Relevant bibliographies by topics / VERHULST MODEL

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'VERHULST MODEL'

Author: Grafiati
Published: 4 June 2021
Last updated: 9 February 2022

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Journal articles on the topic "VERHULST MODEL"

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Side, Syafruddin, Maya Sari Wahyuni, and Arifuddin R. "Solusi Numerik Model Verhulst pada Estimasi Pertumbuhan Hasil Panen Padi dengan Metode Adam Bashforth-Moulton (ABM)." Journal of Mathematics, Computations, and Statistics 2, no. 1 (2020): 91. http://dx.doi.org/10.35580/jmathcos.v2i1.12463.

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Penelitian ini menerapkan metode Adam Bashforth-Moulton untuk menentukan solusi model Verhulst. Bentuk solusi yang diperoleh adalah estimasi hasil panen padi di Kabupaten Gowa dengan menggunakan persamaan berikut . Persamaan model Verhulst terlebih dahulu diselesaikan dengan metode Runge-Kutta orde-4 untuk mendapatkan solusi awal ; ; dan . Selanjutnya nilai awal disubstitusi pada persamaan Adam-Bashforth orde-4 untuk mendapatkan nilai prediksi, kemudian nilai prediksi yang diperoleh diperbaiki menggunakan persamaan korektor Adam Moulton orde-4. Pada iterasi ke-14 yaitu saat menunjukkan tahun diperoleh nilai prediktor dan nilai korektor sehingga estimasi hasil panen padi di Kabupaten Gowa pada tahun 2021 dengan menggunakan metode Adam Bashforth-Moulton saat adalah ton.Kata Kunci: Model Verhulst, Metode Runge-Kutta, Metode Adam Bashforth-Moulton This research applied Adam Bashforth-Moulton Method to determine the solution of Verhust Model. The form of the solution obtained is estimatation of rice harvest in Gowa Regency by using the following equation . Verhulst model equation firstly solved by using 4th order of Runge-Kutta method to get initial solutions of ; ; and . Furthermore, the initial values subtituted on the 4th order of Adam-Bashforth equation to get the prediction value, then the prediction value obtained was corrected using the corrector equation of 4th order of Adam Moulton. On the 14th iteration that is when shows the year of 2021 retrieved the predictor value of and corrector value of so estimation of rice harvets in Gowa Regency in 2021 by using Adam Bashforth-Moulton method when is ton.Keywords: Verhulst Model, Runge-Kutta Method, Adam Bashforth-Moulton
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Wang, Yuhong, Shulin Yang, Wuyong Qian, and Xiaozhong Li. "Forecasting New Product Diffusion Using Grey Time-Delayed Verhulst Model." Journal of Applied Mathematics 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/625028.

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Taking account of the time-delayed phenomenon in diffusion of new products, we propose the time-delayed Verhulst model and then establish a grey time-delayed Verhulst model using the method of grey differential equations. The related parameter packets of this novel model are obtained under the rule of ordinary least squares (OLS). The results show that the traditional grey Verhulst model is a special example of grey time-delayed Verhulst model which can reflect the time-delayed information effectively. A practical example of market diffusion shows that the modeling accuracy is remarkably improved by using the grey time-delayed Verhulst model presented in this paper.
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Cui, Jie, Naiming Xie, Hongyan Ma, Hong liang Hu, Zhengya Yang, and Chaoqing Yuan. "Property of derived grey verhulst model with multiple transformation." Grey Systems: Theory and Application 4, no. 2 (2014): 144–53. http://dx.doi.org/10.1108/gs-11-2013-0026.

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Purpose – The purpose of this paper is to study the properties of derived grey verhulst prediction model with multiplication transformation and reduce its modeling complexity. Design/methodology/approach – The paper discussed the parameter characteristics of grey derived verhulst model under multiple transformation, and demonstrated its effect on its simulative value and predictive value by investigating the multiple transformation acting on the raw data sequence of this grey model. The parameter characteristics of this model under multiple transformations and its effect of the simulation value and forecasting value are analyzed by studying the properties of multiply transformation of this model. Findings – The research finding shows that the modeling accuracy of derived grey verhulst model is in no relation to multiple transformations. Practical implications – The above results imply that the data level can be reduced; the process of building derived grey verhulst model can be simplified; but the simulative and predictive accuracy of this model remain unchanged. Originality/value – The paper succeeds in realising the properties of derived grey verhulst model by using the method of multiplication transformation, which is helpful to understand the modeling mechanism and expand the application range of derived grey verhulst model.
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Ramirez-Cando, Lenin Javier, Cesar Ivan Alvarez-Mendoza, and Patricia Gutierrez-Salazar. "Verhulst-Pearl growth model versus Malthusian growth model for in vitro evaluation of lead removal in wastewater by Photobacterium sp." F1000Research 7 (April 25, 2018): 491. http://dx.doi.org/10.12688/f1000research.14420.1.

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Mathematical modeling of microbial populations has a long history of application in the fields of ecology and environmental remediation. In the present study, the Verhulst-Pearl growth model and the Malthusian growth model were used to model and understand the kinetics of Photobacterium sp exposed to lead. The results show that goodness of fit of the Verhulst-Pearl growth model was better that the Malthusian growth model. Therefore, the Verhulst-Pearl growth model is considered the best option for proving useful and reliable information about Photobacterium sp kinetics growth in vitro.
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Qiang, Zhou. "Deformation Prediction of Slopes Based on Grey Verhulst Model." Advanced Materials Research 594-597 (November 2012): 347–51. http://dx.doi.org/10.4028/www.scientific.net/amr.594-597.347.

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The grey Verhulst nonlinear differential dynamic prediction model is applied to the prediction of the development of rock slope deformation in this paper. And experimental results show that grey Verhulst model is feasible to predict the slope rock mass deformation.
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Zeng, Bo, Chuan Li, Guo Chen, and Wang Zhang. "Verhulst Model of Interval Grey Number Based on Information Decomposing and Model Combination." Journal of Applied Mathematics 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/472065.

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Grey Verhulst models are often employed to simulate the development tendency with the characteristic of saturated process of S curve. However, the uncertainty of interval grey numbers will be increased since the boundaries of interval grey number are extended by the Axiom of nondecreasing grey degree in the existing Verhulst modeling method. In this paper, the interval grey number is divided into two real number parts, that is, “white” and “grey” parts. Then the “white” and “grey” parts are simulated and forecasted by building the grey Verhulst model and DGM (1, 1) model, respectively. To some degree, this method resolves the issue of amplifying the range of interval grey number. Finally, an example is used to compare the simulation performance between the new model and the traditional model, and the results show that the new model is superior to the other model.
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Hu, Xiaomei, Yubin Wang, Yue Yu, Dong Wang, and Yuan Tian. "Research on the Concentration Prediction of Nitrogen in Red Tide Based on an Optimal Grey Verhulst Model." Mathematical Problems in Engineering 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/9786107.

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In order to reduce the harm of red tide to marine ecological balance, marine fisheries, aquatic resources, and human health, an optimal Grey Verhulst model is proposed to predict the concentration of nitrogen in seawater, which is the key factor in red tide. The Grey Verhulst model is established according to the existing concentration data series of nitrogen in seawater, which is then optimized based on background value and time response formula to predict the future changes in the nitrogen concentration in seawater. Finally, the accuracy of the model is tested by the posterior test. The results show that the prediction value based on the optimal Grey Verhulst model is in good agreement with the measured nitrogen concentration in seawater, which proves the effectiveness of the optimal Grey Verhulst model in the forecast of red tide.
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Zhang, Jun, Tongyuan Wang, Jianpeng Chang, and Yan Gou. "Forecasting the Number of the Wounded after an Earthquake Disaster Based on the Continuous Interval Grey Discrete Verhulst Model." Discrete Dynamics in Nature and Society 2021 (April 5, 2021): 1–11. http://dx.doi.org/10.1155/2021/6654288.

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Earthquake disaster causes serious casualties, so the prediction of casualties is conducive to the reasonable and efficient allocation of emergency relief materials, which plays a significant role in emergency rescue. In this paper, a continuous interval grey discrete Verhulst model based on kernels and measures (CGDVM-KM), different from the previous forecasting methods, can help us to efficiently predict the number of the wounded in a very short time, that is, an “S-shape” curve for the numbers of the sick and wounded. That is, the continuous interval sequence is converted into the kernel and measure sequences with equal information quantity by the interval whitening method, and it is combined with the classical grey discrete Verhulst model, and then the grey discrete Verhulst models of the kernel and measure sequences are presented, respectively. Finally, CGDVM-KM is developed. It can effectively overcome the systematic errors caused by the discrete form equation for parameter estimation and continuous form equation for simulation and prediction in classical grey Verhulst model, so as to improve the prediction accuracy. At the same time, the rationality and validity of the model are verified by examples. A comparison with other forecasting models shows that the model has higher prediction accuracy and better simulation effect in forecasting the wounded in massive earthquake disasters.
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Mohamed, Zulkifley, Haniza Hanim Mohd Zain, Illyas Md Isa, and Husni Ibrahim. "Formulasi Inokulan Biosintetik dan Pembinaan Model Statistik Verhulst." Journal of Science and Mathematics Letters 6 (December 15, 2018): 18–31. http://dx.doi.org/10.37134/jsml.vol6.3.2018.

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Long, Xia, Yong Wei, and Zhao Long. "Discrete Verhulst model based on a linear time-varying." Grey Systems: Theory and Application 4, no. 2 (2014): 299–310. http://dx.doi.org/10.1108/gs-12-2013-0039.

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Purpose – The purpose of this paper is to build a linear time-varying discrete Verhulst model (LTDVM), to realise the convert from continuous forms to discrete forms, and to eliminate traditional grey Verhulst model's error caused by difference equations directly jumping to differential equations. Design/methodology/approach – The methodology of the paper is by the light of discrete thoughts and countdown to the original data sequence. Findings – The research of this model manifests that LTDVM is unbiased on the “s” sequential simulation. Practical implications – The example analysis shows that LTDVM embodies simulation and prediction with high precision. Originality/value – This paper is to realise the convert from continuous forms to discrete forms, and to eliminate traditional grey Verhulst model's error caused by difference equations directly jumping to differential equations. Meanwhile, the research of this model manifests that LTDVM is unbiased on the “s” sequential simulation.
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Dissertations / Theses on the topic "VERHULST MODEL"

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Jönsson, Ingela, and Mattias Nilsson. "Klassiska populationsmodeller kontra stokastiska : En simuleringsstudie ur matematiskt och datalogiskt perspektiv." Thesis, Växjö University, School of Mathematics and Systems Engineering, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-2262.

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<p>I detta tvärvetenskapliga arbete studeras från den matematiska sidan tre klassiska populationsmodeller: Malthus tillväxtmodell, Verhulsts logistiska modell och Lotka-Volterras jägarebytesmodell. De klassiska modellerna jämförs med stokastiska. De stokastiska modeller som studeras är födelsedödsprocesser och deras diffusionsapproximation. Jämförelse görs med medelvärdesbildade simuleringar.</p><p>Det krävs många simuleringar för att kunna genomföra jämförelserna. Dessa simuleringar måste utföras i datormiljö och det är här den datalogiska aspekten av arbetet kommer in. Modellerna och deras resultathantering har implementerats i både MatLab och i C, för att kunna möjliggöra en undersökning om skillnaderna i tidsåtgången mellan de båda språken, under genomförandet av ovan nämnda jämförelser. Försök till tidsoptimering utförs och även användarvänligheten under implementeringen av de matematiska problemen i de båda språken behandlas.</p><p>Följande matematiska slutsatser har dragits, att de medelvärdesbildade lösningarna inte alltid sammanfaller med de klassiska modellerna när de simuleras på stora tidsintervall. I den logistiska modellen samt i Lotka-Volterras modell dör förr eller senare de stokastiska simuleringarna ut när tiden går mot oändligheten, medan deras deterministiska representation lever vidare. I den exponentiella modellen sammanfaller medelvärdet av de stokastiska simuleringarna med den deterministiska lösningen, dock blir spridningen stor för de stokastiska simuleringarna när de utförs på stora tidsintervall.</p><p>Datalogiska slutsatser som har dragits är att när det kommer till att implementera få modeller, samt resultatbearbetning av dessa, som ska användas upprepade gånger, är C det bäst lämpade språket då det visat sig vara betydligt snabbare under exekvering än vad MatLab är. Dock måste hänsyn tas till alla de svårigheter som implementeringen i C drar med sig. Dessa svårigheter kan till stor del undvikas om implementeringen istället sker i MatLab, då det därmed finns tillgång till en uppsjö av väl lämpade funktioner och färdiga matematiska lösningar.</p><br><p>In this interdisciplinary study, three classic population models will be studied from a mathematical view: Malthus’ growth, Verhulst’s logistic model and Lotka-Volterra’s model for hunter and prey. The classic models are being compared to the stochastic ones. The stochastic models studied are the birthdeath processes and their diffusion approximation. Comparisons are made by averaging simulations.</p><p>It requires numerous simulations to carry out the comparisons. The simulations must be carried out on a computer and this is where the computer science emerges to the project. The models, along with the handling of the results, have been implemented in both Mat- Lab and in C in order to allow a comparison between the two languages whilst executing the above mentioned study. Attempts to time optimization and an evaluation concerning the user-friendliness regarding the implementation of mathematical problems will be performed.</p><p>Mathematic conclusions, which have been drawn, are that the averaging solutions do not always coincide with the traditional models when they are being simulated over large time. In the logistic model and in Lotka-Volterra’s model the stochastic simulations will sooner or later die when the time is moving towards infinity, whilst their deterministic representation keeps on living. In the exponential model, the mean values of the stochastic simulations and of the deterministic solution coincide. There is, however, a large spread for the stochastic simulations when they are carried out over a large time.</p><p>Computer scientific conclusions drawn from the study includes that when it comes to implementing a few models, along with the handling of the results, to be used repeatedly, C is the most appropriate language as it proved to be significantly faster during execution. However, all of the difficulties during the implementation of mathematical problems in C must be kept in mind. These difficulties can be avoided if the implementation instead takes place in MatLab, where a numerous of mathematical functions and solutions will be available.</p>
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Nilsson, Mattias, and Ingela Jönsson. "Klassiska populationsmodeller kontra stokastiska : En simuleringsstudie ur matematiskt och datalogiskt perspektiv." Thesis, Växjö University, School of Mathematics and Systems Engineering, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-2263.

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<p>I detta tvärvetenskapliga arbete studeras från den matematiska sidan tre klassiska populationsmodeller: Malthus tillväxtmodell, Verhulsts logistiska modell och Lotka-Volterras jägarebytesmodell. De klassiska modellerna jämförs med stokastiska. De stokastiska modeller som studeras är födelsedödsprocesser och deras diffusionsapproximation. Jämförelse görs med medelvärdesbildade simuleringar.</p><p>Det krävs många simuleringar för att kunna genomföra jämförelserna. Dessa simuleringar måste utföras i datormiljö och det är här den datalogiska aspekten av arbetet kommer in. Modellerna och deras resultathantering har implementerats i både MatLab och i C, för att kunna möjliggöra en undersökning om skillnaderna i tidsåtgången mellan de båda språken, under genomförandet av ovan nämnda jämförelser. Försök till tidsoptimering utförs och även användarvänligheten under implementeringen av de matematiska problemen i de båda språken behandlas.</p><p>Följande matematiska slutsatser har dragits, att de medelvärdesbildade lösningarna inte alltid sammanfaller med de klassiska modellerna när de simuleras på stora tidsintervall. I den logistiska modellen samt i Lotka-Volterras modell dör förr eller senare de stokastiska simuleringarna ut när tiden går mot oändligheten, medan deras deterministiska representation lever vidare. I den exponentiella modellen sammanfaller medelvärdet av de stokastiska simuleringarna med den deterministiska lösningen, dock blir spridningen stor för de stokastiska simuleringarna när de utförs på stora tidsintervall.</p><p>Datalogiska slutsatser som har dragits är att när det kommer till att implementera få modeller, samt resultatbearbetning av dessa, som ska användas upprepade gånger, är C det bäst lämpade språket då det visat sig vara betydligt snabbare under exekvering än vad MatLab är. Dock måste hänsyn tas till alla de svårigheter som implementeringen i C drar med sig. Dessa svårigheter kan till stor del undvikas om implementeringen istället sker i MatLab, då det därmed finns tillgång till en uppsjö av väl lämpade funktioner och färdiga matematiska lösningar.</p><br><p>In this interdisciplinary study, three classic population models will be studied from a mathematical view: Malthus’ growth, Verhulst’s logistic model and Lotka-Volterra’s model for hunter and prey. The classic models are being compared to the stochastic ones. The stochastic models studied are the birthdeath processes and their diffusion approximation. Comparisons are made by averaging simulations.</p><p>It requires numerous simulations to carry out the comparisons. The simulations must be carried out on a computer and this is where the computer science emerges to the project. The models, along with the handling of the results, have been implemented in both MatLab and in C in order to allow a comparison between the two languages whilst executing the above mentioned study. Attempts to time optimization and an evaluation concerning the user-friendliness regarding the implementation of mathematical problems will be performed.</p><p>Mathematic conclusions, which have been drawn, are that the averaging solutions do not always coincide with the traditional models when they are being simulated over large time. In the logistic model and in Lotka-Volterra’s model the stochastic simulations will sooner or later die when the time is moving towards infinity, whilst their deterministic representation keeps on living. In the exponential model, the mean values of the stochastic simulations and of the deterministic solution coincide. There is, however, a large spread for the stochastic simulations when they are carried out over a large time.</p><p>Computer scientific conclusions drawn from the study includes that when it comes to implementing a few models, along with the handling of the results, to be used repeatedly, C is the most appropriate language as it proved to be significantly faster during execution. However, all of the difficulties during the implementation of mathematical problems in C must be kept in mind. These difficulties can be avoided if the implementation instead takes place in MatLab, where a numerous of mathematical functions and solutions will be available.</p>
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Ho, Ching-Wen, and 何靜雯. "Application of The Grey Verhulst Model In Forecasting Internet Diffusion: The Case of Taiwan." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/kt679a.

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碩士<br>吳鳳科技大學<br>應用數位媒體研究所<br>103<br>An accurate prediction of the ever-increasing volume of Internet participants is of great value to enterprises in realizing the potential market of business conducted via an electronic medium. In addition, it can aid governments in enacting appropriate public plans. This research applied an integrated prediction approach by combining the Grey Verhulst Model (GVM) with a four-point rolling technique, and also utilized a harmonic-mean-smoothing technique to forecast the number of Internet participants in a gradually saturated market. The mean absolute percentage error criterion was used to compare the performance of our proposed model against three other models: the Ordinary Least Squares Model, the traditional Grey Prediction Model GM(1,1), and the GVM. Empirical results indicate that the GVM is better suited to short-term prediction than the traditional Grey Prediction Model GM(1,1) for gradually saturated systems. Meanwhile, our approach not only helps improve the short-term prediction accuracy of the GVM, but it also outperformed the other two models.
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Екатеринчук, Е. Д., та E. D. Ekaterinchuk. "Анализ стохастических аттракторов модели Ферхюльста с запаздыванием : магистерская диссертация". Master's thesis, 2015. http://hdl.handle.net/10995/36212.

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We investigate attractors of the Verhulst model with delay under the influence of random perturbations. In this work, we study dynamic regimes and bifurcations for the deterministic discrete model in zones of stable equilibria, closed invariant curves and discrete cycles. Here, a stability level of attractors is studied by Lyapunov exponents. Transformations of the closed invariant curve that appears as a result of Neimark-Sacker bifurcation, were analyzed via the rotation number and angular density. A parametric analysis of stochastically forced regular attractors of this model is performed using the stochastic sensitivity functions technique. A spatial arrangement of random states in stochastic attractors is described by confidence domains. The phenomenon of noise-induced transitions in a zone of discrete cycles is discussed.<br>Мы исследуем аттракторы модели Ферхюльста с запаздыванием под влиянием случайных возмущений. В работе мы изучаем динамические режимы и бифуркации для детерминированной дискретной модели в зонах устойчивых равновесий, замкнутых инвариантных кривых и дискретных циклов. Исследована устойчивость регулярных аттракторов. Замкнутая инвариантная кривая, которая появляется в результате бифуркации Неймарка–Сакера, анализируется с помощью числа вращения и секторной плотности. Параметрический анализ стохастически возмущенных регулярных аттракторов этой модели выполняется с помощью техники функции стохастической чувствительности. Пространственное распределение случайных состояний стохастических аттракторов описывается с помощью доверительных областей. Наблюдается явление индуцированных шумом переходов в зоне дискретных циклов.
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Book chapters on the topic "VERHULST MODEL"

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Liang, Qing-wei, Min-quan Zhao, and Pu Yang. "Grey Verhulst Neural Network Model of Development Cost for Torpedo." In Computer Science for Environmental Engineering and EcoInformatics. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-22691-5_6.

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Hasan, Shatha, Samir Hadid, Mohammed Al-Smadi, Omar Abu Arqub, and Shaher Momani. "Solutions of Fractional Verhulst Model by Modified Analytical and Numerical Approaches." In Forum for Interdisciplinary Mathematics. Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-8498-5_11.

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Hu, Yi-Chung, Hang Jiang, Peng Jiang, and Peiyi Kong. "An Improved Grey Multivariable Verhulst Model for Predicting CO2 Emissions in China." In HCI in Business, Government and Organizations. Information Systems and Analytics. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-22338-0_29.

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Jingting, Xu, Feng Jun, Sun Xia, Zhang Lei, and Liu Xiaoning. "Hot News Click Rate Prediction Based on Extreme Learning Machine and Grey Verhulst Model." In Proceedings in Adaptation, Learning and Optimization. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-57421-9_8.

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"Deformation prediction research based on improved Saito’s method with Verhulst grey model." In Boundaries of Rock Mechanics. CRC Press, 2008. http://dx.doi.org/10.1201/9780203883204-181.

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Tan, W., P. Li, S. Miao, and Z. Hou. "Deformation prediction research based on improved Saito’s method with Verhulst grey model." In Boundaries of Rock Mechanics. Taylor & Francis, 2008. http://dx.doi.org/10.1201/9780203883204.ch171.

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Conference papers on the topic "VERHULST MODEL"

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Zhao, Zhong-ming, and Xi-en Chen. "Surface movement and deformation simulated by Verhulst model." In 2009 2nd IEEE International Conference on Computer Science and Information Technology. IEEE, 2009. http://dx.doi.org/10.1109/iccsit.2009.5234502.

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Wang, Qiuping, Yun Li, and Yanting Xiao. "Grey Verhulst Model based on TLS and GA*." In 2018 IEEE International Conference of Safety Produce Informatization (IICSPI). IEEE, 2018. http://dx.doi.org/10.1109/iicspi.2018.8690489.

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Zhengxin Wang, Yaoguo Dang, and Yemei Wang. "A new grey Verhulst model and its application." In 2007 IEEE International Conference on Grey Systems and Intelligent Services. IEEE, 2007. http://dx.doi.org/10.1109/gsis.2007.4443339.

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Liu, Yitong, Dingyu Xue, Feng Pan, and Xue Hu. "Hybrid Gray Model Based on Fractional order Gray Model and Verhulst model." In 2019 Chinese Control And Decision Conference (CCDC). IEEE, 2019. http://dx.doi.org/10.1109/ccdc.2019.8832599.

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Shu, Qing, and Xinping Xiao. "Combination Forecasting Model Using Grey Verhulst Models Coupling to Regression Analysis." In 2016 International Conference on Applied Mathematics, Simulation and Modelling. Atlantis Press, 2016. http://dx.doi.org/10.2991/amsm-16.2016.34.

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Ding, Song, and Yao-guo Dang. "A new optimized grey verhulst model and its application." In 2014 IEEE International Conference on Systems, Man and Cybernetics - SMC. IEEE, 2014. http://dx.doi.org/10.1109/smc.2014.6974158.

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Shu, Hui, Yaoguo Dang, and Pingping Xiong. "Research on characteristics of grey non-equidistant Verhulst model." In 2011 International Conference on Grey Systems and Intelligent Services (GSIS 2011). IEEE, 2011. http://dx.doi.org/10.1109/gsis.2011.6044145.

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Wu, Liyun, Xiaomei Liu, Yingjian Qi, and Zhengpeng Wu. "Propagation Path Loss Prediction Based-on Grey Verhulst Model." In 2018 IEEE/ACIS 17th International Conference on Computer and Information Science (ICIS). IEEE, 2018. http://dx.doi.org/10.1109/icis.2018.8466461.

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Xiaojun, Guo, Liu Sifeng, and Fang Zhigeng. "Study on a grey Verhulst self-memory model and application." In 2013 IEEE International Conference on Grey Systems and Intelligent Services (GSIS). IEEE, 2013. http://dx.doi.org/10.1109/gsis.2013.6714758.

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Xiaojing Wang, Yucong Hu, and Xinshan Zhu. "Study of application on Verhulst-Markov chain combination forecasting model." In 2008 IEEE International Conference on Service Operations and Logistics, and Informatics. IEEE, 2008. http://dx.doi.org/10.1109/soli.2008.4682812.

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