Kaos-land的计算探索
Computational quest for Kaos-land
摘要：
使用双参数扫描的基础上的符号表示，我们揭示了自相似分形结构诱导的鞍奇点的异宿和同宿分支的参数空间中的两个系统的确定性混沌。我们从显示出几个更高余维的同宿分岔的系统开始：共振鞍、轨道翻转和倾斜开关，这些都导致了$Z_2$ -具有同宿蝴蝶的系统中洛伦兹型吸引子的开始。第二个系统是起源于流体力学的1963年的经典洛伦兹模型。
英文摘要：
Using bi-parametric sweeping based on symbolic representation we reveal self-similar fractal structures induced by hetero- and homoclinic bifurcations of saddle singularities in the parameter space of two systems with deterministic chaos. We start with the system which displays several homoclinic bifurcations of higher codimension: resonant saddle, orbit-flip and inclination switch that all give rise to the onset of the Lorenz-type attractor in $Z_2$-systems with the homoclinic butterfly. The second system is the classic Lorenz model of 1963, originated in fluid mechanics.
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