论文标题
渐近稳定和混沌分数图中的循环
Cycles in Asymptotically Stable and Chaotic Fractional Maps
论文作者
论文摘要
幂律记忆的存在是许多自然（生物学，物理等）和社会系统的重要特征。连续和离散的分数演算是用幂律存储器描述系统行为的工具。混沌溶液的存在是非线性动力学（常规和分数）的内在特性。分数系统的行为可能与没有内存的相应系统的行为大不相同。查找周期点对于理解常规和混乱动态至关重要。除固定点外，分数系统没有周期性点。取而代之的是，它们具有渐近的周期点（接收器）。迄今为止，尚无报道的结果（公式），可以计算非线性分数系统的渐近周期点。在本文中，我们得出了允许计算渐近周期性水槽坐标的方程式。
The presence of the power-law memory is a significant feature of many natural (biological, physical, etc.) and social systems. Continuous and discrete fractional calculus is the instrument to describe the behavior of systems with the power-law memory. The existence of chaotic solutions is an intrinsic property of nonlinear dynamics (regular and fractional). The behavior of fractional systems can be very different from the behavior of the corresponding systems with no memory. Finding periodic points is essential for understanding regular and chaotic dynamics. Fractional systems do not have periodic points except for fixed points. Instead, they have asymptotically periodic points (sinks). There have been no reported results (formulae) that would allow calculations of asymptotically periodic points of nonlinear fractional systems so far. In this paper, we derive the equations that allow calculations of the coordinates of the asymptotically periodic sinks.
