@article{01HYJESNCG530S03FE4CM6MDDZ,
  abstract     = {{The study of damage spreading in cellular automata (CA) is essential for understanding chaos and phase transitions in CA and complex systems in general. It helps us make sense of the dynamics and emergent properties of complex systems and informs various practical applications in science and engineering. In this study, we present a novel and comprehensive perspective on damage spreading in CA and Boolean networks. We introduce a novel concept, the tangent space of a CA, enabling us to introduce a methodology for computing the Lyapunov spectrum of both CA and Boolean networks. This approach mirrors the well -established method employed in continuous -state dynamical systems, hence facilitating the application of established theorems from dynamical systems theory. Additionally, our approach reveals how the existing notions related to damage spreading and Lyapunov exponents of CA are related to their configuration space and tangent space, thereby bridging seemingly unrelated approaches. We illustrate the versatility of our approach through the analysis of Lyapunov spectra for Elementary CA (ECA) and the Domany-Kinzel CA, showcasing its effectiveness in scenarios involving probabilistic update rules and network structures. Finally, we explore the relationship between the Lyapunov spectrum and the Kolmogorov-Sinai entropy, affirming our approach by checking the validity of Pesin's theorem. This work contributes to the comprehensive understanding of damage spreading in CA and Boolean networks, unraveling connections between chaos theory, computational systems, and informing various real -world applications across scientific and engineering domains.}},
  articleno    = {{114989}},
  author       = {{Vispoel, Milan and Daly, Aisling and Baetens, Jan}},
  issn         = {{0960-0779}},
  journal      = {{CHAOS SOLITONS & FRACTALS}},
  keywords     = {{Damage spreading,Lyapunov exponent,Boolean networks,Cellular automata}},
  language     = {{eng}},
  pages        = {{15}},
  title        = {{Damage spreading and the Lyapunov spectrum of cellular automata and Boolean networks}},
  url          = {{http://doi.org/10.1016/j.chaos.2024.114989}},
  volume       = {{184}},
  year         = {{2024}},
}

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