We present a case study elaborating on the multiplicity and self-similarity of homoclinic and heteroclinic bifurcation structures in the 2D and 3D parameter spaces of a nonlinear laser model with a Lorenz-like chaotic attractor. In a symbiotic approach combining the traditional parameter continuation methods using MatCont and a newly developed technique called the Deterministic Chaos Prospector (DCP) utilizing symbolic dynamics on fast parallel computing hardware with graphics processing units (GPUs), we exhibit how specific codimension-two bifurcations originate and pattern regions of chaotic and simple dynamics in this classical model. We show detailed computational reconstructions of key bifurcation structures such as Bykov T-point spirals and inclination flips in 2D parameter space, as well as the spatial organization and 3D embedding of bifurcation surfaces, parametric saddles, and isolated closed curves (isolas).

我们提出了一个案例研究，详细阐述了具有Lorenz形混沌吸引子的非线性激光模型的2D和3D参数空间中同斜和异斜分叉结构的多重性和自相似性。在一种共生的方法中，结合了使用MatCont的传统参数连续方法和一项新的技术，即在确定的混沌二维勘探者如何起源于特定的二维维分叉的情况下，该技术利用快速并行计算硬件上的符号动力学在图形处理单元（GPU）上进行确定性混沌勘探者（DCP）。这个经典模型中的混沌和简单动力学的模式区域。我们展示了关键分叉结构（如Bykov T点螺旋和2D参数空间中的倾斜翻转）的详细计算重构，