Impact of predator fear on two competing prey species
Abstract
Predator-prey interaction is a fundamental feature in the ecological
system. The majority of studies has addressed how competition and
predation affect species coexistence. Recent field studies on vertebrate
has shown that fear of predators can influence the behavioural pattern
of prey populations and reduce their reproduction. A natural question
arises whether species coexistence is still possible or not when
predator induce fear on competing species. Based on the above
observation, we propose a mathematical model of two competing prey-one
predator system with the cost of fear that affect reproduction rate of
both the prey population. To make the model more realistic, we
incorporate intraspecific competition within the predator population.
Biological justification of the model is shown through positivity and
boundedness of solutions. Existence and stability of different boundary
equilibria are discussed. Condition for the existence of coexistence
equilibrium point is derived from showing uniform persistence. Local as
well as a global stability criterion is developed. Bifurcation analysis
is performed by choosing the fear effect as the bifurcation parameter of
the model system. The nature of the limit cycle emerging through a Hopf
bifurcation is indicated. Chaotic motion is observed when one of two
prey has bigger competitive capacities than the other. Numerical
experiments are carried out to test the theoretical results obtained for
this model.