Abstract
Little seems to be known about the five-dimensional (5D) differential dynamical system with infinitely many hyperchaotic attractors, which have three positive Lyapunov exponents under no or infinitely many equilibria. This article presents a 5D dynamical system that can generate infinitely many hyperchaotic attractors. Of particular interest is the system exists not only infinitely many hyperchaotic attractors but also infinitely many periodic attractors in the following three cases: (i) no equilibria, (ii) only infinitely many non-hyperbolic equilibria, (iii) only infinitely many hyperbolic equilibria. By numerical analysis, one finds the 5D system could generate infinitely many coexisting hyperchaotic or chaotic or periodic attractors in the three kinds of equilibria cases. And one obtains the global dynamical behavior of the system, such as the Lyapunov exponential spectrum, bifurcation diagram. To study the hyperchaotic complexity of the 5D system, we rigorously show the stability of hyperbolic equilibria and some mathematical characterization for 5D Hopf bifurcation. In particular, the existence of an infinite number of isolated bifurcated periodic orbits is strictly proven. These complex dynamics studies in this paper may further contribute to a deep understanding of the hyperchaotic systems with infinitely many attractors.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
