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The critical patch size problem on networks
Veronica Tora1, Davide Vergni1
1Istituto per le Applicazioni del Calcolo, CNR, Roma, Italy.
Mathematical Biosciences
|June 19, 2026
Summary
Investigating critical patch size on networks, this study finds network structure and "sink" locations determine population survival. These insights are crucial for understanding ecological and disease spread dynamics.
Area of Science:
- Mathematical Biology
- Network Science
- Theoretical Ecology
Background:
- Population dynamics on heterogeneous media present analytical challenges.
- Understanding critical patch size is key for species survival and spread modeling.
- Graph theory offers a framework for analyzing discrete, heterogeneous systems.
Purpose of the Study:
- To investigate the critical patch size for population persistence on complex networks.
- To develop analytical methods for determining survival thresholds in graph-based systems.
- To explore the influence of network topology and sink distribution on population dynamics.
Main Methods:
- Utilized logistic growth at nodes and the graph Laplacian for dispersal modeling.
- Analyzed spectral graph parameters and eigenvalues of the linearized evolution operator.
- Derived bounds on spectral parameters to ensure population persistence.
Main Results:
- Established a framework for analyzing critical patch size on general graphs.
- Demonstrated that network topology and sink distribution significantly impact survival thresholds.
- Provided conditions on spectral graph parameters for population persistence.
Conclusions:
- Network structure and sink placement are critical determinants of population persistence.
- The findings offer a generalized approach to critical patch size problems on networks.
- Applications include ecological network resilience, synthetic biology, and disease propagation modeling.
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