Quapp, W. http://orcid.org/0000-0002-0366-1408
Bofill, J. M. http://orcid.org/0000-0002-0974-4618
Funding for this research was provided by:
Spanish Ministerio de Econom’ia y Competitividad (No. PID2019-109518GB-I00)
Spanish Structures of Excellence Mari’a de Maeztu program (MDM-2017-076)
Generalitat de Catalunya (2017 SGR 348)
Article History
Received: 8 January 2021
Accepted: 2 March 2021
First Online: 22 March 2021
Declarations
:
: We acknowledge the financial support from the Spanish Ministerio de Economía y Competitividad, Projects No.No. PID2019-109518GB-I00, Spanish Structures of Excellence Mariá de Maeztu program through grant MDM-2017-0767 and Generalitat de Catalunya, project no. 2017 SGR 348.
: There is no conflict of interest.
: Data of all stationary states reported in the paper are available on request by WQ. Animations of some periods of the movement of the chain are given as supplementary data. For the front region of Shapiro step 1 it is FKm8DanimaPBCShapiStep1.gif, but for the hindrance region of Shapiro step 3 it is FKm8DanimaPBCShapiStep3fin.gif.
: The Fortran code for the following of a Langevin equation, and the calculation of the Lyapunov exponent, as well as the parallel Mathematica codes for the calculation of stationary points of the FK chain, and representation of the Figures are available on request by WQ.