Pal D, Mahapatra G S, Samanta G P
Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, 711103, India.
Department of Mathematics, National Institute of Technology Puducherry, Karaikal, 609605, India.
Bull Math Biol. 2016 Jul;78(7):1493-519. doi: 10.1007/s11538-016-0192-y. Epub 2016 Jul 13.
This paper deals with a prey-predator model in which both the species are infected by some toxicants which are released by some other species or source with fuzzy biological parameters. The application of fuzzy differential equation in the modeling of prey-predator populations with the effect of toxicants is presented. The dynamical behavior and harvesting of the fuzzy exploited system are studied by using the utility function method. Sufficient conditions for the local stability of the positive equilibrium are obtained by analyzing the characteristic equation. Furthermore, the possibility of the existence of bionomic equilibrium is studied under imprecise biological parameters. The study of the presence of toxic substance and harvesting in the modeling system can have significant impact on the existence of both the species, which is in line with reality. Numerical simulation results are presented to validate the theoretical analysis.
本文研究了一个捕食-食饵模型，其中两个物种都受到某些毒物的感染，这些毒物由其他物种或来源释放，且具有模糊的生物学参数。提出了模糊微分方程在毒物影响下的捕食-食饵种群建模中的应用。利用效用函数方法研究了模糊开发系统的动力学行为和收获问题。通过分析特征方程，得到了正平衡点局部稳定性的充分条件。此外，还研究了在不精确生物学参数下生物经济平衡点存在的可能性。对建模系统中毒物存在和收获情况的研究，可能会对两个物种的生存产生重大影响，这与实际情况相符。给出了数值模拟结果以验证理论分析。
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