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Resilience for stochastic systems interacting via a quasi-degenerate network.

Sara Nicoletti1, Duccio Fanelli1, Niccolò Zagli2

  • 1Dipartimento di Fisica e Astronomia, CSDC and INFN, Università degli Studi di Firenze, via G. Sansone 1, 50019 Sesto Fiorentino, Italy.

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This study shows how network structure and non-normal reactions amplify noise in reaction-diffusion systems. This amplification can make stable systems appear unstable, challenging deterministic resilience assessments.

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Area of Science:

  • Mathematical Biology
  • Complex Systems
  • Network Science

Background:

  • Reaction-diffusion models are crucial for understanding spatially distributed biological processes.
  • Network structures can significantly influence system dynamics and stability.
  • Stochasticity plays a key role in biological pattern formation and system behavior.

Purpose of the Study:

  • To investigate the impact of network topology and reaction kinetics on stochasticity in reaction-diffusion systems.
  • To analyze the amplification of noise in systems with non-normal reaction schemes and quasidegenerate networks.
  • To re-evaluate the concept of deterministic resilience in light of amplified stochasticity.

Main Methods:

  • Development and analysis of a stochastic reaction-diffusion model on a networked support.
  • Investigation of systems with non-normal reaction schemes on directed linear lattices.
  • Analysis of eigenvalue spectra of the Laplacian operator for species diffusion.
  • Examination of system behavior on quasidegenerate networks of varying sizes.

Main Results:

  • Noise amplification occurs via a self-consistent process linked to the degenerate spectrum of the network support.
  • Quasidegenerate networks exhibit eigenvalue accumulation, leading to pronounced noise amplification with increasing network size.
  • Systems considered deterministically stable can exhibit pattern formation beyond a critical network size due to amplified stochasticity.

Conclusions:

  • Non-normality and quasidegenerate network structures can significantly amplify inherent stochasticity.
  • Amplified stochasticity challenges conventional deterministic methods for quantifying system resilience.
  • The findings necessitate a re-evaluation of stability and resilience assessments in complex biological networks.