Analysis of Chaotic Response of Frenkel-Kontorova-Tomlinson Model
Joaquín Solano Ramírez,
Francisco Balibrea Gallego,
José Andrés Moreno Nicolás,
Fulgencio Marín García
Affiliations
Joaquín Solano Ramírez
Faculty of Industrial Engineering, Department of Automation, Electrical Engineering and Electronic Technology, Politechnic University of Cartagena, 30202 Cartagena, Spain
Francisco Balibrea Gallego
Faculty of Mathematics, Department of Mathematics, University of Murcia, 30100 Murcia, Spain
José Andrés Moreno Nicolás
Faculty of Industrial Engineering, Department of Mechanical Engineering, Materials and Manufacturing, Politechnic University of Cartagena, 30202 Cartagena, Spain
Fulgencio Marín García
Faculty of Industrial Engineering, Department of Automation, Electrical Engineering and Electronic Technology, Politechnic University of Cartagena, 30202 Cartagena, Spain
The Frenkel-Kontorova-Tomlinson (FKT) model represents mechanical systems in which the atomic smooth surfaces of two bodies slide against each other. The model is very sensitive to changes of the system parameters, and ranges from simple stable harmonic to chaotic solutions. The design of the model between two bodies for the dynamic problem, following the network method rules, is explained with precision and run on standard electrical circuit simulation software. It provides the phase diagrams of atom displacement for each atom and the total friction force by the summation of all the atom displacements. This article is focused on studying the effect of the selected time step on the result and in the lack of sensitivity of Lyapunov exponents to assess chaotic behaviour.
