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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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Chu Z, Yao J, Yuan C, Zhou Z, Kudryavtsev A, Wang X, Wang Y. Numerical simulation of the bifurcation-remerging process and intermittency in an undriven direct current glow discharge. Phys Rev E 2022; 106:065207. [PMID: 36671090 DOI: 10.1103/physreve.106.065207] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2022] [Accepted: 11/28/2022] [Indexed: 06/17/2023]
Abstract
As a complex nonlinear medium, gas discharge plasma can exhibit various nonlinear discharge behaviors. In this study, in order to investigate the chaos phenomenon in the subnormal glow region of an undriven direct current glow discharge, a two-dimensional plasma fluid model is established coupled with a circuit model as a boundary condition. Using the applied voltage as control parameter in the simulation, the complete period-doubling bifurcation and inverse period-doubling bifurcation processes in the oscillation region are found, and the influence of the applied voltage on the spatiotemporal distribution of plasma parameters during the bifurcation-remerging process is examined. In addition, the spatial distribution of the plasma parameters of the bifurcation-remerging process is also examined. Also, a series of periodic windows are present in the chaotic region, where the positions and relative order are generally consistent with the universal sequence. Additionally, this study showed that the intermittent chaos appears near the period-3 window, and the bursts appearing in the approximate periodic motion becomes more and more frequent as the control parameters move away from the saddle-node bifurcation point, which shows the typical type-I intermittent chaos characteristics.
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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 and Heilongjiang Provincial Key Laboratory of Plasma Physics and Application Technology, Harbin 150001, People's Republic of China
| | - Chengxun Yuan
- School of Physics, Harbin Institute of Technology, Harbin 150001, People's Republic of China and Heilongjiang Provincial Key Laboratory of 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 and Heilongjiang Provincial Key Laboratory of 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 and Heilongjiang Provincial Key Laboratory of 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 and Heilongjiang Provincial Key Laboratory of 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 and Heilongjiang Provincial Key Laboratory of Plasma Physics and Application Technology, Harbin 150001, People's Republic of China
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Di Garbo A, Euzzor S, Ginoux JM, Arecchi FT, Meucci R. Delayed dynamics in an electronic relaxation oscillator. Phys Rev E 2019; 100:032224. [PMID: 31639932 DOI: 10.1103/physreve.100.032224] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2019] [Indexed: 11/07/2022]
Abstract
We present an experimental investigation of the complex dynamics of a modulated relaxation oscillator implemented by using a unipolar junction transistor (UJT) showing the transition to chaos through torus breakdown. In a previous paper a continuous model was introduced for the same system, explaining chaos based on analogy with a memristor. We propose here a new approach based on a piecewise linear model with delay considering a measured parasitic delay effect. The inclusion of this delay, accounting for memory effects, increases the dimensionality of the model, allowing the transition to chaos as observed in the experiment. The piecewise delayed model shows analogies with a two-dimensional leaky integrate-and-fire model used in neurodynamics.
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Affiliation(s)
| | | | | | - F Tito Arecchi
- CNR - National Institute of Optics, Florence, Italy.,Department of Physics and Astronomy, Universitá di Firenze, Firenze, Italy
| | - Riccardo Meucci
- CNR - National Institute of Optics, Florence, Italy.,Department of Physics and Astronomy, Universitá di Firenze, Firenze, Italy
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Effects of noise on the internal resonance of a nonlinear oscillator. Sci Rep 2018; 8:5976. [PMID: 29654287 PMCID: PMC5899175 DOI: 10.1038/s41598-018-24383-2] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2017] [Accepted: 04/03/2018] [Indexed: 11/09/2022] Open
Abstract
We numerically analyze the response to noise of a system formed by two coupled mechanical oscillators, one of them having Duffing and van der Pol nonlinearities, and being excited by a self–sustaining force proportional to its own velocity. This system models the internal resonance of two oscillation modes in a vibrating solid beam clamped at both ends. In applications to nano– and micromechanical devices, clamped–clamped beams are subjected to relatively large thermal and electronic noise, so that characterizing the fluctuations induced by these effects is an issue of both scientific and technological interest. We pay particular attention to the action of stochastic forces on the stability of internal–resonance motion, showing that resonant oscillations become more robust than other forms of periodic motion as the quality factor of the resonant mode increases. The dependence on other model parameters —in particular, on the coupling strength between the two oscillators— is also assessed.
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Meucci R, Euzzor S, Pugliese E, Zambrano S, Gallas MR, Gallas JAC. Optimal Phase-Control Strategy for Damped-Driven Duffing Oscillators. PHYSICAL REVIEW LETTERS 2016; 116:044101. [PMID: 26871335 DOI: 10.1103/physrevlett.116.044101] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2015] [Indexed: 06/05/2023]
Abstract
Phase-control techniques of chaos aim to extract periodic behaviors from chaotic systems by applying weak harmonic perturbations with a suitably chosen phase. However, little is known about the best strategy for selecting adequate perturbations to reach desired states. Here we use experimental measures and numerical simulations to assess the benefits of controlling individually the three terms of a Duffing oscillator. Using a real-time analog indicator able to discriminate on-the-fly periodic behaviors from chaos, we reconstruct experimentally the phase versus perturbation strength stability areas when periodic perturbations are applied to different terms governing the oscillator. We verify the system to be more sensitive to perturbations applied to the quadratic term of the double-well Duffing oscillator and to the quartic term of the single-well Duffing oscillator.
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Affiliation(s)
- R Meucci
- Istituto Nazionale di Ottica, Consiglio Nazionale delle Ricerche, Largo E. Fermi 6, Firenze, Italy
- Departamento de Física, Universidade Federal da Paraíba, 58051-970 João Pessoa, Brazil
- Instituto de Altos Estudos da Paraíba, Rua Infante Dom Henrique 100-1801, 58039-150 João Pessoa, Brazil
| | - S Euzzor
- Istituto Nazionale di Ottica, Consiglio Nazionale delle Ricerche, Largo E. Fermi 6, Firenze, Italy
| | - E Pugliese
- Istituto Nazionale di Ottica, Consiglio Nazionale delle Ricerche, Largo E. Fermi 6, Firenze, Italy
- Dipartimento di Scienze della Terra, Università degli Studi di Firenze, Via G. La Pira 4, Firenze, Italy
| | - S Zambrano
- Università Vita-Salute San Raffaele, Via Olgettina 58, 20132 Milano, Italy
| | - M R Gallas
- Istituto Nazionale di Ottica, Consiglio Nazionale delle Ricerche, Largo E. Fermi 6, Firenze, Italy
- Departamento de Física, Universidade Federal da Paraíba, 58051-970 João Pessoa, Brazil
- Instituto de Altos Estudos da Paraíba, Rua Infante Dom Henrique 100-1801, 58039-150 João Pessoa, Brazil
| | - J A C Gallas
- Istituto Nazionale di Ottica, Consiglio Nazionale delle Ricerche, Largo E. Fermi 6, Firenze, Italy
- Departamento de Física, Universidade Federal da Paraíba, 58051-970 João Pessoa, Brazil
- Instituto de Altos Estudos da Paraíba, Rua Infante Dom Henrique 100-1801, 58039-150 João Pessoa, Brazil
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Gallas MR, Gallas JAC. Nested arithmetic progressions of oscillatory phases in Olsen's enzyme reaction model. CHAOS (WOODBURY, N.Y.) 2015; 25:064603. [PMID: 26117128 DOI: 10.1063/1.4921178] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We report some regular organizations of stability phases discovered among self-sustained oscillations of a biochemical oscillator. The signature of such organizations is a nested arithmetic progression in the number of spikes of consecutive windows of periodic oscillations. In one of them, there is a main progression of windows whose consecutive number of spikes differs by one unit. Such windows are separated by a secondary progression of smaller windows whose number of spikes differs by two units. Another more complex progression involves a fan-like nested alternation of stability phases whose number of spikes seems to grow indefinitely and to accumulate methodically in cycles. Arithmetic progressions exist abundantly in several control parameter planes and can be observed by tuning just one among several possible rate constants governing the enzyme reaction.
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Affiliation(s)
- Marcia R Gallas
- Instituto de Altos Estudos da Paraíba, Rua Infante Dom Henrique 100-1801, 58039-150 João Pessoa, Brazil and Departamento de Física, Universidade Federal da Paraíba, 58051-970 João Pessoa, Brazil
| | - Jason A C Gallas
- Instituto de Altos Estudos da Paraíba, Rua Infante Dom Henrique 100-1801, 58039-150 João Pessoa, Brazil and Departamento de Física, Universidade Federal da Paraíba, 58051-970 João Pessoa, Brazil
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