SELESAIAN MODEL MATEMATIKA FRAKSIONAL MENGGUNAKAN METODE PERTURBASI HOMOTOPI PADA SISTEM PREDASI TIGA SPESIES
Abstract: In an
ecosystem, there are
many organism interacting
with other organism,
similar organism or other organism types, either one species or
more. A relationship between prey
and predator called predation
system. Predation system
which consists of
two species called
Lotka Volterra models. There is
also predation system which consists of
three species. Predation system of three species can be expressed in system of
nonlinear differential equations. In
general, system of nonlinear differential
equations difficult to
find analytic solutions,
so that it
can be searched using the
solutions approach with
stability analysis from
equilibrium point. Other
mathematical models that are
similar to system
of nonlinier differential
equations is system
of fractional differential equations.
To get a
system of differential
equations of fractional,
the order of the
system is modify the order on system of differential equations into fractional
order α and β, 0 < α ≤ 1 and 0 < β
≤ 1, as was done by Das and Gupta (2011).
The system of differential equations of fractional can be solved
analytically using Homotopy Perturbation Method (HPM) approach.
The result is infinite series, further resolved numerically. From the
result show that increase in the first and
second predator will
result in a
decrease in prey,
while decrease in
the first and
second predator will result in a increase in prey.
Keywords: Predation model of three species, fractional
differential equations, Homotopy perturbation method
Penulis: Nur Widyawati, Moh.
Imam Utoyo, Windarto
Kode Jurnal: jpmatematikadd130073
