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External flows of energy, entropy, and matter can cause sudden transitions in the stability of biological and industrial systems, fundamentally altering their dynamical function. How might we control and design these transitions in chemical reaction networks? Here, we analyze transitions giving rise to complex behavior in random reaction networks subject to external driving forces. In the absence of driving, we characterize the uniqueness of the steady state and identify the percolation of a giant connected component in these networks as the number of reactions increases. When subject to chemical driving (influx and outflux of chemical species), the steady state can undergo bifurcations, leading to multistability or oscillatory dynamics. By quantifying the prevalence of these bifurcations, we show how chemical driving and network sparsity tend to promote the emergence of these complex dynamics and increased rates of entropy production. We show that catalysis also plays an important role in the emergence of complexity, strongly correlating with the prevalence of bifurcations. Our results suggest that coupling a minimal number of chemical signatures with external driving can lead to features present in biochemical processes and abiogenesis.
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Noisy deep networks: chaos, multistationarity, and eternal evolution
Abstract We study time-recurrent hierarchical networks that model complex systems in biology, economics, and ecology. These networks resemble real-world topologies, with strongly connected hubs (centers) and weakly connected nodes (satellites). Under natural structural assumptions, we develop a mean-field approach that reduces network dynamics to the central nodes alone. Even in the two-layer case, we establish universal dynamical approximation, demonstrating that these networks can replicate virtually any dynamical behavior by tuning center-satellite interactions. In multilayered networks, this property extends further, enabling the approximation of families of structurally stable systems and the emergence of complex bifurcations, such as pitchfork bifurcations under strong inter-satellite interactions. We also show that internal noise within nodes moderates bifurcations, leading to noise-induced phase transitions. A striking effect emerges where central nodes may lose control over satellites, akin to transitions observed in perceptrons studied by E. Gardner-relevant in complex combinatorial problems. Finally, we examine the networks’ responses to stress, demonstrating that increasing complexity during evolution is crucial for long-term viability.
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- Award ID(s):
- 2102906
- PAR ID:
- 10584478
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- Journal of Physics: Complexity
- Volume:
- 6
- Issue:
- 2
- ISSN:
- 2632-072X
- Format(s):
- Medium: X Size: Article No. 025008
- Size(s):
- Article No. 025008
- Sponsoring Org:
- National Science Foundation
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