Journal
CHINESE JOURNAL OF PHYSICS
Volume 66, Issue -, Pages 327-334Publisher
ELSEVIER
DOI: 10.1016/j.cjph.2020.04.009
Keywords
Fast-slow dynamic; Time delay; Bursting; Bifurcation mechanism; Memristor; Multi-time scale
Categories
Funding
- National Natural Science Foundation of China [6147310]
- Natural Science Foundation of Hunan Province [2015JJ2142]
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Compared with general nonlinear systems, multi-time scale system has complex bursting dynamics and has received widespread attention. A memristor-based Jerk system with parametric excitation is proposed in this study. As the selected excitation frequency is far less than the natural frequency, implying the existence of an order gap between the excitation frequency and the natural one, the system can be considered as a classic fast-slow system with two timescales. In our system, when the slow-varying parameters periodically pass through the critical pitchfork bifurcation point periodically, a distinct time delay behavior can be observed. Complex bursting oscillations induced by the delayed pitchfork are revealed with different excitation amplitudes. By virtue of the fast-slow analysis method, the corresponding generation mechanisms are discussed by the transformed phase portraits, the time series, and the phase portraits. As the delay time interval induced by the pitchfork bifurcation is dependant not only on the excitation amplitude, but also on the excitation frequency, some excitation frequency related bursting patterns are also considered in our study. Finally, numerical simulations are provided to verify the validity of the study.
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