Deterministic sudden changes and stochastic fluctuation effects on
stability and persistence dynamics of two-predator one-prey Model
Abstract
In this paper, we present new results on deterministic sudden changes
and stochastic fluctuations effects on the dynamics of a two-predator
one-prey model. We purpose to study the dynamics of the model with some
impacting factors as problem statement. The methodology depends on
investigating the seasonality and stochastic terms that which makes the
predator- prey interactions more realistic. A theoretical analysis is
introduced for studying the effects of sudden deterministic changes,
using three different cases of sudden changes. We show that the system
in a good situation presents persistence dynamics only as a stable
dynamical behavior. However, the system in a bad situation leads to
three main outcomes, as follows: first, constancy at the initial
conditions of the prey and predators; second, extinction of the whole
system; and third, extinction of both predators, resulting in the growth
of the prey population until it reaches a peak carrying capacity. We
perform numerical simulations to study effects of stochastic
fluctuations, which show that, noise strength leads to an increase in
the oscillations in the dynamical behavior and became more complex,
finally, leads to extinction when the strength of the noise is high. The
random noises transfer the dynamical behavior from the equilibrium case
to the oscillation case, which describes some unstable environments