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Shock and Vibration
Volume 2018 (2018), Article ID 1092812, 8 pages
https://doi.org/10.1155/2018/1092812
Research Article

Multistability in Horizontal Platform System with and without Time Delays

Centre for Nonlinear Dynamics, Defense University, Bishoftu, Ethiopia

Correspondence should be addressed to Karthikeyan Rajagopal

Received 2 September 2017; Revised 25 December 2017; Accepted 11 January 2018; Published 11 February 2018

Academic Editor: José Manoel Balthazar

Copyright © 2018 Karthikeyan Rajagopal et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Chaotic behavior and bifurcation analysis of horizontal platform systems (HPS) have been investigated widely by many researchers. However, the multistable features of such systems have not been investigated, and hence we identified the multistable parameter and investigated the coexisting attractors of the HPS. To understand the effects of time delays on the nonautonomous and autonomous HPS, we introduced a constant time delay in the state feedback variable. Investigation of the bifurcation of the time delayed HPS with time delay and parameters reveals that the system behavior differs between the autonomous and nonautonomous HPS. To investigate the multistability existence in time delayed HPS, we plot the bifurcation of the autonomous HPS and show the multistability and coexisting attractors.