Fuzzy delay predator-prey system: existence theorem and oscillation property of solution

Barzinji, Khabat; Maan, Normah; Aris, Nor’aini

doi:10.12988/ijma.2014.4373

Cited by 8 publications

(6 citation statements)

References 4 publications

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“…Nounou et al (2012) discuss fuzzy intervention in biological phenomena. Fuzzy delay predator-prey system and their existence theorem and oscillation property of solution is nicely delivered by Barzinji (2014). Symptomatic HIV virus infected population with fuzzy concept is done by Jafelice et al (2004).…”

Section: Fuzzy Differential Equationmentioning

confidence: 99%

Discussion on fuzzy quota harvesting model in fuzzy environment: fuzzy differential equation approach

Paul

Mondal

Bhattacharya

2016

Model. Earth Syst. Environ.

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In the recent years much importance has been laid on the role of uncertainty (fuzzy, interval etc.) in mathematical biology. In this paper we tried to study on the quota harvesting model in fuzzy environment. This model is considered in three different ways viz. (1) Initial condition (population density) is a fuzzy number, (2) coefficients of quota harvesting model (intrinsic growth rate and quota harvesting rate) are fuzzy number and (3) both initial condition and coefficients are fuzzy number. We discuss all these fuzzy cases individually. The solution procedure is done by using the concept of fuzzy differential equation approach. We have discussed the equilibrium points and their feasibility in all the three cases. This paper explores the stability analysis of the quota harvesting model at the equilibrium points in fuzzy environment. In order to examine the stability systematically in different fuzzy cases, we have used numerical simulations and discussed them briefly.

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Section: Fuzzy Differential Equationmentioning

confidence: 99%

Discussion on fuzzy quota harvesting model in fuzzy environment: fuzzy differential equation approach

Paul

Mondal

Bhattacharya

2016

Model. Earth Syst. Environ.

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“…Delay differential equation is a branch of functional differential equation arising in several applications from various fields of studies, for instances biology, population dynamics, chemistry, physics, control theory, and many others [2,3,7,14,16,20,21,24,25]. Unlike in the case of ordinary differential equations (ODEs) the unknown functions in DDEs depend not only on the present values of derivatives of independent variables, but also depend on the values of the functions at some previous times.…”

Section: Introductionmentioning

confidence: 99%

“…(5.10) By choosing an initial approximation v 0 (t) = 1 + t 3 − 575t 2 18 and (5.10) we obtained the following components as…”

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confidence: 99%

Analytical technique for neutral delay differential equations with proportional and constant delays

Maan¹,

Barde²

2020

J. Math. Computer Sci.

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Neutral delay differential equations (NDDEs) are a type of delay differential equations (DDEs) that arise in numerous areas of applied sciences and play a vital role in mathematical modelling of real-life phenomena. Some techniques have experienced difficulties in finding the approximate analytical solution which converges rapidly to the exact solution of these equations. In this paper, an analytical approach is proposed for solving linear and nonlinear NDDEs with proportional and constant delays based on the homotopy analysis method (HAM) and natural transform method where the nonlinear terms are simply calculated as a series of, He's polynomial. The proposed method produces solutions in the form of a rapidly convergent series which leads to the exact solution from only a few numbers of iterations. Some illustrative examples are solved, and the convergence analysis of the proposed techniques was also provided. The obtained results reveal that the approach is very effective and efficient in handling both linear and nonlinear NDDEs with proportional and constant delays and can also be used in various types of linear and nonlinear problems.

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“…Paul et al [9] discussed the fuzzy quota harvesting of a single species Lotka-Volterra equation using generalized Hukuhara differentiability. Thus, many authors have utilized this concept for modeling in mathematical biology [10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

“…Although some attempts have already been made [7,[10][11][12][13][14], in this endeavor we carried out the investigations with some new inputs and concepts, which brings a novelty in this framework and provides appropriate applications. The key elements are described as follows:…”

Section: Introductionmentioning

confidence: 99%

Fractional order ecological system for complexities of interacting species with harvesting threshold in imprecise environment

et al. 2019

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The key objective of this paper is to study the imprecise biological complexities in the interaction of two species pertaining to harvesting threshold. It is explained by taking the prey–predator model with imprecise biological parameters and fractional order generalized Hukuhara (fgH) differentiability. In this vain, different possible systems of the model are constructed, according to the increasing and decreasing behavior of population growth. Feasibility and stability analyses of equilibrium points of the stated models are also discussed by means of variational matrix with Routh–Hurwitz conditions. In addition, the numerical elaborations are carried out by taking parametric expansion of fuzzy fractional Laplace transform (FFLT). This significantly helps the researchers in using a novel approach to analyze the constant solutions of the dynamical systems in the presence of fractional index. This would allow the avoidance of any intricacy that occurs while solving fractional order derivatives. Furthermore, this attempt also provides numerical and pictorial results, obtained through some well-known methods, namely fifth-forth Runge–Kutta method (FFRK), Grunwald–Letnikov’s definition (GL) and Adams–Bashforth method (ABM) that are deemed appropriate to scrutinize the dynamics of the system of equations.

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Fuzzy delay predator-prey system: existence theorem and oscillation property of solution

Cited by 8 publications

References 4 publications

Discussion on fuzzy quota harvesting model in fuzzy environment: fuzzy differential equation approach

Discussion on fuzzy quota harvesting model in fuzzy environment: fuzzy differential equation approach

Analytical technique for neutral delay differential equations with proportional and constant delays

Fractional order ecological system for complexities of interacting species with harvesting threshold in imprecise environment

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