  The numerical convergence of a Telegraph Predator-Prey system is studied.
This system of partial differential equations (PDEs) can describe various
biological systems with reactive, diffusive and delay effects. Initially, our
problem is mathematically modeled. Then, the PDEs system is discretized using
the Finite Difference method, obtaining a system of equations in the explicit
form in time and implicit form in space. The consistency of the Telegraph
Predator-Prey system discretization was verified. Next, the von Neumann
stability conditions were calculated for a Predator-Prey system with reactive
terms and for a Telegraph system with delay. For our Telegraph Predator-Prey
system, through numerical experiments, it was verified tat the mesh refinement
and the model parameters (reactive constants, diffusion coefficient and delay
term) determine the stability/instability conditions of the model.
  Keywords: Telegraph-Diffusive-Reactive System. Maxwell-Cattaneo Delay.
Discretization Consistency. Von Neumann Stability. Numerical Experimentation.
