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Blowout bifurcation with non-normal parameters in population dynamics.
1CNRS UMR 7625, Université Pierre et Marie Curie, Quai Saint Bernard, Case 237, 75252 Paris, France. bcazelle@snv.jussieu.fr
Summary
Complex dynamics like riddled basins can occur in interacting populations, potentially leading to species extinction. This study reveals these behaviors are widespread and have implications for biodiversity.
Area of Science:
- Ecology
- Dynamical Systems Theory
- Population Biology
Background:
- Transverse stability of invariant subspaces can exhibit complex dynamics, such as riddled basins and on-off intermittency.
- These behaviors were recently shown to be widespread in models with non-normal parameters.
Purpose of the Study:
- To demonstrate complex dynamics in models of interacting populations.
- To define the invariant subspace by species extinction.
- To discuss implications for population biology amid the biodiversity crisis.
Main Methods:
- Analysis of dynamical behaviors in models of interacting populations.
- Identification of invariant subspaces defined by species extinction.
Main Results:
- Demonstration of complex dynamics (e.g., riddled basins, on-off intermittency) in population models.
- The invariant subspace associated with species extinction exhibits these complex dynamics.
Conclusions:
- Complex dynamics are not limited to abstract models but occur in ecological systems.
- Species extinction can be linked to complex dynamical behaviors.
- Findings highlight potential widespread implications for population biology and biodiversity conservation.