倍周期分岔
李雅普诺夫指数
中央歧管
分叉
混乱的
离散时间和连续时间
霍普夫分叉
博格达诺夫-塔肯分岔
鞍结分岔
分叉理论的生物学应用
数学
级联
控制理论(社会学)
动力系统理论
数学分析
应用数学
计算机科学
物理
统计
人工智能
非线性系统
量子力学
色谱法
化学
控制(管理)
作者
Xiaoli Liu,Dongmei Xiao
标识
DOI:10.1016/j.chaos.2005.10.081
摘要
The dynamics of a discrete-time predator–prey system is investigated in the closed first quadrant R+2. It is shown that the system undergoes flip bifurcation and Hopf bifurcation in the interior of R+2 by using center manifold theorem and bifurcation theory. Numerical simulations are presented not only to illustrate our results with the theoretical analysis, but also to exhibit the complex dynamical behaviors, such as the period-5, 6, 9, 10, 14, 18, 20, 25 orbits, cascade of period-doubling bifurcation in period-2, 4, 8, quasi-periodic orbits and the chaotic sets. These results reveal far richer dynamics of the discrete model compared with the continuous model. The Lyapunov exponents are numerically computed to confirm further the complexity of the dynamical behaviors.
科研通智能强力驱动
Strongly Powered by AbleSci AI