@article{df2b208f47b9499eb213441ce7d23828,

title = "Generalized attracting horseshoe in the R{\"o}ssler attractor",

abstract = "We show that there is a mildly nonlinear three-dimensional system of ordinary differential equations—realizable by a rather simple electronic circuit—capable of producing a generalized attracting horseshoe map. A system specifically designed to have a Poincar{\'e} section yielding the desired map is described, but not pursued due to its complexity, which makes the construction of a circuit realization exceedingly difficult. Instead, the generalized attracting horseshoe and its trapping region is obtained by using a carefully chosen Poincar{\'e} map of the R{\"o}ssler attractor. Novel numerical techniques are employed to iterate the map of the trapping region to approximate the chaotic strange attractor contained in the generalized attracting horseshoe, and an electronic circuit is constructed to produce the map. Several potential applications of the idea of a generalized attracting horseshoe and a physical electronic circuit realization are proposed.",

keywords = "Electronic circuits, Generalized attracting horseshoe, Poincar{\'e} map, Strange attractors",

author = "Karthik Murthy and Ian Jordan and Parth Sojitra and Aminur Rahman and Denis Blackmore",

note = "Funding Information: Acknowledgments: The authors would like to thank the NJIT Provost Research Grants for funding this research. K.M. was funded by the Provost high school internship, and P.S. was funded by Phase-1 Provost Undergraduate Research Grant, with D.B. as faculty mentor and A.R. as graduate student mentor. K.M. appreciates the support of Bridgewater-Raritan High School, P.S. and I.J. appreciate the support of the Electrical and Computer Engineering Department at NJIT, and A.R. and D.B. appreciate the support of the Department of Mathematical Sciences and the Center for Applied Mathematics and Statistics (CAMS) at NJIT. In addition, K.M., I.J., and A.R. would like to acknowledge their current institutions: K.M. appreciates the support of the Department of Computer Science at UI-UC, I.J. appreciates the support of the Department of Applied Mathematics and Statistics at SU, and A.R. appreciates the support of the Department of Applied Mathematics at UW. Finally, the authors would like to give their sincere thanks to the reviewers for their insightful comments that helped improve the manuscript. Funding Information: The authors would like to thank the NJIT Provost Research Grants for funding this research. K.M. was funded by the Provost high school internship, and P.S. was funded by Phase-1 Provost Undergraduate Research Grant, with D.B. as faculty mentor and A.R. as graduate student mentor. K.M. appreciates the support of Bridgewater-Raritan High School, P.S. and I.J. appreciate the support of the Electrical and Computer Engineering Department at NJIT, and A.R. and D.B. appreciate the support of the Department of Mathematical Sciences and the Center for Applied Mathematics and Statistics (CAMS) at NJIT. In addition, K.M., I.J., and A.R. would like to acknowledge their current institutions: K.M. appreciates the support of the Department of Computer Science at UI-UC, I.J. appreciates the support of the Department of Applied Mathematics and Statistics at SU, and A.R. appreciates the support of the Department of Applied Mathematics at UW. Finally, the authors would like to give their sincere thanks to the reviewers for their insightful comments that helped improve the manuscript. Publisher Copyright: {\textcopyright} 2020 by the authors. Licensee MDPI, Basel, Switzerland.",

year = "2021",

month = jan,

doi = "10.3390/sym13010030",

language = "English (US)",

volume = "13",

pages = "1--12",

journal = "Symmetry",

issn = "2073-8994",

publisher = "Multidisciplinary Digital Publishing Institute (MDPI)",

number = "1",

}