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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.
摘要：
在目前的研究中,对时间白噪声扰动的鱼场模型进行了数值检验。该模型包含鱼类和贻贝种群，并提供外部食物。这项工作的主要目的是为此类模型开发具有时间效率的数值方案，以保留动力学特性。为计算结果设计了随机反向欧拉（SBE）和随机隐式有限差分（SIFD）方案。在平均平方意义上，这两个方案都与基础模型一致，方案都是冯·诺依曼稳定的。基础模型具有各种平衡点，并且所有这些点都是通过SIFD方案成功获得的。对于给定的参数值，SIFD方案显示出积极和收敛的行为。由于基础模型是人口模型，其解决方案可以达到最小值零，因此，可以获得小于零的值的解决方案在生物学上是不可能的。所以,随机倒向欧拉获得的数值解是负解和发散解，在此类动力系统中，这不是无用的生物学现象。系统的图形行为表明，外部养分供应是控制给定模型动力学的重要因素。针对参数的各种选择绘制了三维结果。
