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Random variation in model parameters: A comprehensive review of stochastic logistic growth equation

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  • Karim, Md Aktar Ul
  • Aithal, Vikram
  • Bhowmick, Amiya Ranjan

Abstract

Biological growth curves are central to interdisciplinary research that seeks to improve our understanding of natural processes. Applications of growth equations are widespread across domains, with one particular growth equation being the dominant one: the logistic growth model. Nonlinear models that use parameters to vary with time are essential mathematical tools for analyzing growth patterns in different research areas. Recent research has investigated continuous parameter variation and an empirical method of detecting parameter variation has been proposed (Karim et al., 2022). In the literature, instances are abundant where the parameters vary randomly with time. This review article is focused on the stochastic version of the logistic equation, where researchers introduced stochasticity through random variation of one or more parameters in the model. Our survey reports a segmentation of articles based on the logistic growth equations into harvesting and non-harvesting equations and points out some key future study directions that may demand attention from researchers. This study also identifies the need for data-driven research in stochastic growth equations to improve the applicability of these models for real data application.

Suggested Citation

  • Karim, Md Aktar Ul & Aithal, Vikram & Bhowmick, Amiya Ranjan, 2023. "Random variation in model parameters: A comprehensive review of stochastic logistic growth equation," Ecological Modelling, Elsevier, vol. 484(C).
    • Handle: RePEc:eee:ecomod:v:484:y:2023:i:c:s0304380023002053
    DOI: 10.1016/j.ecolmodel.2023.110475
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    References listed on IDEAS

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    1. Liu, Meng & Wang, Ke, 2009. "Survival analysis of stochastic single-species population models in polluted environments," Ecological Modelling, Elsevier, vol. 220(9), pages 1347-1357.
    2. Birendra K. Rai & Chiu Ki So & Aaron Nicholas, 2012. "A Primer On Mathematical Modelling In Economics," Journal of Economic Surveys, Wiley Blackwell, vol. 26(4), pages 594-615, September.
    3. Thomas F. Cooley & Edward C. Prescott, 1973. "Systematic (Non-Random) Variation Models Varying Parameter Regression: A Theory And Some Applications," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 2, number 4, pages 463-473, National Bureau of Economic Research, Inc.
    4. Nuno M. Brites & Carlos A. Braumann, 2020. "Stochastic differential equations harvesting policies: Allee effects, logistic‐like growth and profit optimization," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 36(5), pages 825-835, September.
    5. Mohd, Mohd Hafiz & Murray, Rua & Plank, Michael J. & Godsoe, William, 2016. "Effects of dispersal and stochasticity on the presence–absence of multiple species," Ecological Modelling, Elsevier, vol. 342(C), pages 49-59.
    6. Christos H. Skiadas, 2010. "Exact Solutions of Stochastic Differential Equations: Gompertz, Generalized Logistic and Revised Exponential," Methodology and Computing in Applied Probability, Springer, vol. 12(2), pages 261-270, June.
    7. Fabien Campillo & Marc Joannides & Irène Larramendy-Valverde, 2016. "Analysis and Approximation of a Stochastic Growth Model with Extinction," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 499-515, June.
    8. Engen, Steinar & Cao, Francisco J. & Sæther, Bernt-Erik, 2018. "The effect of harvesting on the spatial synchrony of population fluctuations," Theoretical Population Biology, Elsevier, vol. 123(C), pages 28-34.
    9. Liu, Meng & Wang, Ke, 2013. "Dynamics and simulations of a logistic model with impulsive perturbations in a random environment," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 92(C), pages 53-75.
    10. Karim, Md Aktar Ul & Bhagat, Supriya Ramdas & Bhowmick, Amiya Ranjan, 2022. "Empirical detection of parameter variation in growth curve models using interval specific estimators," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    11. Lishang Jiang, 2005. "Mathematical Modeling and Methods of Option Pricing," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 5855, February.
    12. Todd M. Schmit & Harry M. Kaiser, 2004. "Decomposing the Variation in Generic Advertising Response over Time," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 86(1), pages 139-153.
    13. Lev R. Ginzburg & Lawrence B. Slobodkin & Keith Johnson & Andrew G. Bindman, 1982. "Quasiextinction Probabilities as a Measure of Impact on Population Growth," Risk Analysis, John Wiley & Sons, vol. 2(3), pages 171-181, September.
    14. Ayoubi, Tawfiqullah & Bao, Haibo, 2020. "Persistence and extinction in stochastic delay Logistic equation by incorporating Ornstein-Uhlenbeck process," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    15. Yang, Bin & Cai, Yongli & Wang, Kai & Wang, Weiming, 2019. "Optimal harvesting policy of logistic population model in a randomly fluctuating environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    16. Mao, Xuerong & Marion, Glenn & Renshaw, Eric, 2002. "Environmental Brownian noise suppresses explosions in population dynamics," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 95-110, January.
    17. Vyacheslav Navrotsky, 2000. "Synergetic Approach and modeling of fish population dynamics," Annals of Operations Research, Springer, vol. 94(1), pages 357-373, January.
    18. Sethi, Suresh P. & Thompson, Gerald L., 1970. "Applications of Mathematical Control Theory to Finance: Modeling Simple Dynamic Cash Balance Problems," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 5(4-5), pages 381-394, December.
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