Abstract—The dynamics of a harvested single species that goes extinct when rare is described by a nonlinear differential equation &where r, K, A and h are positive continuous T-periodic functions. N is the population size, A (0 < A < K) is the threshold population size below which N < 0 due to Allee effect, r is the intrinsic growth rate and K is the carrying capacity of the environment and h is the harvesting. The aim of this paper is to study the existence of periodic solutions and their stability properties. We discuss the effect of harvesting on a single species population in a fluctuating environment whose dynamics is described by a nonlinear differential equation.

Index Terms—Nonlinear differential equation; Allee Effect; periodic solutions; stability; existence; harvesting; positive solutions.

F. B. Rizaner and S. P. Rogovchenko are with Eastern Mediterranean University, Dep. of Mathematics, Famagusta, TRNC, Mersin 10, Turkey (e-mail: fatma.bayramoglu@emu.edu.tr).

Cite: Fatma Bayramoğlu Rizaner and Svitlana P. Rogovchenko, "Harvesting in a Periodic Habitat with Allee Effect," International Journal of Applied Physics and Mathematics  vol. 2, no. 3, pp. 175-178, 2012.