follow the master.
- All-or-none or pinching synchronization:
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A kind of master-slave synchronization...
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Bibliography
Bagnoli F (1992) Boolean derivatives and computation of cellular automata. Int J Mod Phys C 3:307. https://doi.org/10.1142/S0129183192000257
Bagnoli F (1998) Cellular automata. In: Bagnoli F, Liò P, Ruffo S (eds) Dynamical modelling in biotechnologies. World Scientific, Singapore, p 3. https://doi.org/10.1142/9789812813053_0001
Bagnoli F, Cecconi F (2001) Synchronization of non-chaotic dynamical systems. Phys Lett A 260:9–17. https://doi.org/10.1016/S0375-9601(01)00154-2
Bagnoli F, Rechtman R (1999) Phys Rev E 59:R1307. https://doi.org/10.1103/PhysRevE.59.R1307
Bagnoli F, Rechtman R (2006) Synchronization universality classes and stability of smooth coupled map lattices. Phys Rev E 73:026202. https://doi.org/10.1103/PhysRevE.73.026202
Bagnoli F, Boccara B, Rechtman R (2001) Nature of phase transitions in a probabilistic cellular automaton with two absorbing states. Phys Rev E 63:046116. https://doi.org/10.1103/PhysRevE.63.046116
Bagnoli F, El Yacoubi S, Rechtman R (2010) Synchronization and control of cellular automata. In: Bandini S, Manzoni S, Umeo H, Vizzari G (eds) Cellular automata, ACRI2010, proceedings of the 9th international conference on cellular automata for research and industry, Lecture notes in computer science, vol 6350. Springer, Berlin, p 188. https://doi.org/10.1007/978-3-642-15979-4_21
Bagnoli F, Rechtman R, El Yacoubi S (2012) Control of cellular automata. Phys Rev E 86:066201. https://doi.org/10.1103/PhysRevE.86.066201
Bagnoli F, El Yacoubi S, Rechtman R (2017) Toward a boundary regional control problem for Boolean cellular automata. Nat Comput. https://doi.org/10.1007/s11047-017-9626-1
Bel Fekih A, El Jai A (2006) Regional analysis of a class of cellular automata models. In: El Yacoubi S, Chopard B, Bandini S (eds) Cellular automata, ACRI 2006, proceedings of the 7th international conference on cellular automata for research and industry, Lecture notes in computer science, vol 4173. Springer, Berlin, pp 48–57. https://doi.org/10.1007/11861201_9
Callier FM, Desoer CA (1991) Linear system theory. Springer, New-York
Cellular Automata (2002). In: Bandini S, Chopard B, Tomassini M (eds) Proceedings of the 5th international conference ACRI2002: cellular automata for research and industry, Lectures notes in computer science, vol 2493. Springer, Berlin. https://doi.org/10.1007/3-540-45830-1
Cellular Automata (2004). In: Sloot P, Chopard B, Hoekstra A (eds) Proceedings of the 6th international conference ACRI2004: cellular automata for research and industry, Lectures notes in computer science, vol 3305. Springer, Berlin. https://doi.org/10.1007/b102055
Cellular Automata (2006). In: El Yacoubi S, Chopard B, Bandini S (eds) Proceedings of the 7th international conference ACRI2006: cellular automata for research and industry, Lectures notes in computer science, vol 4173. Springer, Berlin. https://doi.org/10.1007/11861201
Cellular Automata (2008a). In: Umeo H, Morishita S, Nishinari K, Komatsuzaki T, Bandini S (eds) Proceedings of the 8th international conference ACRI2008: cellular automata for research and industry, Lectures notes in computer science, vol 5191. Springer, Berlin. https://doi.org/10.1007/978-3-540-79992-4
Cellular Automata (2008b). In: Bandini S, Manzoni S, Umeo H, Vizzari G (eds) Proceedings of the 9th international conference ACRI2010: cellular automata for research and industry, Lectures notes in computer science, vol 6350. Springer, Berlin. https://doi.org/10.1007/978-3-642-15979-4
Cellular Automata (2012). In: Sirakoulis GC, Bandini S (eds) Proceedings of the 10th international conference ACRI2012: cellular automata for research and industry, Lectures notes in computer science, vol 7495. Springer, Berlin. https://doi.org/10.1007/978-3-642-33350-7
Cellular Automata (2014). In: Wa˛s J, Sirakoulis GC, Bandini S (eds) Proceedings of the 11th international conference ACRI2014: cellular automata for research and industry, Lectures notes in computer science, vol 8751. Springer, Berlin. https://doi.org/10.1007/978-3-319-11520-7
Cellular Automata (2016). In: El Yacoubi S, Wa˛s J, Bandini S (eds) Proceedings of the 12th international conference ACRI2014: cellular automata for research and industry, lectures notes in computer science, vol 9863. Springer, Berlin. https://doi.org/10.1007/978-3-319-44365-2
Crutchfield JP, Kaneko K (1988) Are attractors relevant to turbulence? Phys Rev Lett 60:2715. https://doi.org/10.1103/PhysRevLett.60.2715
Curtain RF, Zwart H (1995) An introduction to infinite-dimensional linear systems theory. Springer, Heidelberg
Damiani C, Serra R, Villani M, Kauffman SA, Colacci A (2011) Cell-cell interaction and diversity of emergent behaviours. IET Syst Biol 5:137. https://doi.org/10.1049/iet-syb.2010.0039
Deutsch A, Dormann S (2005) Cellular automaton modeling of biological pattern formation: characterization, applications, and analysis, Birkhäuser, Berlin. ISBN: 978-0-8176-4415-4
Domany E, Kinzel W (1984) Equivalence of cellular automata to Ising models and directed percolation. Phys Rev Lett 53:311–314. https://doi.org/10.1103/PhysRevLett.53.311
El Yacoubi S (2008) Mathematical method for control problems on cellular automata models. Int J Syst Sci 39(5):529–538. https://doi.org/10.1080/00207720701847232
El Yacoubi S, El Jai A, Ammor N (2002) Regional controllability with cellular automata models. In: Bandini S, Chopard B, Tomassini M (eds) Cellular automata, ACRI2002, proceedings of the 5th international conference on cellular automata for research and industry, Lecture notes on computer sciences, vol 2493. Springer, Berlin, pp 357–367. https://doi.org/10.1007/3-540-45830-1_34
Ermentrout G, Edelstein-Keshet L (1993) Cellular automata approaches to biological modeling. J Theor Biol 160:97–133. https://doi.org/10.1006/jtbi.1993.1007
Kaneko K (1990) Supertransients, spatiotemporal intermittency and stability of fully developed spatiotemporal chaos. Phys Lett 149A:105. https://doi.org/10.1016/0375-9601(90)90534-U
Kauffman SA (1969) Metabolic stability and epigenesis in randomly constructed genetic nets. J Theor Biol 22:437. https://doi.org/10.1016/0022-5193(69)90015-0
Lee KY, Chow S, Barr RO (1972) On the control of discrete-time distributed parameter systems. Siam J Control 10(2):361–376. https://doi.org/10.1137/0310028
Lions J (1986) Controlabilité exacte des systèmes distribueés. CRAS, Série I 302:471–475
Lions J (1991) Exact controllability for distributed systems. Some trends and some problems. In: Spigler R (ed) Applied and industrial mathematics. Mathematics and its applications, vol 56. Springer, Dordrecht, pp 59–84. https://doi.org/10.1007/978-94-009-1908-2_7
Pecora L, Carroll T (1990) Synchronization in chaotic systems. Phys Rev Lett 64:821. https://doi.org/10.1103/PhysRevLett.64.821
Picton P (1994) Boolean neural networks. In: Introduction to neural networks. Palgrave, London, p 46. https://doi.org/10.1007/978-1-349-13530-1_4
Politi A, Livi R, Oppo G-L, Kapral R (1993) Unpredictable behaviour in stable systems. Europhys Lett 22:571. https://doi.org/10.1209/0295-5075/22/8/003
Russell D (1978) Controllability and stabilizability theory for linear partial differential equations. Recent progress and open questions. SIAM Rev 20:639–739. https://doi.org/10.1137/1020095
Vichniac G (1984) Boolean derivatives on cellular automata. Physica 10D:96. https://doi.org/10.1016/0167-2789(90)90174-N
Wolfram S (1983) Statistical mechanics of cellular automata. Rev Mod Phys 55:601. https://doi.org/10.1103/RevModPhys.55.601
Wolfram S (1984) Universality and complexity in cellular automata. Physica 10D:1. https://doi.org/10.1016/0167-2789(84)90245-8
Zerrik E, Boutoulout A, El Jai A (2000) Actuators and regional boundary controllability for parabolic systems. Int J Syst Sci 31:73–82. https://doi.org/10.1080/002077200291479
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Bagnoli, F., El Yacoubi, S., Rechtman, R. (2018). Control of Cellular Automata. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27737-5_710-1
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