In this paper, a diverse range of travelling wave structures of perturbed Fokas–Lenells model (p-FLM) is obtained by using the extended \(({G{'}}/{G^{2}})\)-expansion technique. The existence of the obtained solutions is guaranteed by reporting constraint conditions. Then, the governing model is converted into the planer dynamical system with the help of Gallelian transformation. Every possible form of phase portraits is plotted for pertinent parameters, viz. \(k, \beta , d_{1}, d_{2}, d_{3}\). We also used the Runge–Kutta fourth-order technique to extract the nonlinear periodic solutions of the considered problem and outcomes are presented graphically. Furthermore, quasiperiodic and chaotic behaviour of p-FLM is analysed for different values of parameters after deploying an external periodic force. Quasiperiodic–chaotic nature is observed for selected values of parameters \(k,\beta , d_{1}, d_{2}, d_{3}\) by keeping the force and frequency of the perturbed dynamical system fixed. The sensitive analysis is employed on some initial value problems (IVPs). It is seen that de-sensitisation is present in the perturbed dynamical system while for the same values of parameters, the unperturbed dynamical system has a nonlinear periodic solution.

本文通过扩展\（（{{G {'}} / {G ^ {2}}）\）-展开获得摄动的Fokas-Lenells模型（p-FLM）的各种行波结构技术。通过报告约束条件来保证获得的解决方案的存在。然后，借助Gallelian变换将控制模型转换为平面动力学系统。绘制相图的每种可能形式以获取相关参数，即。\（k，\ beta，d_ {1}，d_ {2}，d_ {3} \）。我们还使用了Runge-Kutta四阶技术来提取所考虑问题的非线性周期解，并以图形方式给出了结果。此外，在部署外部周期性力之后，针对参数的不同值分析了p-FLM的拟周期和混沌行为。通过保持摄动动力系统的力和频率固定，可以观察到参数\（k，\ beta，d_ {1}，d_ {2}，d_ {3} \的选定值的准周期-混沌性质。敏感分析用于某些初始值问题（IVP）。可以看出，在动力系统中存在脱敏，而对于相同的参数值，动力系统具有非线性周期解。