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Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article A Discrete Equivalent of the Logistic Equation | Hindawi Publishing Corporation Advances in Difference Equations Volume 2010 Article ID 457073 15 pages doi 10.1155 2010 457073 Research Article A Discrete Equivalent of the Logistic Equation Eugenia N. Petropoulou Division of Applied Mathematics and Mechanics Department of Engineering Sciences University of Patras 26500 Patras Greece Correspondence should be addressed to Eugenia N. Petropoulou jenpetro@des.upatras.gr Received 29 September 2010 Accepted 10 November 2010 Academic Editor Claudio Cuevas Copyright 2010 Eugenia N. Petropoulou. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. A discrete equivalent and not analogue of the well-known logistic differential equation is proposed. This discrete equivalent logistic equation is of the Volterra convolution type is obtained by use of a functional-analytic method and is explicitly solved using the z-transform method. The connection of the solution of the discrete equivalent logistic equation with the solution of the logistic differential equation is discussed. Also some differences of the discrete equivalent logistic equation and the well-known discrete analogue of the logistic equation are mentioned. It is hoped that this discrete equivalent of the logistic equation could be a better choice for the modelling of various problems where different versions of known discrete logistic equations are used until nowadays. 1. Introduction The well-known logistic differential equation was originally proposed by the Belgian mathematician Pierre-Franẹois Verhulst 1804-1849 in 1838 in order to describe the growth of a population P f under the assumptions that the rate of growth of the population was proportional to A1 the existing population and A2 the amount of available resources. When this problem is translated into mathematics results to the differential equation dP
