KESTABILAN SISTEM PREDATOR-PREY LESLIE

Abstract

Mathematical models are commonly used to describe physical and nonphysical
phenomena which appeared in the real world. Generally speaking, the
application of mathematical models is usually formed into a differential equation
system. For example, Predator-Prey Leslie system is one mathematical model of
non-linier differential equation system which has been introduced by Leslie
(1948). This system describes an interaction model between two populations
which contain two equations as follows :
ax bx cyx
dt
dx
  

dy 2
 
where a, b, c, e and f are positive constants.
In the Predator-Prey Leslie system, the relationship between each variable
in the interaction process between prey and preadtor is dependend and influenced
by changing value of system. Therefore, this will effect to the stability system.
The method of this research is a study of literature from relevant books
and journals. To obtain a stability system, the stability poits of a system have to be
found firest, then continue with linierization. From this, it will obtained
characteristic roots or eigen values. These values will show a stable state at
system equilibrium points.
As a result, it is found that Predator-Prey Leslie system, in this case,
reaches a stability at equilibrium point K2, but not the case at K1.