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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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Osipov GV, Ivanchenko MV, Kurths J, Hu B. Synchronized chaotic intermittent and spiking behavior in coupled map chains. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:056209. [PMID: 16089636 DOI: 10.1103/physreve.71.056209] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2004] [Revised: 03/02/2005] [Indexed: 05/03/2023]
Abstract
We study phase synchronization effects in a chain of nonidentical chaotic oscillators with a type-I intermittent behavior. Two types of parameter distribution, linear and random, are considered. The typical phenomena are the onset and existence of global (all-to-all) and cluster (partial) synchronization with increase of coupling. Increase of coupling strength can also lead to desynchronization phenomena, i.e., global or cluster synchronization is changed into a regime where synchronization is intermittent with incoherent states. Then a regime of a fully incoherent nonsynchronous state (spatiotemporal intermittency) appears. Synchronization-desynchronization transitions with increase of coupling are also demonstrated for a system resembling an intermittent one: a chain of coupled maps replicating the spiking behavior of neurobiological networks.
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Affiliation(s)
- Grigory V Osipov
- Department of Radiophysics, Nizhny Novgorod University, 23, Gagarin Avenue, 603600 Nizhny Novgorod, Russia
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Ivanchenko MV, Osipov GV, Shalf-eev VD, Kurths J. Phase synchronization of chaotic intermittent oscillations. PHYSICAL REVIEW LETTERS 2004; 92:134101. [PMID: 15089615 DOI: 10.1103/physrevlett.92.134101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2003] [Indexed: 05/24/2023]
Abstract
We study phase synchronization effects of chaotic oscillators with a type-I intermittency behavior. The external and mutual locking of the average length of the laminar stage for coupled discrete and continuous in time systems is shown and the mechanism of this synchronization is explained. We demonstrate that this phenomenon can be described by using results of the parametric resonance theory and that this correspondence enables one to predict and derive all zones of synchronization.
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Affiliation(s)
- Mikhail V Ivanchenko
- Department of Radiophysics, Nizhny Novgorod University, 23 Gagarin Avenue, 603600 Nizhny Novgorod, Russia
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Parthimos D, Edwards DH, Griffith TM. Universal scaling properties of type-I intermittent chaos in isolated resistance arteries are unaffected by endogenous nitric oxide synthesis. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:061906. [PMID: 11736209 DOI: 10.1103/physreve.64.061906] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2001] [Indexed: 05/23/2023]
Abstract
Spontaneous fluctuations in flow in isolated rabbit ear resistance arteries may exhibit almost-periodic behavior interrupted by chaotic bursts that can be classified as type-I Pomeau-Manneville intermittency. This conclusion was supported by the construction of parabolic return maps and identification of the characteristic probability distributions for the number of oscillations per laminar segment (n) associated with the type-I scenario. Pharmacological inhibition of nitric oxide (NO) synthesis by the vascular endothelium modulated the dynamics of the reinjection mechanism, and thus the generic shape of the probability distribution for n. Nevertheless, average laminar length was related to a derived bifurcation parameter epsilon according to power-law scaling of the form <n> approximately epsilon(beta), where the estimated critical exponent beta was close to the theoretical value of -0.5 both in the presence and absence of NO synthesis.
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Affiliation(s)
- D Parthimos
- Department of Diagnostic Radiology, Wales Heart Research Institute, University of Wales College of Medicine, Heath Park, Cardiff CF14 4XN, Wales, United Kingdom
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Covas E, Tavakol R. Multiple forms of intermittency in partial differential equation dynamo models. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:5435-8. [PMID: 11970415 DOI: 10.1103/physreve.60.5435] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/1999] [Indexed: 11/07/2022]
Abstract
We find concrete evidence for the presence of crisis-induced and Pomeau-Manneville type-I intermittencies in an axisymmetric partial differential equation (PDE) mean-field dynamo model. These findings are of potential importance for two different reasons. First, as far as we are aware, this is the first time detailed evidence has been produced for the occurrence of these types of intermittency for such deterministic PDE models. And second, despite the rather idealized nature of these models, the concrete evidence for the occurrence of more than one type of intermittency in such models makes it in principle possible that different types of intermittency may occur in different solar-type stars or even in the same star over different epochs. In this way a multiple intermittency framework may turn out to be of importance in understanding the mechanisms responsible for grand-minima type behavior in the Sun and solar-type stars and in particular in the interpretation of the corresponding observational and proxy evidence.
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Affiliation(s)
- E Covas
- Astronomy Unit, Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London E1 4NS, United Kingdom.
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