  Spatio-temporal pattern formation over the square and rectangular domain has
received significant attention from researchers. A wide range of stationary and
non-stationary patterns produced by two interacting populations is abundant in
the literature. Fragmented habitats are widespread in reality due to the
irregularity of the landscape. This work considers a prey-predator model
capable of producing a wide range of stationary and time-varying patterns over
a complex habitat. The complex habitat is assumed to have consisted of two
rectangular patches connected through a corridor. Our main aim is to explain
how the shape and size of the fragmented habitat regulate the spatio-temporal
pattern formation at the initial time. The analytical conditions are derived to
ensure the existence of a stationary pattern and illustrate the role of most
unstable eigenmodes to determine the number of patches for the stationary
pattern. Exhaustive numerical simulations help to explain the spatial domain's
size and shape on the transient patterns and the duration of transient states.
