Understanding the nature of complexity exhibited by several natural processes whose dynamics depend both on space and time is still a big challenge for scientists. In this context, spatially extended systems constitute a very important class of dynamical systems for which non-trivial and unexpected collective behaviour is observed on the macroscopic scale. They are defined on a lattice and characterized by local interactions and synchronous updating. Accordingly, cellular automata seem to be the natural way to model such systems. They are spatially and temporally discrete mathematical systems characterized by local interaction and synchronous dynamical evolution. Both deterministic and probabilistic cellular automata are widely used for modelling highly non-linear/stochastic phenomena that exhibit emergent behaviours based on simple local interactions. They also may be considered as the discrete equivalent of partial differential equations that usually formed the basic models for spatio-temporal systems.
This Special Issue of International Journal of Parallel, Emergent and Distributed Systems (IJPEDS) is focusing on spatially extended systems studied from both theoretical and practical point of view. The presented papers covered various works related to modelling and analysing spatio-temporal systems mainly via cellular automata approach.
The present volume contains a selection of articles which improve and extend some papers presented at the 12th International Conference on Cellular Automata for Research and Industry ACRI 2016, held in Fez, Morocco, 5–8 September 2016. Other contributions that fit to the scope of this special issue were directly submitted to the journal. Each submitted article received at least two detailed reports for the final recommendation.
The accepted papers cover theoretical aspects as well as practical applications related to spatially extended systems and different kinds of complex phenomena.
The first paper by Merabet et al. is a theoretical work that is concerned with the identification of missing terms in a nonlinear hyperbolic system. The phenomenon is modelled by a boundary value problem for the diffusion equation. The authors use a modified version of the sentinel method proposed by J. L. Lions that allows the detection of the unknown terms. They explain how the problem of determining a sentinel is equivalent to a null-controllability problem for which a variational method is used.
Kassogué et al. addresses the problem of modelling the climate change impact on water resources. The authors propose a cellular automaton approach for modelling water cycle dynamics taking into account the actual terrain attributes and climatic constraints, and they investigate how water resources change under several climate projection scenarios. The approach is applied to a basin in northern Morocco for which a simulation software was developed in Java Object Oriented Programming. Digital terrain models, geological maps and satellites images were used for input data.
In the paper by Wacker, the author considers the study of basic properties of cellular automata on group sets. This is a natural generalization that gives a theoretical framework for cellular automata in hyperbolic space. The author defines a suitable notion of amenability and proves that under this condition, indeed the Garden of Eden theorem holds.
The next paper by Chliamovitch et al. is concerned with the interplay between information theory and complexity. It presents a comparison between the maximum entropy models, which consists in measuring how entropy varies when breaking a system into pieces and the standard Wolfram classification of cellular automata. The authors seek a probability density which has the largest entropy and still satisfies observational constraints.
In Carvalho et al. cellular automata are used to schedule parallel programs over a multiprocessor system. The authors investigate the simplest version called Task Static Scheduling Problem (TSSP) and apply genetic algorithms to search the appropriate cellular automata rules.
In Tinoco et al., the authors investigate a new control model for swarms of robots based on two-dimensional cellular automata (CA) and inverted pheromone called Inverted Ant Cellular Automata with Discrete pheromone diffusion and Inertial motion (IACA-DI). The model is dedicated to the coordination of a swarm of robots performing the surveillance task.
The paper Mangeas et al. presents a spatially explicit Bayesian model which is able to predict the distribution of potential fire ignition over the entire main island of New-Caledonia. This hybrid statistical/mechanistic model is proposed to estimate the impact of fires on specific areas for specific issues such as biodiversity and erosion.
Finally the paper El Yacoubi et al. proposes an original approach for predicting soil vulnerability to erosion based on the use of satellite images. It discusses a Multilayer Perceptron Model for investigating potential correlations between digital data extracted from a satellite image and computed vulnerability factors. The obtained results on a pilot area constitute a promising basis for a deeper study of soil erosion leading to desertification issues.
Notes on contributor
Samira El Yacoubi was born in Safi (Morocco) in 1963. She holds a master in Applied Mathematics at the University of Rabat, and a PhD in Applied Mathematics and automatic control at the University of Perpignan (France) in 1990. She obtained her Habilitation degree in Systems Theory in 1999 and since there she has focused mostly on mathematical modelling and computer simulation for distributed parameters systems and Cellular Automata. She is a professor at the University of Perpignan and the head of the department of Mathematics and Computer Science. She is also a researcher in Espace-Dev laboratory, UMR 228 and participated in several national and international projects. She is the author of about 60 publications on international journals and the supervisor of several master and PhD thesis.
Acknowledgements
I would like to thank all the authors who have contributed towards this special issue. I am also extremely grateful to all the reviewers who have accepted the difficult task for selecting papers. The expertise they have done was very efficient so as to ensure a high quality of the issue and fit to the good reputation of the journal. Finally, my sincere thanks go to Prof. Andrew Adamatzky as Editor in Chief of IJPEDS for helping me to have this special issue.