Numerical convergence of a Telegraph Predator-Prey system is studied. This partial differential equation (PDE) system can describe various biological systems with reactive, diffusive, and delay effects. Initially, the PDE system was discretized by the Finite Differences method. Then, a system of equations in a time-explicit form and in a space-implicit form was obtained. The consistency of the Telegraph Predator-Prey system discretization was verified. Von Neumann stability conditions were calculated for a Predator-Prey system with reactive terms and for a Delayed Telegraph system. On the other hand, for our Telegraph Predator-Prey system, it was not possible to obtain the von Neumann conditions analytically. In this context, numerical experiments were carried out and it was verified that the mesh refinement and the model parameters, reactive constants, diffusion coefficients and delay constants, determine the stability/instability conditions of the discretized equations. The results of numerical experiments were presented.

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