ANALISIS MODEL PREDATOR-PREY DENGAN PEMANENAN SEBAGAI VARIABEL KONTROL PADA PENANGKAPAN IKAN DENGAN AREA KONSERVASI
Abstract: The activities
of overfishing there
is often we
problem that caused
reduced fish populations and even
extinction. Therefore, do some protection efforts fish from overfishing, by the
holding of the conservation area. This effort is expected to maintain fish populations from extinction and increase
the sustainability of
marine ecosystems. Accordingly,
in this thesis
discussed the predator-prey models
with harvesting as a control
variable in fishing
conservation area. Mathematical
modelling of the predator-prey that describes the fishery resources in the sea
divided into three compartments, that is prey in the free area (x), prey on the conservation area (y), and predators (z). Based on the results
of analysis predator -prey models with constant harvesting thereare three
equilibria, namely is the extinction
equilibrium populations (𝐸0), the
predator free equilibrium (𝐸1), and three populations coexist
equilibrium (𝐸2). We futher analyzed the stability of the
equilibria. By using the Pontryagin Maximum Principle we derive the existence
of the optimal control of the effort harvesting. The numerical simulations is
given to illustrate the optimal control strategy. The
simulation results show
that the optimal
harvesting effort effectively
to maximize results and minimize
costs in the harvesting effort, while increasing value of revenues.
Keywords: Predator-prey model, Harvesting, Conservation
zone, Asimtomatis stability, Optimal control
Penulis: Titik Didayanti,
Fatmawati, Miswanto
Kode Jurnal: jpmatematikadd130073
