  This paper investigates the competition of two species in a heterogeneous
environment subject to the effect of harvesting. The most realistic harvesting
case is connected with the intrinsic growth rate, and the harvesting functions
are developed based on this clause instead of random choice. We prove the
existence and uniqueness of the solution to the model we consider.
Theoretically, we state that when species coexist, one may drive the other to
die out, and both species extinct, considering all possible rational values of
parameters. These results highlight a comparative study between two harvesting
coefficients. Finally, we solve the model using a backward-Euler, decoupled,
and linearized time-stepping fully discrete algorithm and observe a match
between the theoretical and numerical findings.
