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Updated: Apr 19, 2026

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Spatio-temporal pattern formation under varying functional response parametrizations.

Indrajyoti Gaine1, Malay Banerjee2

  • 1Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, 208016, Uttar Pradesh, India.

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|April 17, 2026
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Summary
This summary is machine-generated.

Ecological models face uncertainty due to limited data. This study introduces structural sensitivity analysis to spatio-temporal predator-prey models, improving prediction robustness.

Keywords:
Functional responsePattern formationStabilityStructural sensitivityTuring instability

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Systems Ecology

Background:

  • Limited ecological data creates uncertainty in nonlinear population dynamics models.
  • Alternative mathematical formulations can improve model fit beyond parameter tuning.
  • Structural sensitivity analyzes prediction uncertainty from different function formulations.

Purpose of the Study:

  • Extend structural sensitivity to spatio-temporal ecological systems.
  • Analyze the impact of functional response formulation on model dynamics.
  • Provide tools for robust ecological modeling.

Main Methods:

  • Analytical derivation of parametric conditions for steady states and bifurcations.
  • Extension of structural sensitivity to spatio-temporal predator-prey models.
  • Numerical simulations using generalized and specific functional responses.

Main Results:

  • Derived conditions for homogeneous and heterogeneous steady states.
  • Established criteria for local bifurcations and Turing instability.
  • Demonstrated that functional response choice significantly impacts model outcomes.

Conclusions:

  • Structural sensitivity is crucial for spatio-temporal ecological models.
  • Careful selection of mathematical formulation enhances model prediction accuracy.
  • Analytical and numerical approaches validate the importance of functional response choice.