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  • 1
    Online Resource
    Online Resource
    Analysis of the fast-slow hyperchaotic Lorenz system
    Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences ; 2009
    In:  Acta Physica Sinica Vol. 58, No. 9 ( 2009), p. 6006-
    Details
    In: Acta Physica Sinica, Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences, Vol. 58, No. 9 ( 2009), p. 6006-
    Abstract: The stability of the origin of the hyperchaotic Lorenz system with two time scales is investigated. The characteristics of Hopf bifurcation from the origin, including the existence condition, the direction as well as the stability of bifurcating periodic solutions are discussed in detail, which can be demonstrated by the numerical simulations. With certain parameter, the fast-slow system can exhibit symmetric bursting and further lead to hyperchaotic movement. Based on the method of slow-fast analysis, different bifurcation forms between quiescent state and spiking has been revealed and the influence of coupling strength on slow passage effect is disscussed.
    Type of Medium: Online Resource
    ISSN: 1000-3290 , 1000-3290
    URL: Journal
    URL: Article
    DOI: 10.7498/aps
    DOI: 10.7498/aps.58.6006
    Language: Unknown
    Publisher: Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences
    Publication Date: 2009
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    Online Resource
  • 2
    Online Resource
    Online Resource
    Evolution from regular movement patterns to chaotic attractors in a nonlinear electrical circuit
    Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences ; 2010
    In:  Acta Physica Sinica Vol. 59, No. 5 ( 2010), p. 3057-
    Details
    In: Acta Physica Sinica, Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences, Vol. 59, No. 5 ( 2010), p. 3057-
    Type of Medium: Online Resource
    ISSN: 1000-3290
    URL: Article
    DOI: 10.7498/aps.59.3057
    Language: Unknown
    Publisher: Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences
    Publication Date: 2010
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    Online Resource
  • 3
    Online Resource
    Online Resource
    Bifurcation analysis of slow-fast behavior in modified Chua's circuit
    Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences ; 2012
    In:  Acta Physica Sinica Vol. 61, No. 1 ( 2012), p. 010202-
    Details
    In: Acta Physica Sinica, Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences, Vol. 61, No. 1 ( 2012), p. 010202-
    Abstract: The dynamics of four-order modified Chua's circuit with slow-fast effect has been investigated in this letter. Different types of bursting phenomena can be observed in numerical simulations. By introducing slow-fast analysis, the bifurcation mechanism for the periodic bursting solutions, especially for Fold/Fold bursting and Fold/Hopf bursting, is presented, which is different from the usual case. With the variation of the parameter, the periodic bursting can evolve to chaotic bursting.
    Type of Medium: Online Resource
    ISSN: 1000-3290 , 1000-3290
    URL: Journal
    URL: Article
    DOI: 10.7498/aps
    DOI: 10.7498/aps.61.010202
    Language: Unknown
    Publisher: Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences
    Publication Date: 2012
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    Online Resource
  • 4
    Online Resource
    Online Resource
    Oscillation behaviors and mechanism of Rayleigh oscillator with periodic switches
    Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences ; 2014
    In:  Acta Physica Sinica Vol. 63, No. 1 ( 2014), p. 010504-
    Details
    In: Acta Physica Sinica, Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences, Vol. 63, No. 1 ( 2014), p. 010504-
    Abstract: A system, which alternates between autonomous and non-autonomous circuit systems observing the time periodic switched rules, is investigated in order to explore its complicated dynamical behaviors. By analyzing the equilibrium point, limiting cycles, and the stability of the autonomous subsystems, as well as deriving the Lyapunov exponents of the switching systems in theory and numerical calculation, we have studied the variation of periodic oscillation behaviors of the compound systems with different stable solutions to the two subsystems. By using the bifurcation diagram of the switched systems and their corresponding largest Lyapunov exponent diagrams, we can observe the complex dynamical behaviors and oscillating mechanism of alternating periodic oscillations, quasi-periodic oscillations and chaotic oscillations with different parameters in the switched systems. Furthermore, dynamical evolutions of the switching system to chaos by period-doubling bifurcations, saddle-node bifurcations and torus bifurcations are observed.
    Type of Medium: Online Resource
    ISSN: 1000-3290 , 1000-3290
    URL: Journal
    URL: Article
    DOI: 10.7498/aps
    DOI: 10.7498/aps.63.010504
    Language: Unknown
    Publisher: Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences
    Publication Date: 2014
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    Online Resource
  • 5
    Online Resource
    Online Resource
    Non-smooth bifurcation analysis of a piecewise linear chaotic circuit
    Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences ; 2010
    In:  Acta Physica Sinica Vol. 59, No. 11 ( 2010), p. 7612-
    Details
    In: Acta Physica Sinica, Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences, Vol. 59, No. 11 ( 2010), p. 7612-
    Abstract: The dynamics of a nonlinear capacitor circuit is investigated in this paper. The symmetric periodic solution and the chaotic attractor can be observed in numerical simulations. Furthermore, the generalized Jacobian matrix at the non-smooth boundaries is introduced to explore the non-smooth bifurcation mechanism for the periodic solutions. Discontinuous bifurcation in the combination of the Hopf bifurcation and the turning point bifurcation occurs at the non-smooth boundaries. Here, the Hopf bifurcation may result in a new frequency, which leads to periodic oscillation. With the variation of the parameter, the periodic symmetric solution oscillates more quickly, which can also be explained through non-smooth bifurcation, and the conclusion accord well with the numerical results.
    Type of Medium: Online Resource
    ISSN: 1000-3290 , 1000-3290
    URL: Journal
    URL: Article
    DOI: 10.7498/aps
    DOI: 10.7498/aps.59.7612
    Language: Unknown
    Publisher: Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences
    Publication Date: 2010
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    Online Resource
  • 6
    Online Resource
    Online Resource
    Analysis of bursting phenomena in Chen’s system with periodic excitation
    Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences ; 2010
    In:  Acta Physica Sinica Vol. 59, No. 6 ( 2010), p. 3802-
    Details
    In: Acta Physica Sinica, Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences, Vol. 59, No. 6 ( 2010), p. 3802-
    Abstract: For the periodically excited Chens system, when there exists order gap between the natural frequency of the original system and the excited frequency, dynamical behaviors associated with the two different time scales can be observed. Bifurcations of the system have been presented by considering the variation of the excited term. Fast-slow analysis is employed to explore the evolution of the system with different parameter conditions, which gives different types of bursters such as symmetric fold bursting, symmetric subHopf bursting and symmetric Hopf-homoclinic bursting, as well as the bifurcation mechanism. Furthermore, the influence of both the amplitude and the frequency of the excitation on the bursting is discussed in detail.
    Type of Medium: Online Resource
    ISSN: 1000-3290 , 1000-3290
    URL: Journal
    URL: Article
    DOI: 10.7498/aps
    DOI: 10.7498/aps.59.3802
    Language: Unknown
    Publisher: Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences
    Publication Date: 2010
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  • 7
    Online Resource
    Online Resource
    Oscillations and non-smooth bifurcation analysis of Chen system with periodic switches
    Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences ; 2013
    In:  Acta Physica Sinica Vol. 62, No. 2 ( 2013), p. 020508-
    Details
    In: Acta Physica Sinica, Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences, Vol. 62, No. 2 ( 2013), p. 020508-
    Abstract: Complicated behaviors of a compound system with periodic switches between different types of Chen systems are investigated in detail. In the local analysis, the critical conditions such as fold bifurcation and Hopf bifurcation are derived to explore the bifurcations of the compound systems with different stable solutions in the two subsystems. Different types of oscillations of this switched system are observed, of which the mechanism is presented to show that the trajectories of the oscillations can be divided into several parts by the switching points, governed by the two subsystems respectively. Because of the non-smooth characteristics at the switching points, different forms of bifurcations may occur in the compound system, which may result in complicated dynamics such as chaotic oscillations, instead of the simple connections between the trajectories of the two subsystems. By the Poincaré mapping, the location of the fixed point and Floquet characteristic multiplier of switching system are discussed.With the variation of the parameter, the system can evolve into chaos via the cascading of period-doubling bifurcation. Besides, the system can evolve into chaos immediately by saddle-node bifurcations from period solutions.The non-smooth bifurcation mechanism of periodic switching system can be revealed by the research.
    Type of Medium: Online Resource
    ISSN: 1000-3290 , 1000-3290
    URL: Journal
    URL: Article
    DOI: 10.7498/aps
    DOI: 10.7498/aps.62.020508
    Language: Unknown
    Publisher: Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences
    Publication Date: 2013
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    Online Resource
  • 8
    Online Resource
    Online Resource
    Complicated oscillations in coupled electrical circuits
    Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences ; 2009
    In:  Acta Physica Sinica Vol. 58, No. 5 ( 2009), p. 2963-
    Details
    In: Acta Physica Sinica, Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences, Vol. 58, No. 5 ( 2009), p. 2963-
    Abstract: The dynamical evolution process of the coupled system connecting two nonlinear electrical circuits with suitable circuit is investigated. The bifurcation behavior as well as the ways to chaos of the two subsystems is presented. It is pointed out when both of the two subsystems behave as periodic, the coupled system may also be led to chaos via cascading of period-doubling bifurcations. Meanwhile, in the chaotic region, critical increase of period as well as period-adding bifurcation can be observed. As to the interaction between periodic movement and the chaotic oscillation, the original periodic subsystem may chaotically oscillate around the original orbit. The amplitude associated with the oscillation increases rapidly, resulting in the obvious chaotic characteristics. On the contrary, the periodic subsystem may not only cause the instability of the chaotic subsystem, but also lead to change of the chaotic structures.
    Type of Medium: Online Resource
    ISSN: 1000-3290 , 1000-3290
    URL: Journal
    URL: Article
    DOI: 10.7498/aps
    DOI: 10.7498/aps.58.2963
    Language: Unknown
    Publisher: Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences
    Publication Date: 2009
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  • 9
    Online Resource
    Online Resource
    Bursting phenomenon and the bifurcation mechanism in generalized Chua’s circuit
    Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences ; 2010
    In:  Acta Physica Sinica Vol. 59, No. 4 ( 2010), p. 2326-
    Details
    In: Acta Physica Sinica, Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences, Vol. 59, No. 4 ( 2010), p. 2326-
    Abstract: By introducing the electrical controlling circuit composed of inductance and capacitance, a fourth order model of generalized Chuas circuit with fast-slow effect has been established for certain parameter conditions. The conditions for fold bifurcation as well as Hopf bifurcation of the fast subsystem are investigated with the variation of the slow variable. Furthermore, the dynamical evolution of the entire system is explored, in which the fast-slow effect existing in the system is focused. Two types of bursting phenomenon, namely, the symmetric fold/fold and fold/Hopf periodic bursters, as well as their mechanism, are presented, which discloses the difference between the two burstings from the view point of bifurcation.
    Type of Medium: Online Resource
    ISSN: 1000-3290 , 1000-3290
    URL: Journal
    URL: Article
    DOI: 10.7498/aps
    DOI: 10.7498/aps.59.2326
    Language: Unknown
    Publisher: Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences
    Publication Date: 2010
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    Online Resource
  • 10
    Online Resource
    Online Resource
    Implicit solitary wave solutions for a class of nonlinear dispersive Boussinesq equation
    Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences ; 2010
    In:  Acta Physica Sinica Vol. 59, No. 12 ( 2010), p. 8343-
    Details
    In: Acta Physica Sinica, Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences, Vol. 59, No. 12 ( 2010), p. 8343-
    Abstract: By applying the bifurcation method of dynamical systems to a class of nonlinear dispersive Boussinesq equations, the analytic expressions of implicit solitary wave solutions are obtained under different parameter conditions. Numerical simulations are given to show the correctness of our results.
    Type of Medium: Online Resource
    ISSN: 1000-3290 , 1000-3290
    URL: Journal
    URL: Article
    DOI: 10.7498/aps
    DOI: 10.7498/aps.59.8343
    Language: Unknown
    Publisher: Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences
    Publication Date: 2010
    Location Call Number Limitation Availability
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