Bifurcation Analysis of Charged Particles Moving on a Rough Surface Under Different Damping Effects

Abstract

This paper deals with two types of bifurcation behaviors of charged particles moving on rough surface under different damping effects. Based on the derived models, the stability of the particle system is judged by eigenvalue analysis and then the eigenvalue movement of the Jacobian matrix is analyzed to reveal the underlying mechanism of the dynamical evolution. It is shown that in the particle system with constant damping force, the system loses stability via Neimark–Sacker bifurcation, whereas in the system with time-dependent damping force, the stability is lost by way of period-doubling bifurcation. In addition, a powerful tool called manifold is employed to meticulously characterize the phase space so as to clearly describe the process of energy evolution, which leads to the inherent understanding of the complex behaviors and particularly the global dynamical properties in the particle system. Finally, some bifurcation diagrams are obtained to give a more evident explanation of complex behaviors. These results are very useful for the entire transport knowledge of charged particle system.