Abstract:
The pest control is of great interest in agriculture domain because the
pests have been the major factor that reduces the agricultural production in
the world. An agricultural ecosystem consists of a dynamic web of
relationships among crop plants or trees, herbivores, predators, weeds, etc.
Organisms in a cropping system interact in many ways — through
competition. There are different approaches in regard the possibility of the
modeling of these complex systems. Over the last decade, there has been
considerable progress in generalizing the concept of synchronization to
include the case of coupled chaotic oscillators especially for biological
systems. Many examples of biological synchronization have been documented
in the literature, but currently theoretical understanding of the phenomena
lags behind experimental studies. From mathematical viewpoint, biological
control has been modeled as a two-species interaction. Arneodo et al.(1980)
have demonstrated that one can obtain chaotic behavior for the system with
three species and Samardzija and Greller(1988) propose a two-predator, one
prey generalization of the Lotka-Volterra problem into three dimensions.
In order to formulate the pest control in this work the synchronization
of two Lotka–Volterra systems with three species, one prey and two predators
is presented. The transient time until synchronization depends on initial
conditions of two systems and on the control number. Our results show that
the synchronization is about three times faster for all three controllers than
for one controller. The synchronization for all species is possible with one
controller only if we interfere on predator population. The control method
described in this work is very easy and might be useful in the case of the
other chaotic systems.
