This paper considers a class of ratio-dependent Holling-Taner model with infinite delay and prey harvest, which is of periodic coefficients. By means of the coincidence degree theory, a set of sufficient conditions fo...This paper considers a class of ratio-dependent Holling-Taner model with infinite delay and prey harvest, which is of periodic coefficients. By means of the coincidence degree theory, a set of sufficient conditions for the existence of at least two positive periodic solutions of this model is established.展开更多
We study a non-autonomous ratio-dependent predator-prey model with exploited terms. This model is of periodic coefficients, which incorporates the periodicity of the varying environment. By means of the coincidence de...We study a non-autonomous ratio-dependent predator-prey model with exploited terms. This model is of periodic coefficients, which incorporates the periodicity of the varying environment. By means of the coincidence degree theory, we establish sufficient conditions for the existence of at least four positive periodic solutions of this model.展开更多
A delayed semi-ratio-dependent predator-prey system in a periodic environment is investigated in this paper.By using a continuation theorem based on Gaines and Mawhin's coincidence degree,the global existence of p...A delayed semi-ratio-dependent predator-prey system in a periodic environment is investigated in this paper.By using a continuation theorem based on Gaines and Mawhin's coincidence degree,the global existence of positive periodic solution is studied.A set of easily verifiable sufficient conditions are obtained.展开更多
The problem of collinear periodic cracks in an infinite piezoelectric body is studied. Effect of saturation strips at the crack-tips is taken into account. By means of the Stroh formalism and the conformal mapping tec...The problem of collinear periodic cracks in an infinite piezoelectric body is studied. Effect of saturation strips at the crack-tips is taken into account. By means of the Stroh formalism and the conformal mapping technique, the general periodic solutions for collinear cracks are obtained. The stress intensity factors and the size of saturation strips are derived analytically, and their dependencies on the ratio of the periodicity on the half-length of the crack are analyzed in detail. Numerical results show the following two facts. （1） When h/l 〉 4.0, the stress intensity factors become almost identical to those of a single crack in an infinite piezoelectric body. This indicates that the interaction between cracks can be ignored in establishing the criterion for the crack initiation in this case. （2） The speed of the saturation strip size of periodic cracks approaching that of a single crack depends on the electric load applied at infinity. In general, a large electric load at infinity is associated with a slow approaching speed.展开更多
This paper studies the phenomenon of stochastic resonance in an asymmetric bistable system with time-delayed feedback and mixed periodic signal by using the theory of signal-to-noise ratio in the adiabatic limit. A ge...This paper studies the phenomenon of stochastic resonance in an asymmetric bistable system with time-delayed feedback and mixed periodic signal by using the theory of signal-to-noise ratio in the adiabatic limit. A general approximate Fokker-Planck equation and the expression of the signal-to-noise ratio are derived through the small time delay approximation at both fundamental harmonics and mixed harmonics. The effects of the additive noise intensity Q, multiplicative noise intensity D, static asymmetry r and delay time T on the signal-to-noise ratio are discussed. It is found that the higher mixed harmonics and the static asymmetry r can restrain stochastic resonance, and the delay time τ can enhance stochastic resonance. Moreover, the longer the delay time τ is, the larger the additive noise intensity Q and the multiplicative noise intensity D are, when the stochastic resonance appears.展开更多
文摘This paper considers a class of ratio-dependent Holling-Taner model with infinite delay and prey harvest, which is of periodic coefficients. By means of the coincidence degree theory, a set of sufficient conditions for the existence of at least two positive periodic solutions of this model is established.
基金Supported by the China Postdoctoral Science Foundation (20060400267)
文摘We study a non-autonomous ratio-dependent predator-prey model with exploited terms. This model is of periodic coefficients, which incorporates the periodicity of the varying environment. By means of the coincidence degree theory, we establish sufficient conditions for the existence of at least four positive periodic solutions of this model.
文摘A delayed semi-ratio-dependent predator-prey system in a periodic environment is investigated in this paper.By using a continuation theorem based on Gaines and Mawhin's coincidence degree,the global existence of positive periodic solution is studied.A set of easily verifiable sufficient conditions are obtained.
基金Project supported by the Postdoctoral Science Foundation of China (No.20070410944)
文摘The problem of collinear periodic cracks in an infinite piezoelectric body is studied. Effect of saturation strips at the crack-tips is taken into account. By means of the Stroh formalism and the conformal mapping technique, the general periodic solutions for collinear cracks are obtained. The stress intensity factors and the size of saturation strips are derived analytically, and their dependencies on the ratio of the periodicity on the half-length of the crack are analyzed in detail. Numerical results show the following two facts. （1） When h/l 〉 4.0, the stress intensity factors become almost identical to those of a single crack in an infinite piezoelectric body. This indicates that the interaction between cracks can be ignored in establishing the criterion for the crack initiation in this case. （2） The speed of the saturation strip size of periodic cracks approaching that of a single crack depends on the electric load applied at infinity. In general, a large electric load at infinity is associated with a slow approaching speed.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10872165 and 10902085)
文摘This paper studies the phenomenon of stochastic resonance in an asymmetric bistable system with time-delayed feedback and mixed periodic signal by using the theory of signal-to-noise ratio in the adiabatic limit. A general approximate Fokker-Planck equation and the expression of the signal-to-noise ratio are derived through the small time delay approximation at both fundamental harmonics and mixed harmonics. The effects of the additive noise intensity Q, multiplicative noise intensity D, static asymmetry r and delay time T on the signal-to-noise ratio are discussed. It is found that the higher mixed harmonics and the static asymmetry r can restrain stochastic resonance, and the delay time τ can enhance stochastic resonance. Moreover, the longer the delay time τ is, the larger the additive noise intensity Q and the multiplicative noise intensity D are, when the stochastic resonance appears.
