Stationary and non-stationary pattern formation over fragmented habitat

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