Noise-induced stabilization in a chemical reaction network without boundary effects

2025/06/13 by Andréa Agazzi, Agazzi, Andrea, Lucie Laurence +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Physics and Astronomy · #FOS: Biological sciences #FOS: Mathematics #Gene Regulatory Network Analysis #Molecular Networks (q-bio.MN) #Nonlinear Dynamics and Pattern Formation #Probability (math.PR) #stochastic dynamics and bifurcation

paper · pdf · doi:10.48550/arxiv.2506.12163

openalex publication_date 2025/06/13 · openalex created_date 2025/10/13 · openalex updated_date 2026/07/28

Abstract

We present a chemical reaction network that is unstable under deterministic mass action kinetics, exhibiting finite-time blow-up of trajectories in the interior of the state space, but whose stochastic counterpart is positive recurrent. This provides an example of noise-induced stabilization of the model's dynamics arising due to noise perturbing transversally the divergent trajectories of the system that is independently of boundary effects. The proof is based on a careful decomposition of the state space and the construction of suitable Lyapunov functions in each region.

Citations

• Analysis of Stochastic Chemical Reaction Networks with a Hierarchy of Timescales
• Stochastic Chemical Reaction Networks with Discontinuous Limits and AIMD processes
• Large deviations for Markov jump processes with uniformly diminishing rates
• Seemingly stable chemical kinetics can be stable, marginally stable, or unstable
• Discrepancies between extinction events and boundary equilibria in reaction networks
• Tier structure of strongly endotactic reaction networks
• Non-explosivity of stochastically modeled reaction networks that are\n complex balanced
• Large deviations theory for Markov jump models of chemical reaction networks
• Noise-Induced Stabilization of Planar Flows I
• Noise-Induced Stabilization of Planar Flows II
• Separation of time-scales and model reduction for stochastic reaction networks
• General mass action kinetics

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• Design principles of noise-induced oscillation in biochemical reaction networks: II. coupled positive and negative feedback loops
• Noise-induced Mixing and Multimodality in Reaction Networks
• Seemingly stable chemical kinetics can be stable, marginally stable, or unstable