First Order Linear Homogeneous Ordinary Differential Equation in Fuzzy Environment Based On Laplace Transform

In this paper the First Order Linear Ordinary Differential Equations (FOLODE) are described in fuzzy environment. Here coefficients and /or initial condition of FOLODE are taken as Generalized Triangular Fuzzy Numbers (GTFNs).The solution procedure of the FOLODE is developed by Laplace transform. It is illustrated by numerical examples. Finally imprecise bank account problem and concentration of drug in blood problem are described

Generalized intuitionistic fuzzy laplace transform and its application in electrical circuit

In this paper we describe the generalized intuitionistic fuzzy laplace transform method for solving first order generalized intutionistic fuzzy differential equation. The procedure is applied in imprecise electrical circuit theory problem. Here the initial condition of those applications is taken as Generalized Intuitionistic triangular fuzzy numbers (GITFNs).Publisher's Versio

First Order Linear Non Homogeneous Ordinary Differential Equation in Fuzzy Environment

In this paper, the solution procedure of a first order linear non homogeneous ordinary differential equation in fuzzy environment is described. It is discussed for three different cases. They are i) Ordinary Differential Equation with initial value as a fuzzy number, ii) Ordinary Differential Equation with coefficient as a fuzzy number and iii) Ordinary Differential Equation with initial value and coefficient are fuzzy numbers. Here fuzzy numbers are taken as Generalized Triangular Fuzzy Numbers (GTFNs). An elementary application of population dynamics model is illustrated with numerical example. Keywords: Fuzzy Ordinary Differential Equation (FODE), Generalized Triangular fuzzy number (GTFN), strong solution

Numerical Solution of First-Order Linear Differential Equations in Fuzzy Environment by Runge-Kutta-Fehlberg Method and Its Application

The numerical algorithm for solving “first-order linear differential equation in fuzzy environment” is discussed. A scheme, namely, “Runge-Kutta-Fehlberg method,” is described in detail for solving the said differential equation. The numerical solutions are compared with (i)-gH and (ii)-gH differential (exact solutions concepts) system. The method is also followed by complete error analysis. The method is illustrated by solving an example and an application

The behavior of logistic equation with alley effect in fuzzy environment: fuzzy differential equation approach

In this paper a fuzzy logistic equation with alley effect is introduced by considering some parameter as fuzzy numbers. Due to presence of the fuzzy number the corresponding differential equation in logistic equation model with alley effect becomes fuzzy differential equation. Considering generalized Hukuhara derivative approach the fuzzy logistic equation converted to system of two crisp differential equations. We obtain the conditions of stability criterion for different cases. Different numerical examples are given to support our work

Some Comparison of Solutions by Different Numerical Techniques on Mathematical Biology Problem

We try to compare the solutions by some numerical techniques when we apply the methods on some mathematical biology problems. The Runge-Kutta-Fehlberg (RKF) method is a promising method to give an approximate solution of nonlinear ordinary differential equation systems, such as a model for insect population, one-species Lotka-Volterra model. The technique is described and illustrated by numerical examples. We modify the population models by taking the Holling type III functional response and intraspecific competition term and hence we solve it by this numerical technique and show that RKF method gives good results. We try to compare this method with the Laplace Adomian Decomposition Method (LADM) and with the exact solutions

Influence of impreciseness in designing tritrophic level complex food chain modeling in interval environment

Abstract In this paper, we construct a tritrophic level food chain model considering the model parameters as fuzzy interval numbers. We check the positivity and boundedness of solutions of the model system and find out all the equilibrium points of the model system along with its existence criteria. We perform stability analysis at all equilibrium points of the model system and discuss in the imprecise environment. We also perform meticulous numerical simulations to study the dynamical behavior of the model system in detail. Finally, we incorporate different harvesting scenarios in the model system and deploy maximum sustainable yield (MSY) policies to determine optimum level of harvesting in the imprecise environment without putting any unnecessary extra risk on the species toward its possible extinction

QCA based error detection circuit for nano communication network

This paper outlines low power nano-scale circuit design for even parity generator as well as even parity checker circuit using quantum-dot cellular automata (QCA). The proposed even parity generator and even parity checker is achieved by using a new layout of XOR gate. This new XOR gate is much denser and faster than existing ones in the state of the art. The proposed parity generator has out shined the existing design by reducing the cell count as 10proposed parity checker has also out shined the existing design with an improvement in cell count as 17.94circuits are denser and faster than existing one. Nanocommunication architecture with the proposed circuits is also demonstrated. The bit-error coverage by the proposed method is described. Besides, the defects in the circuits are explored to facilitate guide to proper implementation. The tests vectors are proposed to identify the defects in the designs and the defect coverage by those test vector are also described. The estimation of dissipated energy by the layouts established the very low energy dissipation nature of the designs. Different parameters like logic gate, density and latency are utilized to evaluate the designs that demonstrate the faster processing speed at nano-scale

Security Analysis With Novel Image Masking Based Quantum-Dot Cellular Automata Information Security Model

Mask of an image is generated in this article using Quantum Dot Cellular Automata. An encoder circuit is drafted to produce the Mask Image. This encoder can function as a decoder as well. A mask image is used to retrieve the original image,although the secret key remains unknown. Power dissipation calculations are performed to comprehend the proposed circuit consumes lower power dissipation at nano-scale level design.The security of the proposed circuit is guaranteed by validating with different security standards. The design paradigm matches the theoretical values, which authorizes the accurateness of the proposed circuit. The Structural Similarity (SSIM) index of the retrieved image is calculated to establish the degradation of the image quality is minimal. The stuck-at-fault analysis is performed to prove the stability of the circuit