https://doi.org/10.1140/epjp/i2017-11550-5
Regular Article
Bursting and delay behavior in the Belousov-Zhabotinsky reaction with external excitation
1
Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang, China
2
Department of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang, China
* e-mail: lixh@stdu.edu.cn
Received:
21
January
2017
Accepted:
15
May
2017
Published online:
28
June
2017
The dynamics of a typical Belousov-Zhabotinsky (BZ) reaction with two time scales and low perturbation frequency is investigated in this paper. For specific parameters, the typical phenomenon called as double-Hopf bursting is observed, and the corresponding generation mechanism is presented based on the slow-fast dynamical analysis method. With the decrease of the amplitude of external excitation, the double-Hopf bursting evolves into a single-Hopf one. Furthermore, periodic bifurcation delay behaviors are found when the time-varying parameter slowly passes through the critical point of Hopf bifurcation, which results into spiking state (SP) delay behaviors. The detailed delay phenomena as well as their mechanisms are exhibited by theoretical analysis and numerical simulation.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, 2017
