Abstract
This paper attempts to further extend the results of dynamical analysis carried out on a recent 4D Lorenz-type hyperchaotic system while exploring new analytical results concerns its local and global dynamics. In particular, the equilibrium points of the system along with solution’s continuous dependence on initial conditions are examined. Then, a detailedZ2symmetrical Bogdanov-Takens bifurcation analysis of the hyperchaotic system is performed. Also, the possible first integrals and global invariant surfaces which exist in system’s phase space are analytically found. Theoretical results reveal the rich dynamics and the complexity of system behavior. Finally, numerical simulations and a proposed circuit implementation of the hyperchaotic system are provided to validate the present analytical study of the system.
Highlights
Nonlinear dynamics analysis of various phenomena and systems of physics, engineering, biology, chemistry, economy, and industry has attracted a great interest among scientists and considered a very active area of research from 1960s in the last century till [1–4]
The first one is that the dynamical systems tools help scientists better comprehend and analyze the varieties of nonlinear characteristics and new phenomena exhibited by systems from different disciplines
The second reason is that engineers and scientists can utilize some of the fascinating features of nonlinear dynamical systems in wide range of interesting applications
Summary
Nonlinear dynamics analysis of various phenomena and systems of physics, engineering, biology, chemistry, economy, and industry has attracted a great interest among scientists and considered a very active area of research from 1960s in the last century till [1–4]. The tools of dynamical systems such as the applied bifurcation theories are successfully employed to investigate the qualitative behaviors of nonlinear systems [5–7]. This includes investigation of equilibrium points and their stability, creation, destruction and stability of periodic orbits, quasiperiodic behavior, homoclinic orbits, creation or destruction of chaotic attractors, and chaos control and synchronization. In the last two decades, some interesting highdimensional hyperchaotic systems, in science and engineering, have been explored and their dynamics have been extensively investigated [18, 24, 27, 28, 34, 35] It is of great importance from theoretical and practical aspects to explain complicated phenomena and internal structural characteristics of hyperchaotic systems.
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