Generating multi-directional hyperchaotic attractors: A novel multi-scroll system based on Julia fractal

Min Yang, Chengwei Dong and Hepeng Pan

Physica A: Statistical Mechanics and its Applications, 2024, vol. 637, issue C

Abstract: Fractals and chaos are two central concepts in the theory of complex systems and play a crucial role in the field of nonlinear dynamics and complexity studies. Despite the relative maturity of research on fractal and chaotic systems, combining them to produce multi-scroll chaotic attractors has received insufficient attention. Firstly, we design a new four-dimensional hyperchaotic system containing the sgn symbolic function, which has no equilibrium point. Next, we delve into the complex dynamical features of this system, via bifurcation diagrams, Lyapunov exponents, and basins of attraction, and we discuss various multistability phenomena. Furthermore, we integrate the Julia fractal process with the new system to create a unique multi-scroll attractor and investigate the effect of the parameters and complex constants in the Julia fractal on the new system. By analyzing the complexity and the Poincaré diagram, we find that the new system incorporating the Julia fractal mapping has richer dynamical properties. Lastly, we performed NIST testing and DSP digital circuit implementation to verify the feasibility and applicability of the new system. The results of this study enrich our understanding of fractals and chaos in practical applications.

Keywords: Hidden attractors; Multistability; Julia fractal; SE and C0 complexity; NIST test; DSP implementation (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437124000943
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:637:y:2024:i:c:s0378437124000943

DOI: 10.1016/j.physa.2024.129586

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().