# Numerical study of diffusive fish farm system under time noise

## TL;DR

This paper studies a fish farm model with random time noise and evaluates numerical methods for simulating population dynamics.

## Contribution

The study introduces and compares two numerical schemes for preserving biological dynamics in noisy population models.

## Key findings

- The SIFD scheme successfully captures equilibrium points and maintains biological feasibility.
- The SBE scheme produces non-physical negative solutions, making it unsuitable for population modeling.
- External nutrient supply significantly influences the system's dynamics.

## Abstract

In the current study, the fish farm model perturbed with time white noise is numerically examined. This model contains fish and mussel populations with external food supplied. The main aim of this work is to develop time-efficient numerical schemes for such models that preserve the dynamical properties. The stochastic backward Euler (SBE) and stochastic Implicit finite difference (SIFD) schemes are designed for the computational results. In the mean square sense, both schemes are consistent with the underlying model and schemes are von Neumann stable. The underlying model has various equilibria points and all these points are successfully gained by the SIFD scheme. The SIFD scheme showed positive and convergent behavior for the given values of the parameter. As the underlying model is a population model and its solution can attain minimum value zero, so a solution that can attain value less than zero is not biologically possible. So, the numerical solution obtained by the stochastic backward Euler is negative and divergent solution and it is not a biological phenomenon that is useless in such dynamical systems. The graphical behaviors of the system show that external nutrient supply is the important factor that controls the dynamics of the given model. The three-dimensional results are drawn for the various choices of the parameters.