Mathematical interpretation of Brownian motor model: Limit cycles and directed transport phenomena

作者：Yang, Jianqiang; Ma, Hong; Zhong, Suchuang^*

来源：Communications in Nonlinear Science & Numerical Simulation, 2018, 56: 467-480.

DOI：10.1016/j.cnsns.2017.08.008

• Smoluchowski-Feynman (SF) ratchet model
• Attractor
• Limit cycle
• Thermodynamic equilibrium
• Directed Transport Phenomenon

In this article, we first suggest that the attractor of Brownian motor model is one of the reasons for the directed transport phenomenon of Brownian particle. We take the classical Smoluchowski-Feynman (SF) ratchet model as an example to investigate the relationship between limit cycles and directed transport phenomenon of the Brownian particle. We study the existence and variation rule of limit cycles of SF ratchet model at changing parameters through mathematical methods. The influences of these parameters on the directed transport phenomenon of a Brownian particle are then analyzed through numerical simulations. Reasonable mathematical explanations for the directed transport phenomenon of Brownian particle in SF ratchet model are also formulated on the basis of the existence and variation rule of the limit cycles and numerical simulations. These mathematical explanations provide a theoretical basis for applying these theories in physics, biology, chemistry, and engineering.

• 出版日期2018-3
• 单位四川大学; 红河学院