tailieunhanh - The logistic modeling population; having harvesting factor

The present paper deals with the logistic equation having harvesting factor, which is studied in two cases constant and non-constant. In fact, the nature of equilibrium points and solutions behavior has been analyzed for both of the above cases by finding the first integral, solution curve and phase diagram. Finally, a theorem describing the stability of a real model of single species is proved. | Yugoslav Journal of Operations Research 25 (2015), Number 1, 107-115 DOI: THE LOGISTIC MODELING POPULATION; HAVING HARVESTING FACTOR Rahmani . DOUST Department of Mathematics, Faculty of Sciences, Neyshabur University, Neyshabur –IRAN Mansour SARAJ Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University, Ahvaz –IRAN msaraj@ Received: May 2013 / Accepted: October 2013 Abstract: The present paper deals with the logistic equation having harvesting factor, which is studied in two cases constant and non-constant. In fact, the nature of equilibrium points and solutions behavior has been analyzed for both of the above cases by finding the first integral, solution curve and phase diagram. Finally, a theorem describing the stability of a real model of single species is proved. Keywords: Equilibrium Points, Harvesting Factor, Logistic Equation, . MSC: 78A70, 92D25, 92D40, 35E15. 1. INTRODUCTION Main concern of population ecology is growth (or decay) and interaction rates of the entire population. Study of population change started with , the greatest European mathematician of the middle ages, who introduced a mathematical model for a growing rabbit population in his arithmetic book [2]. If population is defined as a collection of individuals of a particular species that live within a well-defined area, then the occurred changes are due to the number of its individuals, caused by reproduction, death or migration. This notion of population change is illustrated in the following form which is known as population balance equation or conservation equation for population: 108 . Doust, M. Saraj / The Logistic Modeling Population Population Change = Births - Deaths – Migration The phrase “balance equation” refers to the fact that any change in population abundance is a balance between processes that may decrease or increase it. Population .