Bifurcation analysis, quasi-periodic and chaotic behavior of generalized Pochhammer-Chree equation

Abstract

We take into account the bifurcation analysis of the generalized Pochhammer-Chree (PC) equation that describes the dynamics of several systems in science and engineering. The considered model is changed into a planar dynamical system by applying the Galilean transformation. The phase portraits are plotted by considering suitable values of the bifurcation parameters. The considered model is solved using the RK method to compute the supernonlinear and nonlinear wave solutions. All phase portraits and wave solutions are depicted in the phase plane by simply fixing the relevant parameters values. The equilibrium points are obtained, and the same are classified. Moreover, sensitive analysis for different initial value problems is applied to analyze the quasiperiodic, chaotic behavior and time series after introducing an extrinsic periodic perturbation term. In addition, the Lyapunov characteristic exponents, Poincare section and bifurcation diagrams are also discussed to examine the chaotic pattern of the model. Numerical simulation results show that changing the frequencies and amplitude values impacts the dynamical features of the considered model.