Nandi Amitabha, Dutta Debabrata, Bhattacharjee Jayanta K, Ramaswamy Ramakrishna
School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110 067, India.
Chaos. 2005 Jun;15(2):23107. doi: 10.1063/1.1914755.
We study the logistic mapping with the nonlinearity parameter varied through a delayed feedback mechanism. This history dependent modulation through a phaselike variable offers an enhanced possibility for stabilization of periodic dynamics. Study of the system as a function of nonlinearity and modulation parameters reveals new phenomena: In addition to period-doubling and tangent bifurcations, there can be bifurcations where the period increases by unity. These are extensions of crises that arise in nonlinear dynamical systems. Periodic orbits in this system can be systematized via the kneading theory, which in the present case extends the analysis of Metropolis, Stein, and Stein for unimodal maps.
我们研究了通过延迟反馈机制改变非线性参数的逻辑斯谛映射。这种通过类相位变量的历史依赖调制为周期动力学的稳定提供了更大的可能性。将该系统作为非线性和调制参数的函数进行研究揭示了新现象：除了倍周期分岔和切分岔外，还可能存在周期增加 1 的分岔。这些是在非线性动力系统中出现的危机的扩展。该系统中的周期轨道可以通过揉搓理论进行系统化，在当前情况下，该理论扩展了梅特罗波利斯、斯坦因和斯坦因对单峰映射的分析。
