This paper deals with the transient characteristics of the cascade DC–DC Boost converter under a large disturbance by using nonlinear modal series method. Based on the power balance principle, a nonlinear averaged model is derived to describe the nonlinear dynamics of the cascade converter. And then, the modal series method is described in detail and the second order approximate solutions are derived by this method. Furthermore, the simulation results and the theoretical analysis demonstrate that there are plenty of modal interactions, particularly the stronger second order modal interactions, which can affect the transient behavior significantly in the disturbed transient process. The modified approximate solutions considering the dominant nonlinear interaction modes of some state variables are subsequently obtained. In addition, by selecting appropriate system parameters, we can improve the transient behavior of the system under disturbance so that the amplitude and duration of the oscillation can be effectively reduced to satisfy the requirements of the system tolerance during the transient process. Moreover, the dominant oscillation modes of each state variable are also studied, which will help us improve the understanding of the salient transient behaviors in DC–DC cascade converters with disturbance. Finally, PSpice circuit experiments are performed to verify the above theoretical and numerical results.

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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.