Soliton outcomes and dynamical properties of the fractional Phi-4 equation
Md Mostafa, Mohammad Safi Ullah
Abstract
This paper uses the unified solver process to acquire soliton outcomes for the fractional Phi-4 model. The dynamic characteristic of the governing model is investigated for its planar dynamical system by applying the bifurcation method. Under the given parameters, 2D and 3D phase portraits, time series, return map, Lyapunov exponent, recurrence plot, strange attractor, bifurcation diagram, and fractal dimension plot are provided. These plots show the periodic, quasi-periodic, and chaotic nature of the suggested nonlinear problem. Moreover, the sensitivity and multistability assessments of the stated model are studied for a clear understanding of chaotic behavior. To understand the system’s long-term behavior, we also test the stability of our results. Our results agree with previous results and may help researchers better understand the behavior of nonlinear systems. Furthermore, other fields such as biology, economics, and engineering can apply our results.