# Infinite lattice of hyperchaotic strange
attractors

Chunbiao Li^{a,b,∗}, Julien Clinton
Sprott^{c}, Tomasz Kapitaniak^{d}, Tianai Lu^{a,b}

^{a}* Jiangsu Key Laboratory of
Meteorological Observation and Information Processing, Nanjing
University of Information Science & Technology, Nanjing
210044, China *

* *^{b}* Collaborative Innovation Center on
Forecast and Evaluation of Meteorological Disasters, Nanjing
University of Information Science & Technology, Nanjing
210044, China *

* *^{c}* Department of Physics, University
of Wisconsin–Madison, Madison, WI 53706, USA*

* *^{d}* Division of Dynamics, Lodz
University of Technology, Stefanowskiego 1/15, Lodz 90-924,
Poland*

* *

* *Received 5 September 2017, Revised 5 December 2017,
Accepted 16 February 2018

### ABSTRACT

By introducing trigonometric functions in a 4-D hyperchaotic snap
system, infinite 1-D, 2-D, and 3-D lat tices of hyperchaotic strange
attractors were produced. Furthermore a general approach was
developed for constructing self-reproducing systems, in which
infinitely many attractors share the same Lyapunov exponents. In
this case, cumbersome constants are necessary to obtain offset
boosting; correspondingly additional periodic functions are needed
for attractor hatching. As an example, a hyperchaotic system with a
hidden attractor was transformed for reproducing 1-D, 2-D infinite
lattices of hyperchaotic attractors and a 4-D lattice of chaotic
attractors.

Ref: C. Li, J. C. Sprott, T.
Kapitaniak, and T. Lu, Chaos Solitons & Fractals 109, 76-82 (2018)

The complete paper is available in
PDF format.

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