Regular Article

Dynamical analysis, FPGA implementation and its application to chaos based random number generator of a fractal Josephson junction with unharmonic current-phase relation

¹ Department of Mechanical, Petroleum and Gas Engineering, Faculty of Mines and Petroleum Industries, University of Maroua, PO Box 46, Maroua, Cameroon
² Center for Nonlinear Dynamics, Defence University, Bishoftu 6020, Ethiopia
³ Institute of Energy, Mekelle University, Mekelle 121, Ethiopia
⁴ Department of Electronic and Automation, Vocational School of Hacibektaş, Nevşehir Hacibektaş Veli University, 50800 Hacibektaş, Nevşehir, Turkey
⁵ Research Unit of automation and applied computer, Electrical Engineering Department of IUT-FV, University of Dschang, PO Box 134, Bandjoun, Cameroon
⁶ Department of Telecommunication and Network Engineering, IUT-Fotso Victor of Bandjoun, University of Dschang, PO Box 134, Bandjoun, Cameroon
⁷ Department of Physics, Higher Teacher Training College, University of Bamenda, PO Box 39, Bamenda, Cameroon

^a e-mail: stkingni@gmail.com

Received: 17 November 2019
Received in final form: 27 January 2020
Published online: 4 March 2020

Abstract

The dynamical characteristics and its applications to random number generator of a fractal Josephson junction with unharmonic current-phase relation (FJJUCPR) described by a linear resistive-capacitive-inductance shunted junction (LRCLSJ) model are investigated in this paper. The dependence of the equilibrium points of the system to the external current source or the unharmonic current-phase relation (UCPR) parameter is revealed and their stability are analysed. The inclusion of unharmonic current-phase relation in an ideal or a fractal Josephson junction leads to transform the spiking, bursting and relaxations oscillations to an excitable mode. While the inclusion of fractal characteristics in insulating layer of Josephson junction leads to an increase of the amplitude of the spiking, bursting and relaxations oscillations. The numerical simulations results also indicate that FJJUCPR exhibits self-excited chaotic attractors and two different shapes of hidden chaotic attractors. The FJJUCPR is implemented in field programmable gate arrays (FPGA) in order to validate the numerical simulations results. In addition, random number generator design is performed using chaotic signals of the FJJUCPR. The random number generator design results are successful in the NIST SP 800-22 test.