Stability and bionomic analysis of fuzzy parameter based prey–predator harvesting model using UFM

Pal, D.; Mahapatra, G. S.; Samanta, G. P.

doi:10.1007/s11071-014-1784-4

Cited by 37 publications

(14 citation statements)

References 46 publications

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“…There are many types of fuzzy numbers, such as triangular, trapezoidal, sigmoid, and Gaussian. Triangular fuzzy numbers are intuitive, simple to calculate, and easy to understand and can well express Mathematical Problems in Engineering 3 multiple linguistic variables [35]; therefore, in this study, triangular fuzzy numbers were used to measure affective responses.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Application of Fuzzy-Based Hybrid Taguchi Method for Multiobjective Optimization of Product Form Design

Shieh

Yang

et al. 2018

Mathematical Problems in Engineering

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In today’s competitive market, industrial product form design is moving towards being consumer centric. Affective responses relate to customers’ affective needs and are receiving increasing attention. To design a product form that can appeal to consumers, designers should consider multiple affective responses (MARs). This paper proposes a robust design approach that uses a fuzzy-based hybrid Taguchi method to derive the optimal product form design concerning MARs. First, design analysis is used to identify design variables and MARs. According to the results, a Taguchi experiment is designed in which fuzzy sets are used to measure the MARs; then, signal-to-noise (S/N) ratios are calculated. Subsequently, a fuzzy questionnaire with multiple answers is employed to acquire consumers’ preference weights for MARs, following which Vlsekriterijumska Optimizacija I Kompromisno Resenje (VIKOR) is adopted to transform the multiple S/N ratios into a multiperformance characteristic index (MPCI). On the basis of the MPCI, the effects of design variables are identified through analysis of variance and the response table and the response graph are obtained. Consequently, the optimal form design is achieved. A car profile design was used as an example to demonstrate the proposed approach. The results indicate that this approach can effectively improve consumers’ affective response qualities and can be used as a robust design approach to optimize product form design.

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Section: Theoretical Backgroundmentioning

confidence: 99%

Application of Fuzzy-Based Hybrid Taguchi Method for Multiobjective Optimization of Product Form Design

Shieh

Yang

et al. 2018

Mathematical Problems in Engineering

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“…Barros, Bassanezi, and Tonelli (2000) used the concept of fuzzy differential equations in population dynamics. There are various research papers (Pal, Mahapatra, & Samanta, 2015; Panja, 2018; Panja, Kumar Mondal, & Chattopadhyay, 2017; Peixoto, Barros, & Bassanezi, 2008) in which the stability and bifurcation analyses have been carried out and uncertainties of parameters considered. Given all these facts, in this paper, we have extended the work of Devi and Gupta (2018) in the fuzzy environment by considering all biological parameters as triangular fuzzy numbers.…”

Section: Introductionmentioning

confidence: 99%

Comparative study of the effects of different growths of vegetation biomass on CO₂ in crisp and fuzzy environments

Devi

Gupta

2020

Natural Resource Modeling

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In this paper, three fuzzy nonlinear mathematical models, corresponding to crisp models described in Devi and Gupta (2018), are formulated to study the comparative behavior of carbon dioxide concerning vegetation biomass in crisp and fuzzy environments.Logistic growth and regrowth of vegetation biomass are considered in the first two models, and delay is incorporated in the regrowth of vegetation biomass in the third one. Conditions for boundedness and persistence of the solutions, the existence of equilibrium points, and the stability of equilibrium points are carried out for each model. We also derived the formula for the critical value of time delay. Further, we also analyzed the existence, stability, and direction of the Hopf bifurcation. Numerical simulations were performed to complement analytical findings and to see the comparison between crisp and fuzzy environments. In fuzzy environment, it is observed that increment in the minimum value of regrowth rate shifts the destabilizing value of delay forward while if the maximum value of regrowth rate decreases, variables will become unstable before the estimated time. The overall analysis demonstrates that the behavior of the models in crisp and fuzzy environments is quite different. Recommendations for resource managers• An increasing level of CO 2 is the major factor for greenhouse effect, therefore to reduce the destructive effects of global warming, implementation of policies related to mitigation of the atmospheric CO 2 is of paramount importance.• Vegetation biomass has considerable regrowth rate as compared with the rest of the plants. But, there is some time lag in the process of regrowth, therefore for the growth rate of vegetation biomass regrowth with delay must be considered to avoid the fluctuations in the results. • In the real world, the biological parameters are not always fixed because they vary according to the environment. So, scientists should consider fuzzy parameters for more precise results.

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“…[20][21][22][23][24]proposed prey-predator harvesting model under impreciseness by considering biological parameters as interval number, Naji and Mustafa [19] studied the dynamics of an eco-epidemiological model with nonlinear incidence rate. Majeed and Shawka studied prey-predator model involving SI and SIS infectious disease in prey population and the disease transmitted within the same species by contact and external…”

Section: …………………………………………………………………………………………………… Introduction:-mentioning

confidence: 99%

A Food Chain Structures and Dynamics Across a Refuge Stage- Structure Prey-Predator Model.

Majeed¹,

Rahi.²

2017

IJAR

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In the present paper the structures and dynamics of a food chain preypredator model are proposed and studied. The two stages and refuge in prey and two predators (top and mid) are considered. Different types of functional responses have been proposed. The conditions, which guarantee the existence of equilibrium points, have been investigated. Uniqueness and boundedness of the solution of the system are proven. The local and global dynamical behaviors are discussed and analyzed. Finally, numerical simulations are carried out not only to confirm the theoretical results obtained, but also to show the effects of the refuge and the variation of each parameter on our proposed system. …………………………………………………………………………………………………….... Introduction:-The first pattern formation of predator-prey model was introduced in 1927 by the well-known Lotka[15] and Volterra[28] which starting from a simple and classical supposition, more complexity but factual predator-prey models have been constructed by mathematicians and ecologists. In 1992, Berryman [6] considered that the dynamic interaction between predators and preys has long taken and go on to be one of the most important and central subjects which play a great role in each of the mathematical ecology, natural, social, and technological sciences, especially in the research on biology and ecology [5,17,26,27].Many researchers working in these fields paying a great amount of attention to improve and generalize the pattern formation of prey-predator models to more involvement and realistic system, and merging this advantage into many applications that give the nature of existence and global asymptotic stability of predator-prey models a great interest.On the other hand, the dynamical behavior of prey-predator models has been investigated by a lot of articles and peppers which results a significant expansion in the structural of the prey -predator models to involve multispecies; different functional responses, several types of food chain, refuge, harvesting, stage-structure, several types of diseases…etc.Lately, Samantha[25] studied the existence and global asymptotic stability of a delay predator-prey model with disease in the prey, Paletal. [20][21][22][23][24]proposed prey-predator harvesting model under impreciseness by considering biological parameters as interval number, Naji and Mustafa [19] studied the dynamics of an eco-epidemiological model with nonlinear incidence rate. Majeed and Shawka studied prey-predator model involving SI and SIS infectious disease in prey population and the disease transmitted within the same species by contact and external

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Stability and bionomic analysis of fuzzy parameter based prey–predator harvesting model using UFM

Cited by 37 publications

References 46 publications

Application of Fuzzy-Based Hybrid Taguchi Method for Multiobjective Optimization of Product Form Design

Application of Fuzzy-Based Hybrid Taguchi Method for Multiobjective Optimization of Product Form Design

Comparative study of the effects of different growths of vegetation biomass on CO₂ in crisp and fuzzy environments

A Food Chain Structures and Dynamics Across a Refuge Stage- Structure Prey-Predator Model.

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Stability and bionomic analysis of fuzzy parameter based prey–predator harvesting model using UFM

Cited by 37 publications

References 46 publications

Application of Fuzzy-Based Hybrid Taguchi Method for Multiobjective Optimization of Product Form Design

Application of Fuzzy-Based Hybrid Taguchi Method for Multiobjective Optimization of Product Form Design

Comparative study of the effects of different growths of vegetation biomass on CO2 in crisp and fuzzy environments

A Food Chain Structures and Dynamics Across a Refuge Stage- Structure Prey-Predator Model.

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Comparative study of the effects of different growths of vegetation biomass on CO₂ in crisp and fuzzy environments