Research ArticleOpen AccessGoogle Scholar indexed
Stochastic Logistic Model for Fish Growth
Department of Statistics, University of Rajshahi, Rajshahi, Bangladesh
- 1 Department of Statistics, University of Rajshahi, Rajshahi, Bangladesh
Open Journal of Statistics·Volume 04 (2014)·Pages 11–18·Published 27 January 2014·DOI10.4236/ojs.2014.41002
Copy link · social · email
Abstract
Two extensions of stochastic logistic model for fish growth have been examined. The basic features of a logistic growth rate are deeply influenced by the carrying capacity of the system and the changes are periodical with time. Introduction of a new parameter , enlarges the scope of investing the growth of different fish species. For rapid growth lying between 1 and 2 and for slowly growing .
KeywordsCarrying CapacityNon-LinearityMultiplicative FluctuationsWhite NoiseFokker-Planck EquationPeriodic PhenomenaErlang Distribution
- K. E. F. Watt, “Ecology and Resource Management,” McGraw-Hill, New York, 1968.
- R. G. Coyle, “Management System Dynamics,” Chapter-II, Wiley, New York, 1977.
- M. A. Shah and U. Sharma, “Optimal Harvesting Policies for a Generalized Gordon-Schaefer Model in Randomly Varying Environment,” Applied Stochastic Models in Business and Industry, John Wiley & Sons, Ltd., 2002.
- R. Pearl, “The Biology of Population Growth,” Knopf, New York, 1930.
- W. Feller, “On Logistic Law of Growth and Its Empirical Verification in Biology,” Acta Biotheoretica, Vol. 5, No. 2, 1940, pp. 51-66. http://dx.doi.org/10.1007/BF01602862
- J. R. Beddington and R. M. May, “Harvesting Natural Populations in a Randomly Fluctuating Environment,” Science, Vol. 197, No. 4302, 1977, pp. 463-465. http://dx.doi.org/10.1126/science.197.4302.463
- M. F. Laham, I. S. Krishnarajah and J. M. Shariff, “Fish Harvesting Management Strategies Using Logistic Growth Model,” Sains Malaysiana, Vol. 41, No. 2, 2012, pp. 171-177.
- D. A. Dawson, “Qualitative Behavior of Geostochastic Systems,” Stochastic Processes and Their Applications, Vol. 10, No. 1, 1980, pp. 1-31. http://dx.doi.org/10.1016/0304-4149(80)90002-2
- N. Keiding, “Extinction and Exponential Growth in Random Environments,” Theoretical Population Biology, Vol. 8, No. 1, 1975, pp. 49-63. http://dx.doi.org/10.1016/0040-5809(75)90038-6
- D. Ludwig, “A Singular Perturbation Problem in the Theory of Population Extinction,” SIAM-AMS Proceedings, Vol. 10, 1976.
- M. Turelli, “A Re-Examination of Stability in Randomly Varying versus Deterministic Environments with Comments on the Stochastic Theory of Limiting Similarity,” Theoretical Population Biology, Vol. 13, No. 2, 1978, pp. 244-267. http://dx.doi.org/10.1016/0040-5809(78)90045-X
- M. C. Wang and G. E. Uhlenbeck, “On the Theory of the Brownian Motion-II,” Reviews of Modern Physics, Vol. 17, No. 2-3, 1945, pp. 323-342. http://dx.doi.org/10.1103/RevModPhys.17.323
- W. Feller, “Diffusion processes in one dimension,” Transactions of the American Mathematical Society, Vol. 77, 1954, pp. 1-31. http://dx.doi.org/10.1090/S0002-9947-1954-0063607-6