On non-monotonic steady state response curves
Abstract
Non-monotonic steady state response curves can readily arise from an incoherent feedforward loop (IFFL), which has also been conjectured to be a necessary mechanism. In a previous work, we showed this conjecture to be false for systems where the control parameter directly influences only one state variable. Here, we extend this result to arbitrary systems. We show that a stable non-monotonic response requires either an IFFL or a combination of positive and negative feedback loops. Finally, we apply our theoretical findings to three network-structured biological contexts: signaling pathways, gene regulation, and ecological consumer-resource models. For the first two contexts, we identify necessary motifs for non-monotonic responses, while for consumer-resource models, we provide an alternative proof of the Competitive Exclusion Principle.
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BibTeX
@misc{yu2026nonmonotonic,
title = {{On non-monotonic steady state response curves}},
author = {Polly Y. Yu and Eduardo D. Sontag},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04029},
eprint = {2610.04029},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04029},
}
RIS
TY - UNPB
TI - On non-monotonic steady state response curves
AU - Polly Y. Yu
AU - Eduardo D. Sontag
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.04029
UR - https://arxiv.org/abs/2610.04029
AB - Non-monotonic steady state response curves can readily arise from an incoherent feedforward loop (IFFL), which has also been conjectured to be a necessary mechanism. In a previous work, we showed this conjecture to be false for systems where the control parameter directly influences only one state variable. Here, we extend this result to arbitrary systems. We show that a stable non-monotonic response requires either an IFFL or a combination of positive and negative feedback loops. Finally, we apply our theoretical findings to three network-structured biological contexts: signaling pathways, gene regulation, and ecological consumer-resource models. For the first two contexts, we identify necessary motifs for non-monotonic responses, while for consumer-resource models, we provide an alternative proof of the Competitive Exclusion Principle.
ER -