In this article, we have studied a cylindrically symmetric self-gravitating dynamical object via complexity factor which is obtained through orthogonal splitting of Reimann tensor in $f(R,T)$ theory of gravity. Our study is based on the definition of complexity for dynamical sources, proposed by Herrera et al. (2019). We actually want to analyze the behavior of complexity factor for cylindrically symmetric dynamical source in modified theory. For this, we define the scalar functions through orthogonal splitting of Reimann tensor in $f(R,T)$ gravity and work out structure scalars for cylindrical geometry. We evaluated the complexity of the structure and also analyzed the complexity of the evolutionary patterns of the system under consideration. In order to present simplest mode of evolution, we explored homologous condition and homogeneous expansion condition in $f(R,T)$ gravity and discussed dynamics and kinematics in the background of a generic viable non-minimally coupled $f(R,T)={\alpha }_1{R}^m{T}^n+{\alpha }_{2}T(1+{\alpha }_3{T}^p{R}^q)$ model. In order to make a comprehensive analysis, we considered three different cases (representing both minimal and non-minimal coupling) of the model under consideration and found that complexity of a system is increased in the presence of higher order curvature terms, even in the simplest modes of evolution. However, higher order trace terms affects the complexity of the system but they are not crucial for simplest modes of evolution in the case of minimal coupling. The stability of vanishing of complexity factor has also been discussed.

在本文中，我们研究了通过复杂因子分解的圆柱对称自重动力物体，该复杂物体是通过将Reimann张量正交分解得到的。 $F（\mathrm{[R}，Ť）$引力理论。我们的研究基于Herrera等人提出的动力学源复杂性的定义。（2019）。我们实际上是想在修正理论中分析圆柱对称动力源的复杂度因子的行为。为此，我们通过正交分解Reimann张量来定义标量函数。$F（\mathrm{[R}，Ť）$重力并计算圆柱几何的结构标量。我们评估了结构的复杂性，还分析了所考虑系统的演化模式的复杂性。为了呈现最简单的进化模式，我们探索了同源条件和均匀扩展条件。$F（\mathrm{[R}，Ť）$ 通用可行非最小耦合的背景下的重力和讨论的动力学和运动学 $F（\mathrm{[R}，Ť）={\alpha }_{\mathrm{1个}}{\mathrm{[R}}^{米}{Ť}^{ñ}+{\alpha }_2Ť（\mathrm{1个}+{\alpha }_3{Ť}^p{\mathrm{[R}}^q）$模型。为了进行全面的分析，我们考虑了所考虑模型的三种不同情况（代表最小和非最小耦合），并且发现即使存在最简单的曲率项，系统的复杂度也会增加进化方式。但是，高阶跟踪项会影响系统的复杂性，但是在最小耦合的情况下，它们对于最简单的演化模式而言并不是至关重要的。还讨论了复杂度因子消失的稳定性。