Authors: Haitao Wu; Jing Li; Qinlong Wang
Addresses: School of Information and Mathematics, Yangtze University, Jingzhou 434023, P.R. China; School of Sciences, Hezhou University, Hezhou 542899, P.R. China ' Department of Basic Courses, College of Science Arts of Jianghan University, Wuhan 430056, P.R. China ' School of Sciences, Hezhou University, Hezhou 542899, P.R. China
Abstract: In this paper, exact wave solutions to the single-species population dynamical model with density-dependent migrations and Allee effect are studied. First, the non-linear evolution equation is reduced to a planar system by transformation of variables, then based on the planar dynamical systems theory, its first integral is determined by computing singular point quantities, and a phase-portrait analysis of its singular points is presented. From this, some explicit expressions of the bounded travelling-wave solutions are obtained for the single-species model, which correspond to the real patterns of spread during biological invasions. In terms of the technique of finding exact travelling-wave solutions of a non-linear partial differential equation, the work is new.
Keywords: exact solution; integrability; population dynamical model; singular point quantity.
International Journal of Dynamical Systems and Differential Equations, 2017 Vol.7 No.1, pp.82 - 93
Received: 01 Jul 2016
Accepted: 01 Oct 2016
Published online: 11 Apr 2017 *