数字置换：非线性动力系统的一般映射
Digit replacement: A generic map for nonlinear dynamical systems
摘要：
提出了一种简单的不连续映射作为非线性动力系统的通用模型。该地图的轨道承认精确的解决方案，在参数空间和方法（数字操作）允许有用的信号，如定期或非周期性振荡与特定波形的数学设计，建设复杂的吸引子与非平凡的属性，以及共存的不同盆地的吸引力在相空间中具有不同的定性属性。对映射的动态行为的详细分析表明，后者如何用于复杂非线性动态的建模，例如，非周期非混沌吸引子和不同尺寸的颗粒在表面上的分级沉积。
英文摘要：
A simple discontinuous map is proposed as a generic model for nonlinear dynamical systems. The orbit of the map admits exact solutions for wide regions in parameter space and the method employed (digit manipulation) allows the mathematical design of useful signals, such as regular or aperiodic oscillations with specific waveforms, the construction of complex attractors with nontrivial properties as well as the coexistence of different basins of attraction in phase space with different qualitative properties. A detailed analysis of the dynamical behavior of the map suggests how the latter can be used in the modeling of complex nonlinear dynamics including, e.g., aperiodic nonchaotic attractors and the hierarchical deposition of grains of different sizes on a surface.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
