Robust steady states in ecosystems with symmetries

Abstract

Steady states of dynamical systems, whether stable or unstable, are critical for understanding future evolution. Robust steady states, ones that persist under small changes in the model parameters, are desired when modelling ecological systems, where it is common for accurate and detailed information on functional form and parameters to be unavailable. Previous work by Jahedi et al. [Robustness of solutions of almost every system of equations, SIAM J. Appl. Math. 82(5) (2022), pp. 1791–1807; Structured systems of nonlinear equations, SIAM J. Appl. Math. 83(4) (2023), pp. 1696–1716.] has established criteria to imply the prevalence of robust steady states for systems with minimal predetermined structure, including conventional structured systems. We review that work and extend it by allowing symmetries in the system structure, which present added obstructions to robustness.

KEYWORDS:

• Ecological modelling
• steady states of dynamical systems
• solutions of systems of equations
• symmetric structure

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research was partially supported by NSERC grant RGPIN-2016-06493 and the ARO grant 75868-CS-ACI.