Autonomous jerk oscillator with cosine hyperbolic nonlinearity: analysis, FPGA implementation, and synchronization
type: Item
instance of: scholarly article
title: Autonomous jerk oscillator with cosine hyperbolic nonlinearity: analysis, FPGA implementation, and synchronization
zbMATH Open document ID: 1440.34037
DOI: 10.1155/2018/7273531
author: Karthikeyan Rajagopal
author: Sifeu Takougang Kingni
author: Gaetan Fautso Kuiate
author: Victor Kamdoum Tamba
author: Viet-Thanh Pham
published in: Advances in Mathematical Physics
publication date: 2018-12-11T00:00:00Z
review text: Summary: A two-parameter autonomous jerk oscillator with a cosine hyperbolic nonlinearity is proposed in this paper. Firstly, the stability of equilibrium points of proposed autonomous jerk oscillator is investigated by analyzing the characteristic equation and the existence of Hopf bifurcation is verified using one of the two parameters as a bifurcation parameter. By tuning its two parameters, various dynamical behaviors are found in the proposed autonomous jerk oscillator including periodic attractor, one-scroll chaotic attractor, and coexistence between chaotic and periodic attractors. The proposed autonomous jerk oscillator has period-doubling route to chaos with the variation of one of its parameters and reverse period-doubling route to chaos with the variation of its other parameter. The proposed autonomous jerk oscillator is modelled on Field Programmable Gate Array (FPGA) and the FPGA chip statistics and phase portraits are derived. The chaotic and coexistence of attractors generated in the proposed autonomous jerk oscillator are confirmed by FPGA implementation of the proposed autonomous jerk oscillator. A good qualitative agreement is illustrated between the numerical and FPGA results. Finally synchronization of unidirectional coupled identical proposed autonomous jerk oscillators is achieved using adaptive sliding mode control method.
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34D06
Mathematics Subject Classification ID: 34H10
Mathematics Subject Classification ID: 93B12
Mathematics Subject Classification ID: 93D21
zbMATH DE Number: 6992008
describes a project that uses: FOMNE
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/7273531
OpenAlex ID: W2890844088
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description: scientific article; zbMATH DE number 6992008