Bifurcation Analysis and Poincare’ Map of a Hyperchaotic System - Kheshti, Mohammadreza; Taghvaei, Sajjad; Salehi, Mohammad; Baraijany, Amir Masrour (Journal of Applied Nonlinear Dynamics, 2026)
In this paper, the nonlinear behavior of an eleven-term 4-dimensional hyperchaotic Lorenz-type dynamic system is studied. The dynamic response of a hyperchaotic model is investigated. The phase portrait and Lyapunov exponent of the 4-D system are discussed. The phase portrait of the presented system shows the behavior which is like the Lorenz system’s phase portrait. The nonlinear model is proved to be hyperchaotic since it has two positive Lyapunov exponents. The main goal of this research is to depict bifurcation and Poincare maps so as to investigate the occurrence of the periodic behavior, period-doubling, crisis, and chaotic motion. Therefore, bifurcation analysis is shown that by increasing the θ _2, the behavior of the system will change from periodic into chaotic and vice versa. Also, the period-doubling, and crisis happened by changing the bifurcation parameter in a specific range. Finally, the Poincare map indicates that the chaotic motion appears when θ _2 is 0.17.