Title: The behaviour of logistic equation in fuzzy environment: fuzzy differential equation approach

Authors: Animesh Mahata; Sachindra Nath Matia; Banamali Roy; Shariful Alam; Hirak Sinha

Addresses: Mahadevnagar High School, Mahadevnagar, Maheshtala, Dist. South 24 Pargana, Kolkata-7000141, West Bengal, India ' Kukrahati High School (H.S), Kukrahati, Sutahata, Dist-Purba Medinipur, West Bengal 721658, India ' Department of Mathematics, Bangabasi Evening College, 19, Rajkumar Chakraborty Sarani, Kolkata-700009,West Bengal, India ' Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711-103, West Bengal, India ' Barjuri High School, Bankura, West Bengal 722169, India

Abstract: Mathematical modelling on uncertainty in the field of biological science is progressively increasing to get more realistic outcome during the last few years. This article applies Hukuhara differentiable concept for solving FDE i.e., fuzzy differential equation. In this paper, we analyse the behaviour of logistic (Verhulst) model in imprecise environment particularly fuzzy environment. At first the logistic model form a fuzzy logistic model because of initial condition, co-efficient of the model and both initial condition and co-efficient contain fuzzy number, using generalised differentiable concepts this fuzzy logistic model is converted a system of crisp differential equation with a parameter α (0 ≤ α ≤ 1). Critical points and fuzzy stability of fuzzy logistic model are illustrated clearly. Suitable examples corresponding the model have been properly discussed in numerical discussion and also verified graphically.

Keywords: logistic model; generalised differentiability; fuzzy stability.

DOI: 10.1504/IJHI.2021.10035135

International Journal of Hybrid Intelligence, 2021 Vol.2 No.1, pp.26 - 46

Received: 16 May 2020
Accepted: 18 Aug 2020

Published online: 26 Sep 2021 *

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