ABSTRACT
Sigmoid curves can describe a lot of phenomena in the world: iteration history of optimization algorithms, time history of sports world records, competition of populations, product lifetime, etc. Approximation of a sigmoid curve can give many interesting and useful information about the most important characteristics of the growth speed, expectable maximum of the phenomenon, maximum possible value achievable, steepness of the curve. The investigation of the derivative and the integral of the sigmoid curve can give more information about where is the maximum of the growth speed, and how durable the maximum speed is. These results could increase our knowledge when investigating a phenomenon (growth history, saturation, future behaviour of the phenomenon). In this paper, the quantity of plastic contamination of the world oceans is investigated. The history curve of the world’s plastic production is a sigmoid curve (logistic curve), so every useful information which can be derived from the curve, from its derivative and integral can be applied to the present and to the future of the contamination quantity, because there is a strong connection between the quantity of produced plastics and of the plastic contamination quantity of the seas. The results of the investigation of the sigmoid curve of the plastic contamination will give us information about the history and the future of the contamination process. A better understanding of these characteristics of the phenomena could help to design better the future steps to stop or at least decrease this dangerous contamination form. During the approximation of the sigmoid curves, the Nelder – Mead optimization technique is applied for the solution of the least squares approximation problem.
