Constructing Infinitely Many Attractors in a Programmable Chaotic Circuit

CHUNBIAO LI^1,2, (Member, IEEE), WESLEY JOO-CHEN THIO³, JULIEN CLINTON SPROTT⁴,
HERBERT HO-CHING IU⁵, (Senior Member, IEEE), AND YUJIE XU^1,2

¹Jiangsu Key Laboratory of Meteorological Observation and Information Processing, Nanjing University of Information Science and Technology,
Nanjing 210044, China
²School of Electronic and Information Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China
³Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH 43210, USA
⁴Department of Physics, University of WisconsinMadison, Madison, WI 53706, USA
⁵School of Electrical, Electronic, and Computing Engineering, The University of Western Australian, Crawley, WA 6009, Australia

ABSTRACT

In this paper, we modify the Sprott M chaotic system to provide innitely many co-existing attractors by replacing the offset boosting parameter with a periodic function giving what we call a self-reproducing system. Consequently, a chaotic signal with either polarity can be obtained by selecting different initial conditions. Various periodic functions are introduced in the same offset-boostable system for producing coexisting attractors. We used a field programmable analog array to construct a programmable chaotic circuit, and the predicted attractors were observed on an oscilloscope.