文章基本信息

标题：Dynamic behaviors of a discrete-time predator–prey bioeconomic system
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作者：Weiyi Liu ; Donghan Cai ; Jie Shi 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2018
卷号：2018
期号：1
页码：133
DOI：10.1186/s13662-018-1592-0
语种：English
出版社：Hindawi Publishing Corporation
摘要：Bifurcation and chaotic behavior of a discrete-time singular bioeconomic system are investigated. First, the traditional catch equation is modified after accounting for the handling time of the catch in a singular bioeconomic system. To discover the richer dynamics compared with the continuous form, the proposed system is considered difference scheme. Specially, the tangent space local parameterization condensed method for DAEs is generalized. The new local parameterization method is sufficiently general to be applicable to this type of discrete singular system. Also the dynamic behaviors of the system are investigated, by using normal form theory, center manifold theorem and bifurcation theory, it is shown that the system undergoes a Neimark–Sacker bifurcation and a flip bifurcation, on varying step-size in some range. In addition, numerical simulations are presented not only to illustrate our results with the theoretical analysis, but also to exhibit the complex dynamical behaviors.
关键词：Generalized local parameterization method ; Discrete singular system ; Bioeconomic system ; Nonlinear harvesting rate ; Stability ; Codimension-one bifurcation ; Chaotic behavior