Stability and Bifurcation of a Multi-Trait Eco-Evolutionary Logistic-Type Model
- 1Departamento de Matemática, Universidade da Madeira, 9000-072 Funchal, Portugal
- 2Center for Mathematical Analysis, Geometry, and Dynamical Systems, Instituto Superior Técnico, University of Lisbon, 1649-004 Lisbon, Portugal
Abstract
We extend a two-dimensional discrete-time eco-evolutionary logistic model to the case of finitely many quantitative traits. The original planar model couples population density to a single mean trait under stabilizing selection; the extension retains this mechanism while allowing trait-specific evolutionary response rates and feedback coefficients. We establish a positively invariant ecological core and construct compact absorbing boxes, which yield a compact global attractor for the restricted dynamics. All equilibria are characterized through a scalar equation, and the positive equilibrium is shown to exist uniquely exactly when the intrinsic growth factor exceeds one. The Jacobian at this equilibrium has an arrowhead structure, leading to an explicit characteristic polynomial. We prove that the persistence threshold is a transcritical boundary bifurcation and formulate complete spectral and nondegeneracy conditions for flip and Neimark–Sacker bifurcations. Numerical bifurcation diagrams illustrate the transcritical, period-doubling, and Neimark–Sacker bifurcations predicted by the analytical results.
Related
- Stability and Hopf Bifurcation with Optimal Control in a Delayed Tripartite Evolutionary Game
- Stability and Hopf Bifurcation of a Delayed Fractional-Order ISR Rumor Propagation Model with Saturation Incidence
- Explainable machine learning and multivariable logistic regression for identifying prevalent self-reported physician-diagnosed chronic lung disease in postmenopausal women: development and multi-cohort external validation
- Prevalence and Associated Factors of Full Immunization Coverage among children aged 12–23 months in Kenya: A multi-level logistic regression analysis
- Homeostasis-Inspired, Quality-Adaptive Preprocessing for Multi-Label ECG Diagnosis: A Pre-Registered Multi-Objective Evolutionary Study with Negative Findings and Falsifiable Design Principles.
BibTeX
@article{luis2026stability,
title = {{Stability and Bifurcation of a Multi-Trait Eco-Evolutionary Logistic-Type Model}},
author = {Rafael Luís},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14193621},
url = {https://www.mdpi.com/2227-7390/14/19/3621},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Stability and Bifurcation of a Multi-Trait Eco-Evolutionary Logistic-Type Model
AU - Rafael Luís
PY - 2026
DA - 2026/10/07
JO - Mathematics
DO - 10.3390/math14193621
UR - https://www.mdpi.com/2227-7390/14/19/3621
AB - We extend a two-dimensional discrete-time eco-evolutionary logistic model to the case of finitely many quantitative traits. The original planar model couples population density to a single mean trait under stabilizing selection; the extension retains this mechanism while allowing trait-specific evolutionary response rates and feedback coefficients. We establish a positively invariant ecological core and construct compact absorbing boxes, which yield a compact global attractor for the restricted dynamics. All equilibria are characterized through a scalar equation, and the positive equilibrium is shown to exist uniquely exactly when the intrinsic growth factor exceeds one. The Jacobian at this equilibrium has an arrowhead structure, leading to an explicit characteristic polynomial. We prove that the persistence threshold is a transcritical boundary bifurcation and formulate complete spectral and nondegeneracy conditions for flip and Neimark–Sacker bifurcations. Numerical bifurcation diagrams illustrate the transcritical, period-doubling, and Neimark–Sacker bifurcations predicted by the analytical results.
SN - 2227-7390
ER -