A quantitative analysis of limit cycles and homoclinic orbits, and the bifurcation curve for the Bogdanov-Takens system are discussed. The parameter incremental method for approximate analytical-expressions of these p...A quantitative analysis of limit cycles and homoclinic orbits, and the bifurcation curve for the Bogdanov-Takens system are discussed. The parameter incremental method for approximate analytical-expressions of these problems is given. These analytical-expressions of the limit cycle and homoclinic orbit are shown as the generalized harmonic functions by employing a time transformation. Curves of the parameters and the stability characteristic exponent of the limit cycle versus amplitude are drawn. Some of the limit cycles and homoclinic orbits phase portraits are plotted. The relationship curves of parameters μ and A with amplitude a and the bifurcation diagrams about the parameter are also given. The numerical accuracy of the calculation results is good.展开更多
The dynamic magnetic behavior of the kinetic metamagnetic spin-5/2 Blume-Capel model is examined, within a mean-field approach, under a time-dependent oscillating magnetic field. To describe the kinetics of the system...The dynamic magnetic behavior of the kinetic metamagnetic spin-5/2 Blume-Capel model is examined, within a mean-field approach, under a time-dependent oscillating magnetic field. To describe the kinetics of the system, Glauber- type stochastic dynamics has been utilized. The mean-field dynamic equations of the model are obtained from the Master equation. Firstly, these dynamic equations are solved to find the phases in the system. Then, the dynamic phase transition temperatures are obtained by investigating the thermal behavior of dynamic sublattice magnetizations. Moreover, from this investigation, the nature of the phase transitions （first- or second-order） is characterized. Finally, the dynamic phase diagrams are plotted in five different planes. It is found that the dynamic phase diagrams contain the paramagnetic （P）, antiferromagnetic （AF5/2, AF3/2, AF1/2） phases and five different mixed phases. The phase diagrams also display many dynamic critical points, such as tricritical point, triple point, quadruple point, double critical end point and separating point.展开更多
基金the National Natural Science Foundation of China (No.10672193)
文摘A quantitative analysis of limit cycles and homoclinic orbits, and the bifurcation curve for the Bogdanov-Takens system are discussed. The parameter incremental method for approximate analytical-expressions of these problems is given. These analytical-expressions of the limit cycle and homoclinic orbit are shown as the generalized harmonic functions by employing a time transformation. Curves of the parameters and the stability characteristic exponent of the limit cycle versus amplitude are drawn. Some of the limit cycles and homoclinic orbits phase portraits are plotted. The relationship curves of parameters μ and A with amplitude a and the bifurcation diagrams about the parameter are also given. The numerical accuracy of the calculation results is good.
文摘The dynamic magnetic behavior of the kinetic metamagnetic spin-5/2 Blume-Capel model is examined, within a mean-field approach, under a time-dependent oscillating magnetic field. To describe the kinetics of the system, Glauber- type stochastic dynamics has been utilized. The mean-field dynamic equations of the model are obtained from the Master equation. Firstly, these dynamic equations are solved to find the phases in the system. Then, the dynamic phase transition temperatures are obtained by investigating the thermal behavior of dynamic sublattice magnetizations. Moreover, from this investigation, the nature of the phase transitions （first- or second-order） is characterized. Finally, the dynamic phase diagrams are plotted in five different planes. It is found that the dynamic phase diagrams contain the paramagnetic （P）, antiferromagnetic （AF5/2, AF3/2, AF1/2） phases and five different mixed phases. The phase diagrams also display many dynamic critical points, such as tricritical point, triple point, quadruple point, double critical end point and separating point.
