Nonlinear Dynamics and Bifurcations in the Generalized Shimizu-Morioka Model

This paper focuses on the study of the generalized Shimizu-Morioka model and the search for hyperchaotic and pseudohyperbolic attractors. The study considers the Shimizu-Morioka model but, contrary to previous studies, uses a four-dimensional system as the basis. We used the method for calculating Lyapunov exponents, the method for constructing phase portraits, and the method for finding stationary points. The conditions for finding a hyperchaotic attractor and the necessary condition for pseudohyperbolic dynamics are also used. The work consists of studying bifurcations of the system, finding parameters under which the system could possibly satisfy the conditions of pseudohyperbolic or hyperchaotic attractors, and verifying these parameters. It is shown that pseudohyperbolic dynamics is possible in this system. Chaotic, periodic, and quasiperiodic types of dynamics are also present. In addition, it is found that for the discussed parameters there is no hyperchaotic dynamics in the system.