Consider the reducibility of a class of nonlinear quasi-periodic systems with multiple eigenvalues under perturbational hypothesis in the neighborhood of equilibrium. That is, consider the following system x = （A ＋ ...Consider the reducibility of a class of nonlinear quasi-periodic systems with multiple eigenvalues under perturbational hypothesis in the neighborhood of equilibrium. That is, consider the following system x = （A ＋ εQ（ t） ）x ＋ eg（t） ＋ h（x, t）, where A is a constant matrix with multiple eigenvalues; h = O（x2） （x-4）） ; and h（x, t）, Q（t）, and g（t） are analytic quasi-periodic with respect to t with the same frequencies. Under suitable hypotheses of non-resonance conditions and non-degeneracy conditions, for most sufficiently small ε, the system can be reducible to a nonlinear quasi-periodic system with an equilibrium point by means of a quasi-periodic transformation.展开更多
By the use of cross-correlation measures, the response of a symmetric Schmitt trigger (ST) driven by a random binary signal and white Gaussian noise is investigated. The results show that the information transmission...By the use of cross-correlation measures, the response of a symmetric Schmitt trigger (ST) driven by a random binary signal and white Gaussian noise is investigated. The results show that the information transmission can be enhanced when a certain amount of noise is presented, i.e., aperiodic stochastic resonance (ASR). Then, the influence of signal amplitude and the ST threshold on ASR is examined, the applicability of the ST in reducing the noise level of random signal transmission and improving the quality of output signal via ASR effect is illustrated. This research is of great interest in the field of digital communications.展开更多
In this paper, we consider the phenomenon of stochastic resonance （SR） in a quartic bistable system under the simultaneous action of a multiplicative non-Gaussian and an additive Gaussian noises and a weak periodic ...In this paper, we consider the phenomenon of stochastic resonance （SR） in a quartic bistable system under the simultaneous action of a multiplicative non-Gaussian and an additive Gaussian noises and a weak periodic signal. The expression of the signal-to-noise ratio R is derived by applying the two-state theory in adiabatic limit. We discuss the effects of the parameter q indicating the departure of the non-Gaussian noise from the Gaussian noise, the correlation time r of the non-Gaussian noise, and coupling intensity A between two noise terms on the stochastic resonance. It is found that the signM-to-noise ratio of the system, as a function of the additive noise intensity, undergoes the transition from having one peak to having two peaks, and then to having one peak again when the parameter q or the noise correlation time τ is increased. The parameter q and τ play opposite roles in the SR of the system.展开更多
A triad mode resonance, or three-wave resonance, is typical of dynamical systems with quadratic nonlinearities. Suspended cables are found to be rich in triad mode resonant dynamics. In this paper, modulation equation...A triad mode resonance, or three-wave resonance, is typical of dynamical systems with quadratic nonlinearities. Suspended cables are found to be rich in triad mode resonant dynamics. In this paper, modulation equations for cable's triad resonance are formulated by the multiple scale method. Dynamic conservative quantities, i.e., mode energy and Manley-Rowe relations, are then constructed. Equilibrium/dynamic solutions of the modulation equations are obtained, and full investigations into their stability and bifurcation characteristics are presented. Various bifurcation behaviors are detected in cable's triad resonant responses, such as saddle-node, Hopf, pitchfork and period-doubling bifurcations. Nonlinear behaviors, like jump and saturation phenomena, are also found in cable's responses. Based upon the bifurcation analysis, two interesting properties associated with activation of cable's triad resonance are also proposed, i.e., energy barrier and directional dependence. The first gives the critical amplitude of high-frequency mode to activate cable's triad resonance, and the second characterizes the degree of difficulty for activating cable's triad resonance in two opposite directions, i.e., with positive or negative internal detuning parameter.展开更多
文摘Consider the reducibility of a class of nonlinear quasi-periodic systems with multiple eigenvalues under perturbational hypothesis in the neighborhood of equilibrium. That is, consider the following system x = （A ＋ εQ（ t） ）x ＋ eg（t） ＋ h（x, t）, where A is a constant matrix with multiple eigenvalues; h = O（x2） （x-4）） ; and h（x, t）, Q（t）, and g（t） are analytic quasi-periodic with respect to t with the same frequencies. Under suitable hypotheses of non-resonance conditions and non-degeneracy conditions, for most sufficiently small ε, the system can be reducible to a nonlinear quasi-periodic system with an equilibrium point by means of a quasi-periodic transformation.
文摘By the use of cross-correlation measures, the response of a symmetric Schmitt trigger (ST) driven by a random binary signal and white Gaussian noise is investigated. The results show that the information transmission can be enhanced when a certain amount of noise is presented, i.e., aperiodic stochastic resonance (ASR). Then, the influence of signal amplitude and the ST threshold on ASR is examined, the applicability of the ST in reducing the noise level of random signal transmission and improving the quality of output signal via ASR effect is illustrated. This research is of great interest in the field of digital communications.
基金supported by the Natural Science Foundation of Yunnan Province under Grant No.2005A0002M
文摘In this paper, we consider the phenomenon of stochastic resonance （SR） in a quartic bistable system under the simultaneous action of a multiplicative non-Gaussian and an additive Gaussian noises and a weak periodic signal. The expression of the signal-to-noise ratio R is derived by applying the two-state theory in adiabatic limit. We discuss the effects of the parameter q indicating the departure of the non-Gaussian noise from the Gaussian noise, the correlation time r of the non-Gaussian noise, and coupling intensity A between two noise terms on the stochastic resonance. It is found that the signM-to-noise ratio of the system, as a function of the additive noise intensity, undergoes the transition from having one peak to having two peaks, and then to having one peak again when the parameter q or the noise correlation time τ is increased. The parameter q and τ play opposite roles in the SR of the system.
基金Supporting Program for Young Investigators,Hunan UniversityNational Science Foundation of China(Grant Nos.11502076 and 11572117)
文摘A triad mode resonance, or three-wave resonance, is typical of dynamical systems with quadratic nonlinearities. Suspended cables are found to be rich in triad mode resonant dynamics. In this paper, modulation equations for cable's triad resonance are formulated by the multiple scale method. Dynamic conservative quantities, i.e., mode energy and Manley-Rowe relations, are then constructed. Equilibrium/dynamic solutions of the modulation equations are obtained, and full investigations into their stability and bifurcation characteristics are presented. Various bifurcation behaviors are detected in cable's triad resonant responses, such as saddle-node, Hopf, pitchfork and period-doubling bifurcations. Nonlinear behaviors, like jump and saturation phenomena, are also found in cable's responses. Based upon the bifurcation analysis, two interesting properties associated with activation of cable's triad resonance are also proposed, i.e., energy barrier and directional dependence. The first gives the critical amplitude of high-frequency mode to activate cable's triad resonance, and the second characterizes the degree of difficulty for activating cable's triad resonance in two opposite directions, i.e., with positive or negative internal detuning parameter.
