Investigating pseudo parabolic dynamics through phase portraits, sensitivity, chaos and soliton behavior

Abstract This research examines pseudoparabolic nonlinear Oskolkov-Benjamin-Bona-Mahony-Burgers (OBBMB) equation, widely applicable in fields like optical fiber, soil consolidation, thermodynamics, nonlinear networks, wave propagation, and fluid flow in rock discontinuities. Wave transformation and the generalized Kudryashov method is utilized to derive ordinary differential equations (ODE) and obtain analytical solutions, including bright, anti-kink, dark, and kink solitons. The system of ODE, has been then examined by means of bifurcation analysis at the equilibrium points taking parameter variation into account. Furthermore, in order to get insight into the influence of some external force perturbation theory has been employed. For this purpose, a variety of chaos detecting techniques, for instance poincaré diagram, time series profile, 3D phase portraits, multistability investigation, lyapounov exponents and bifurcation diagram are implemented to identify the quasi periodic and chaotic motions of the perturbed dynamical model. These techniques enabled to analyze how perturbed dynamical system behaves chaotically and departs from regular patterns. Moreover, it is observed that the underlying model is quite sensitivity, as it changing dramatically even with slight changes to the initial condition. The findings are intriguing, novel and theoretically useful in mathematical and physical models. These provide a valuable mechanism to scientists and researchers to investigate how these perturbations influence the system’s behavior and the extent to which it deviates from the unperturbed case.