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In this work, a Gause type predator-prey model is analyzed, \ considering a
non-monotonic functional response .
One of the main tarjet is to establish the number of limit cycles
surrounding a positive fixed point of sytem, showing the existence of two
concentric limit cycles.
It is also shown the system has two equilibrium points at inside of the
first quadrant for a wide subset of parameter values, where one is always a
saddle point. When this points collapses a cusp point due to a
Bogdanov-Takens bifurcation is obtained.
Other behaviours of system are given and in particular the model predicts
the populations can coexist for all parameters value since $(0,0)$ is saddle
point, but a great probability of extinction of predadors exists, because
the singularity $(K,0)$ is a local atractor.
Then, the phenomenon of bistability appears since two singularities can be
local attractor at the first quadrant, or else, a stable limit cycle
coexists with a locally asymptotically stable point. |
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