The focus of the paper is on a continuous model of a resource-constrained, three-species competitive ecology. The effort to outlive the other competitors is referred to as competition. There is competition between species for survival when they attempt to coexist in the same community, with the same resources, and in the same environment. When resources are scarce, a struggle for survival would ensue. Three simultaneous non-linear first ODEs make up the mathematical model equations. The model's eight equilibrium points are all found. If every eigen value in a complex system is negative, or if the values are real and have negative real parts, the system would be stable. The trajectories over the equilibrium locations are depicted. And next, there has been established system's global stability with the use of a suitably designed Lyapunov's function. Further, the Runge-Kutta fourth order technique is used to compute the numerical solutions for the growth rate equations.