Homoclinic bifurcation for a general state-dependent Kolmogorov type predator–prey model with harvesting. (December 2015)

• Record Type: Journal Article
• Authors: Xiao, Qizhen; Dai, Binxiang; Xu, Bingxiang; Bao, Longsheng
• Is Part Of: Nonlinear analysis. Volume 26(2015)
• Page Start: 263
• Page End: 273
• Publication Date: 2015-12
• Subjects: Kolmogorov model -- Constant-yield harvesting -- Impulsive control -- Homoclinic bifurcation -- Geometry analysis; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2015.05.012
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, a general Kolmogorov type predator–prey model is considered. Together with a constant-yield predator harvesting, the state dependent feedback control strategies which take into account the impulsive harvesting on predators as well as the impulsive stocking on the prey are incorporated in the process of population interactions. We firstly study the existence of an order-1 homoclinic cycle for the system. It is shown that an order-1 positive periodic solution bifurcates from the order-1 homoclinic cycle through a homoclinic bifurcation as the impulsive predator harvesting rate crosses some critical value. The uniqueness and stability of the order-1 positive periodic solution are derived by applying the geometry theory of differential equations and the method of successor function. Finally, some numerical examples are provided to illustrate the main results. These results indicate that careful management of resources and harvesting policies is required in the applied conservation and renewable resource contexts.