Abstract
The aim of this paper is to investigate three species Lotka-Volterra system with the immigration and harvesting effect. This work verifies the parametric conditions for the existence of the non-negative equilibrium points and its asymptotic stability. First, the sign stability of the system is analyzed through signed digraphs associated with the Jacobian matrix. Second, the asymptotic stability of the system is obtained by attaining the suitable parameters which are satisfying the Routh-Hurwitz stability criterion. In this model, the focus is mainly on the role of the immigration effect of every species. The paper is concluded with the immigration effect that supports to stabilize the unstable system and how the numerical result provides the guarantee to achieve the theoretical results.
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