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[38]Geometric analysis of ecological models with slow and fast processes
[39]S Rinaldi, [40]M Scheffer - Ecosystems, 2000 - Springer
[41]S Rinaldi, [42]M Scheffer
Ecosystems, 2000 o Springer
The interaction of fast and slow processes is an integral part of the sudden
large shifts that
sometimes occur in ecosystems. To study the effects of slow/fast variables on
ecosystems,
we used a range of examples from natural and exploited aquatic and terrestrial
systems. So-
called catastrophic bifurcations in the dynamics of the fast components are at
the heart of
such dramatic shifts. We discuss some of the most important bifurcations and show
how they
can be analyzed. Subsequently, we show how the interaction with slowly changing
variables ...
Abstract
The interaction of fast and slow processes is an integral part of the sudden
large shifts that sometimes occur in ecosystems. To study the effects of
slow/fast variables on ecosystems, we used a range of examples from natural and
exploited aquatic and terrestrial systems. So-called catastrophic bifurcations in
the dynamics of the fast components are at the heart of such dramatic shifts. We
discuss some of the most important bifurcations and show how they can be
analyzed. Subsequently, we show how the interaction with slowly changing
variables can be understood from graphs constructed in a simple way using the
singular perturbation approach.
Springer
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