Speaker
Description
Recent experiments show that cannibalism in predators and de-
fense in prey can both occur concurrently. Motivated by this, we investigate
a predator-prey system where cannibalism occurs in predators and defense in
prey simultaneously. System analysis show that depending on the prey defense
(µ) and predator cannibalism (c) parameters respectively, one can have global
stability of the coexistence and prey free states, bi-stability dynamics or up
to three interior equilibria. Local stability analysis shows that, the combined
effects of c and µ cannot drive both populations to extinction and for certain
parameter choices can destabilize the system. After varying the parameters µ
and c, the system undergoes standard co-dimension one bifurcations includ-
ing Hopf bifurcation, transcritical bifurcation and saddle-node bifurcation. In
addition, the system undergoes co-dimension two bifurcations such as cusp bi-
furcation and Bogdanov-Takens bifurcation. For the spatially explicit model,
we observe that in the absence of both µ and c, the system cannot exhibit Tur-
ing instability, whereas the system can produce Turing instability depending
on system parameters when present. We support our results with numerical
experiments and discuss their ecological implications.
