In this paper, a novel concept of fuzzy preypredator model is introduced by considering the imprecise nature of the biological parameters. We consider the imprecise biological parameters as a form of triangular fuzzy number in nature. These imprecise parameters first transform to the corresponding intervals and then using interval mathematics the related differential equation is converted to two differential equations. Then using utility function method, the converted differential equations is changed to a single differential equation. The possibility of existence of both biological and bionomic equilibrium is presented. We obtain the conditions of local and global stability under impreciseness. We also study the optimal harvesting policy and derive the optimal solution under imprecise biological parameters. Lastly, numerical examples are presented to the support of our proposed approach.
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.
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