In this manuscript, we focus on the brief study of finding the solution to and analyzingthe homogeneous linear difference equation in a neutrosophic environment, i.e., we interpreted the solution of the homogeneous difference equation with initial information, coefficient and both as a neutrosophic number. The idea for solving and analyzing the above using the characterization theorem is demonstrated. The whole theoretical work is followed by numerical examples and an application in actuarial science, which shows the great impact of neutrosophic set theory in mathematical modeling in a discrete system for better understanding the behavior of the system in an elegant manner. It is worthy to mention that symmetry measure of the systems is employed here,which shows important results in neutrosophic arena application in a discrete system.
Optimal harvesting modeling is a matter of great importance for the sustainability of the eco-system. It is customary to consider the population dynamics in a continuous frame of time. In this paper, a discrete analogue of the study of the Logistic quota harvesting model under uncertainty is developed. The corresponding mathematical model is discussed in terms of nonlinear fuzzy difference equation. Different possible combinations of the fuzzy initial conditions and fuzzy coefficients are used for the manifestation of the difference equation. The equilibrium points and the subsequent stability analysis are carried out with the help of the characterization theorem which converts the fuzzy difference equation to a system of crisp difference equations. The numerical and graphical simulation are practiced to make a clear insight advocated by this study.
In this chapter, the authors discuss the solution of spread of infectious diseases in terms of SI model in fuzzy environment, which is modelled in a typical discrete system. As the system is discrete in nature, the concept of difference equation has been embarked. In order to understand the underlying uncertainty perspective, they explored the fuzzy difference equations to study the problem.
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