The lock-in periodic solutions of the Stuart-Landau equation with a periodic excitation are studied. Using singularity theory, the bifurcation behavior of these solutions with respect to the excitation amplitude and f...The lock-in periodic solutions of the Stuart-Landau equation with a periodic excitation are studied. Using singularity theory, the bifurcation behavior of these solutions with respect to the excitation amplitude and frequency are investigated in detail, respectively.The results show that the universal unfolding with respect to the excitation amplitude possesses codimension 3. The transition sets in unfolding parameter plane and the bifurcation diagrams are plotted under some conditions. Additionally, it has also been proved that the bifurcation problem with respect to frequence possesses infinite codimension. Therefore the dynamical bifurcation behavior is very complex in this case. Some new dynamical phenomena are presented, which are the supplement of the results obtained by Sun Liang et al.展开更多
We study synchronization in a system of Stu art-Landau oscillators with frequency-weighted coupling. For three typical unimodal frequency distributions, namely, the Lorentzian, the triangle, and the uniform, we found ...We study synchronization in a system of Stu art-Landau oscillators with frequency-weighted coupling. For three typical unimodal frequency distributions, namely, the Lorentzian, the triangle, and the uniform, we found that the first-order transition occurs when the frequency distribution is relatively compact, while the synchronization transition is continuous when it is relatively wide. In both cases, t here is a regime of Bellerophon state between the incoherent state and the synchronized st ate. Remarkably, we revealed novel transition behavior for such coupled oscillators w计h amplitudes, i.e., the regime of Bellerophon st ate actually contains two stages. In the first stage, the oscillators achieve chaotic phase synchronization;while in the second st age, oscillators form periodical phase synchronization. Our results suggest that Bellerophon state also exists in coupled oscillators with amplitude dynamics.展开更多
We investigate the onset and the decay of Taylor-Couette flow in finite cylinders, and we report the estimated time scales in the azimuthal section of the flow state transition between the super-critical state and the...We investigate the onset and the decay of Taylor-Couette flow in finite cylinders, and we report the estimated time scales in the azimuthal section of the flow state transition between the super-critical state and the sub-critical state by fitting the numerical result to the solution of the Stuart-Landau equation. The inner cylinder rotates, and the outer cylinder and both end walls of the cylinders are stationary. Near the end walls of the cylinders, the value of the time scale is small. In the inner region, the radial velocity component has a large time scale near the center of the vortices, while the axial velocity component has a large time scale between the vortices.展开更多
文摘The lock-in periodic solutions of the Stuart-Landau equation with a periodic excitation are studied. Using singularity theory, the bifurcation behavior of these solutions with respect to the excitation amplitude and frequency are investigated in detail, respectively.The results show that the universal unfolding with respect to the excitation amplitude possesses codimension 3. The transition sets in unfolding parameter plane and the bifurcation diagrams are plotted under some conditions. Additionally, it has also been proved that the bifurcation problem with respect to frequence possesses infinite codimension. Therefore the dynamical bifurcation behavior is very complex in this case. Some new dynamical phenomena are presented, which are the supplement of the results obtained by Sun Liang et al.
基金the National Natural Science Foundation of China (Grant Nos. 11875132, 11835003, and 11872182)the Natural Science Foundation of Shanghai (Grant Nos. 18ZR1411800 and 17ZR1444800).
文摘We study synchronization in a system of Stu art-Landau oscillators with frequency-weighted coupling. For three typical unimodal frequency distributions, namely, the Lorentzian, the triangle, and the uniform, we found that the first-order transition occurs when the frequency distribution is relatively compact, while the synchronization transition is continuous when it is relatively wide. In both cases, t here is a regime of Bellerophon state between the incoherent state and the synchronized st ate. Remarkably, we revealed novel transition behavior for such coupled oscillators w计h amplitudes, i.e., the regime of Bellerophon st ate actually contains two stages. In the first stage, the oscillators achieve chaotic phase synchronization;while in the second st age, oscillators form periodical phase synchronization. Our results suggest that Bellerophon state also exists in coupled oscillators with amplitude dynamics.
文摘We investigate the onset and the decay of Taylor-Couette flow in finite cylinders, and we report the estimated time scales in the azimuthal section of the flow state transition between the super-critical state and the sub-critical state by fitting the numerical result to the solution of the Stuart-Landau equation. The inner cylinder rotates, and the outer cylinder and both end walls of the cylinders are stationary. Near the end walls of the cylinders, the value of the time scale is small. In the inner region, the radial velocity component has a large time scale near the center of the vortices, while the axial velocity component has a large time scale between the vortices.
