摘要
The dynamics of a non-smooth electric circuit with an order gap between its parameters is investigated in this paper. Different types of symmetric bursting phenomena can be observed in numerical simulations. Their dynamical behaviours are discussed by means of slow-fast analysis. Furthermore, the generalized Jacobian matrix at the non-smooth boundaries is introduced to explore the bifurcation mechanism for the bursting solutions, which can also be used to account for the evolution of the complicated structures of the phase portraits. With the variation of the parameter, the periodic symmetric bursting can evolve into chaotic symmetric bursting via period-doubling bifurcation.
The dynamics of a non-smooth electric circuit with an order gap between its parameters is investigated in this paper. Different types of symmetric bursting phenomena can be observed in numerical simulations. Their dynamical behaviours are discussed by means of slow-fast analysis. Furthermore, the generalized Jacobian matrix at the non-smooth boundaries is introduced to explore the bifurcation mechanism for the bursting solutions, which can also be used to account for the evolution of the complicated structures of the phase portraits. With the variation of the parameter, the periodic symmetric bursting can evolve into chaotic symmetric bursting via period-doubling bifurcation.
基金
Project supported by the National Natural Science Foundation of China(Grant Nos.10972091,20976075 and 10872080)
