tailieunhanh - A new approach to the logistic modeling population having harvesting factor

The present paper deals with the logistic equation having harvesting factor by a new approach. This approach is an attempt to sketch the solutions to the model Rahmani Doust and Saraj. | Yugoslav Journal of Operations Research 26 (2016), Number 3, 381–392 DOI: A NEW APPROACH TO THE LOGISTIC MODELING POPULATION HAVING HARVESTING FACTOR Chao-Pao HO Department of Applied Mathematics, Tunghai University Taichung, Taiwan cpho@ Che-Hao LIN Department of Applied Mathematics, Tunghai University, Taichung, Taiwan linch@ Received: August 2014 / Accepted: May 2015 Abstract: The present paper deals with the logistic equation having harvesting factor by a new approach. This approach is an attempt to sketch the solutions to the model Rahmani Doust and Saraj [1]. Keywords: Equilibrium Points, Logistic Growth Model, Harvesting Model. MSC: 34D23, 37N25, 78A70, 92D25, 92D40. 1. INTRODUCTION . Rahmani Doust and M. Staraj [1] solved, and obtained the solution x(t) of the logistic equation having harvesting factor x x˙ = rx 1 − −h () K They analyzed the solution of the system (). However, the solution x(t) of ()is an implicit function, and the graph of the solution x(t) with respect to t is not sketched. We are trying to sketch the graph of the solution x(t) with respect to t by a new approach. That is, we will sketch the solution x(t) with respect to t directly. In general, before sketching the graph of the solution x(t) with respect to t, we need 382 . Ho, . Lin / A New Approach to the Logistic Modeling Population ˙ ¨ to solve and obtain the solution x(t) of (). Then, we can use the data of x(t), x(t) and limt→∞ x(t) to sketch the graph of x(t). Actually, now we know that x ˙ = rx 1 − −h x(t) K and ¨ =− x(t) 2r K ˙ x− x. K 2 () So, we can use the information () and () to sketch the graph of the solution x(t) with respect to t even though we don’t know the solution x(t) of (). This paper is organized as follows. In section 2, we use the new approach to analyze the logistic population. In section 3, we use the new approach to analyze the Logistic equation having constant .