Investigate the dynamics of lie symmetry, bifurcation and sensitivity analysis to the (4 + 1)-dimensional Fokas model

In this paper, the nonlinear (4 + 1)-dimensional Fokas model is studied and its dynamic character is predicted. This inquiry aims to accomplish two main objectives. First, the Lie symmetries are created and the associated transformation is applied to reduce the model to ordinary differential equations. Plots are used to demonstrate and establish invariant solutions. Second, several methods such as bifurcation, sensitivity analysis, and chaos are used to investigate the dynamic behavior of the model. Bifurcation theories are used to analyse a dynamical system’s bifurcation at equilibrium points. The nonperturbed system introduces the perturbation period, which deviates from regular patterns. Different initial conditions are used to investigate the sensitivity analysis the model is found to be highly sensitive. The findings are unique, stimulating and mathematically helpful to comprehend the model. It is essential to comprehend the systems and processes that behave dynamically to investigate new technology, suggest interventions and forecast the future.