We perform both analytical and numerical bifurcation analysis of an alternating forest and grassland ecosystem model coupled with human interaction. The model consists of two nonlinear ordinary differential equations incorporating the human perception of the value of the forest. The system displays multiple steady states corresponding to different forest densities as well as regimes characterized by both stable and unstable limit cycles. We derive analytically the conditions with respect to the model parameters that give rise to various types of codimension-one criticalities such as transcritical, saddle-node, and Andronov–Hopf bifurcations and codimension-two criticalities such as cusp and Bogdanov–Takens bifurcations at which homoclinic orbits occur. We also perform a numerical continuation of the branches of limit cycles. By doing so, we reveal turning points of limit cycles marking the appearance/disappearance of sustained oscillations. Such critical points that cannot be detected analytically give rise to the abrupt loss of the sustained oscillations, thus leading to another mechanism of catastrophic shifts.
Keywords: Analytical and numerical bifurcation analysis, ecosystem model, catastrophic shifts, cusp bifurcations, Bogdanov–Takens bifurcations
@article{M2AN_2021__55_S1_S653_0,
author = {Spiliotis, Konstantinos and Russo, Lucia and Giannino, Francesco and Siettos, Constantinos},
title = {Analytical and numerical bifurcation analysis of a forest ecosystem model with human interaction},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {S653--S675},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {Suppl\'ement},
doi = {10.1051/m2an/2020054},
mrnumber = {4221317},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2020054/}
}
TY - JOUR AU - Spiliotis, Konstantinos AU - Russo, Lucia AU - Giannino, Francesco AU - Siettos, Constantinos TI - Analytical and numerical bifurcation analysis of a forest ecosystem model with human interaction JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2021 SP - S653 EP - S675 VL - 55 IS - Supplément PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2020054/ DO - 10.1051/m2an/2020054 LA - en ID - M2AN_2021__55_S1_S653_0 ER -
%0 Journal Article %A Spiliotis, Konstantinos %A Russo, Lucia %A Giannino, Francesco %A Siettos, Constantinos %T Analytical and numerical bifurcation analysis of a forest ecosystem model with human interaction %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2021 %P S653-S675 %V 55 %N Supplément %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2020054/ %R 10.1051/m2an/2020054 %G en %F M2AN_2021__55_S1_S653_0
Spiliotis, Konstantinos; Russo, Lucia; Giannino, Francesco; Siettos, Constantinos. Analytical and numerical bifurcation analysis of a forest ecosystem model with human interaction. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021), pp. S653-S675. doi: 10.1051/m2an/2020054
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