In this paper, we investigate the stability properties of soft gluons in SIBYLL 2.1 with reference to its original version 1.7 that corresponds to hadronic hard interactions. In order to investigate the stability structures, we classify the regions of the gluon density fluctuations in its double leading logarithmic approximation and its equivalent description as the fractional power law. In the parameter space of initial transverse momentum $Q$ and QCD renormalization scale $L$ that correspond to extensive air showers of cosmic rays, we have categorized the surface of parameters over which the proton is stable. We further discuss the nature of local and global correlations and stability properties where the concerning statistical basis yields a stable system or undergoes a geometric phase transition. Finally, we give a phenomenological understanding towards the stability of soft interactions, Pomeron particle productions in minijet model, string fragmentation and verify our result corresponding to the experiments - CDF, P238, UAS, GEUS and UA4 collaborations.

中文翻译：

---

具有多重软相互作用的胶子系统的稳定性

在本文中，我们参考对应于强子硬相互作用的原始版本 1.7，研究了 SIBYLL 2.1 中软胶子的稳定性特性。为了研究稳定性结构，我们将胶子密度波动区域分类为双领先对数近似及其等效描述为分数幂律。在初始横向动量$Q$和QCD重整化标度$L$对应于广泛的宇宙线空气簇射的参数空间中，我们对质子稳定的参数表面进行了分类。我们进一步讨论了局部和全局相关性和稳定性属性的性质，其中相关的统计基础产生稳定的系统或经历几何相变。最后，