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Damage spreading and the Lyapunov spectrum of cellular automata and Boolean networks

Author

Listed:
  • Vispoel, Milan
  • Daly, Aisling J.
  • Baetens, Jan M.

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.

Suggested Citation

  • Vispoel, Milan & Daly, Aisling J. & Baetens, Jan M., 2024. "Damage spreading and the Lyapunov spectrum of cellular automata and Boolean networks," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:chsofr:v:184:y:2024:i:c:s0960077924005411
    DOI: 10.1016/j.chaos.2024.114989
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