Analysis of unstable periodic orbits and chaotic orbits in the one-dimensional linear piecewise-smooth discontinuous map

Bhooshan Rajpathak; Harish K Pillai; Santanu Bandyopadhyay

doi:10.1063/1.4929382

Analysis of unstable periodic orbits and chaotic orbits in the one-dimensional linear piecewise-smooth discontinuous map

Chaos. 2015 Oct;25(10):103101. doi: 10.1063/1.4929382.

Authors

Bhooshan Rajpathak¹, Harish K Pillai¹, Santanu Bandyopadhyay²

Affiliations

¹ Department of Electrical Engineering, IIT Bombay, Mumbai 400076, India.
² Department of Energy Science and Engineering, IIT Bombay, Mumbai 400076, India.

PMID: 26520067
DOI: 10.1063/1.4929382

Abstract

In this paper, we analytically examine the unstable periodic orbits and chaotic orbits of the 1-D linear piecewise-smooth discontinuous map. We explore the existence of unstable orbits and the effect of variation in parameters on the coexistence of unstable orbits. Further, we show that this structuring is different from the well known period adding cascade structure associated with the stable periodic orbits of the same map. Further, we analytically prove the existence of chaotic orbit for this map.