非线性离散捕食-捕食模型的复杂动力学与混沌控制

Q3 Mathematics
K. Mokni, H. Ben Ali, M. Ch-Chaoui
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引用次数: 0

摘要

捕食者-猎物相互作用的动力学通常用微分或差分方程来建模。本文研究了一类二维离散捕食-捕食系统的动力学行为。该模型采用差分方程形式,并采用非标准有限差分格式(NSFD)推导,该格式考虑了非重叠代。证明了不动点的存在性及其局部渐近稳定性。进一步证明了在一定参数条件下,该模型在唯一正不动点的小邻域内经历neimmark - sacker分岔(NSB)和倍周期分岔(PDB)。这种分析运用了分岔理论和中心流形定理。NSB和PDB产生的混沌是稳定的。最后,我们使用数值模拟和计算机分析来验证我们的理论并展示更复杂的行为。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Complex dynamics and chaos control in a nonlinear discrete prey–predator model
The dynamics of prey–predator interactions are often modeled using differential or difference equations. In this paper, we investigate the dynamical behavior of a two-dimensional discrete prey–predator system. The model is formulated in terms of difference equations and derived by using a nonstandard finite difference scheme (NSFD), which takes into consideration the non-overlapping generations. The existence of fixed points as well as their local asymptotic stability are proved. Further, it is shown that the model experiences Neimark–Sacker bifurcation (NSB for short) and period-doubling bifurcation (PDB) in a small neighborhood of the unique positive fixed point under certain parametric conditions. This analysis utilizes bifurcation theory and the center manifold theorem. The chaos produced by NSB and PDB is stabilized. Finally, we use numerical simulations and computer analysis to check our theories and show more complex behaviors.
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来源期刊
Mathematical Modeling and Computing
Mathematical Modeling and Computing Computer Science-Computational Theory and Mathematics
CiteScore
1.60
自引率
0.00%
发文量
54
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