  Product cannibalisation is a well-known phenomenon in marketing and
technological research and describes the case when a new product steals sales
from another product under the same brand. A very special case of
cannibalisation may occur when the older product react to the competitive
strength of the newer one, absorbing the corresponding market shares. Given its
special character, we call this phenomenon inverse product cannibalisation. We
suppose that a case of inverse cannibalisation is observed between two products
of Apple Inc., the iPhone and the more recent iPad, and the first has been able
to succeed at the expense of the second. To explore this hypothesis, within a
diffusion of innovations perspective, we propose a modified Lotka-Volterra
model for mean trajectories in asymmetric competition, allowing us to test the
presence and the extent of the inverse cannibalisation phenomenon. A SARMAX
refinement integrates the short term predictions with seasonal and
autodependent components. A non-dimensional representation of the proposed
model shows that the penetration of the second technology has been beneficial
for the first, both in terms of market size and life cycle length.
