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Chu Z, Yao J, Wang H, Yuan C, Zhou Z, Kudryavtsev A, Wang Y, Wang X. Experimental investigation of the period-adding bifurcation route to chaos in plasma. Phys Rev E 2023; 108:055210. [PMID: 38115498 DOI: 10.1103/physreve.108.055210] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2023] [Accepted: 11/07/2023] [Indexed: 12/21/2023]
Abstract
Since the characteristic timescales of the various transport processes inside the discharge plasma span several orders of magnitude, it can be regarded as a typical fast-slow system. Interestingly, in this work, a special kind of complex oscillatory dynamics composed of a series of large-amplitude relaxation oscillations and small-amplitude near-harmonic oscillations, namely, mixed-mode oscillations (MMOs), was observed. By using the ballast resistance as the control parameter, a period-adding bifurcation sequence of the MMOs, i.e., from L^{s} to L^{s+1}, was obtained in a low-pressure DC glow discharge system. Meanwhile, a series of intermittently chaotic regions caused by inverse saddle-node bifurcation was embedded between the two adjacent periodic windows. The formation mechanism of MMOs was analyzed, and the results indicated that the competition between electron production and electron loss plays an important role. Meanwhile, the nonlinear time series analysis technique was used to study the dynamic behavior quantitatively. The attractor in the reconstructed phase space indicated the existence of the homoclinic orbits of type Γ^{-}. In addition, by calculating the largest Lyapunov exponent (LLE), the chaotic nature of these states was confirmed and quantitatively characterized. With the decrease in the ballast resistance, the return map of the chaotic state gradually changed from the nearly one-dimensional single-peak structure to the multibranch structure, which indicates that the dissipation of the system decreased. By further calculating the correlation dimension, it was shown that the complexity of the strange attractors increased for higher-order chaotic states.
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Affiliation(s)
- Zijia Chu
- School of Physics, Harbin Institute of Technology, Harbin 150001, People's Republic of China
| | - Jingfeng Yao
- School of Physics, Harbin Institute of Technology, Harbin 150001, People's Republic of China
- Heilongjiang Provincial Key Laboratory of Plasma Physics and Application Technology, Harbin 150001, China
- Heilongjiang Provincial Innovation Research Center for Plasma Physics and Application Technology, Harbin 150001, People's Republic of China
| | - Hailu Wang
- Institute of Defense Engineering, AMS, PLA, Luoyang 471023, China
| | - Chengxun Yuan
- School of Physics, Harbin Institute of Technology, Harbin 150001, People's Republic of China
- Heilongjiang Provincial Key Laboratory of Plasma Physics and Application Technology, Harbin 150001, China
- Heilongjiang Provincial Innovation Research Center for Plasma Physics and Application Technology, Harbin 150001, People's Republic of China
| | - Zhongxiang Zhou
- School of Physics, Harbin Institute of Technology, Harbin 150001, People's Republic of China
- Heilongjiang Provincial Key Laboratory of Plasma Physics and Application Technology, Harbin 150001, China
- Heilongjiang Provincial Innovation Research Center for Plasma Physics and Application Technology, Harbin 150001, People's Republic of China
| | - Anatoly Kudryavtsev
- School of Physics, Harbin Institute of Technology, Harbin 150001, People's Republic of China
- Heilongjiang Provincial Key Laboratory of Plasma Physics and Application Technology, Harbin 150001, China
- Heilongjiang Provincial Innovation Research Center for Plasma Physics and Application Technology, Harbin 150001, People's Republic of China
| | - Ying Wang
- School of Physics, Harbin Institute of Technology, Harbin 150001, People's Republic of China
- Heilongjiang Provincial Key Laboratory of Plasma Physics and Application Technology, Harbin 150001, China
- Heilongjiang Provincial Innovation Research Center for Plasma Physics and Application Technology, Harbin 150001, People's Republic of China
| | - Xiaoou Wang
- School of Physics, Harbin Institute of Technology, Harbin 150001, People's Republic of China
- Heilongjiang Provincial Key Laboratory of Plasma Physics and Application Technology, Harbin 150001, China
- Heilongjiang Provincial Innovation Research Center for Plasma Physics and Application Technology, Harbin 150001, People's Republic of China
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