We study numerically the critical behaviour during the break-up of the spiral mean torus in a four-dimensional symplectic map. At each point of the parameter space, the stability indices of a serial of periodic orbits...We study numerically the critical behaviour during the break-up of the spiral mean torus in a four-dimensional symplectic map. At each point of the parameter space, the stability indices of a serial of periodic orbits are calculated with their winding numbers approaching the spiral mean torus. The critical values of the parameters when the torus breaks are determined by the criterion that the variance of the distribution on the indices reaches a minimum. Some evidence is revealed about the possible existence of a universal distribution on the stability indices of the periodic orbits at the critical This confirms the picture given by the approximate renormalization theory of the Hamiltonian systems with three degrees of freedom.展开更多
Phase synchronized entrainment of coupled oscillators with distributed natural frequencies is studied by exploring the dynamical manifestation.The route from partial to complete phase synchronization is identified as ...Phase synchronized entrainment of coupled oscillators with distributed natural frequencies is studied by exploring the dynamical manifestation.The route from partial to complete phase synchronization is identified as a cascade of transitions from high-to low-dimensional tori(quasiperiodicities)interrupted by intermittent chaos.Torus ON-OFF intermittency is found at the onset of desynchronization.Desynchronization-induced chaos originates from the mixing of intermittent ON-OFF time scales.展开更多
To explain the long-term existence of Uranian narrow rings, we study the dynamical evolution of Uranian epsilon ring under the influence of its two shepherding satellites: Cordelia and Ophelia. The model of planar-ell...To explain the long-term existence of Uranian narrow rings, we study the dynamical evolution of Uranian epsilon ring under the influence of its two shepherding satellites: Cordelia and Ophelia. The model of planar-elliptic restricted three-body problem is employed, in which the three bodies are Uranus, a satellite and a test particle. Dissipations due to interparticle collisions are also taken into consideration. A mapping system has been obtained based on the differential equation system. Numerical results show that only those particles originally lying in the libration region of the resonance can be shepherded. The size of the libration region depends mainly on the orbital eccentricity and mass of the shepherd satellite. For the outer shepherd Ophelia with larger orbital eccentricity, if its mass is a third of the nominal mass 2.5 × 1019 g, most of the orbits are regular and the outer edge of the ring can be shepherded, but more fuzzy than the inner edge. Thus we infer that Ophelia has a smaller mass.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.19903001the Special Funds for Major State Basic Research Projects,and Hong Kong Research Grant Council.
文摘We study numerically the critical behaviour during the break-up of the spiral mean torus in a four-dimensional symplectic map. At each point of the parameter space, the stability indices of a serial of periodic orbits are calculated with their winding numbers approaching the spiral mean torus. The critical values of the parameters when the torus breaks are determined by the criterion that the variance of the distribution on the indices reaches a minimum. Some evidence is revealed about the possible existence of a universal distribution on the stability indices of the periodic orbits at the critical This confirms the picture given by the approximate renormalization theory of the Hamiltonian systems with three degrees of freedom.
基金Supported by the National Natural Science Foundation of China under Grant Nos.19805002 and 19835020the Special Funds for Major State Basic Research Projects(G2000077304)+1 种基金the Foundation for University Key Teachers by the Ministry of Education(GG-140-87501-1370)the Hong Kong Research Grant Council and the Hong Kong Baptist University Faculty Research Grant.
文摘Phase synchronized entrainment of coupled oscillators with distributed natural frequencies is studied by exploring the dynamical manifestation.The route from partial to complete phase synchronization is identified as a cascade of transitions from high-to low-dimensional tori(quasiperiodicities)interrupted by intermittent chaos.Torus ON-OFF intermittency is found at the onset of desynchronization.Desynchronization-induced chaos originates from the mixing of intermittent ON-OFF time scales.
文摘To explain the long-term existence of Uranian narrow rings, we study the dynamical evolution of Uranian epsilon ring under the influence of its two shepherding satellites: Cordelia and Ophelia. The model of planar-elliptic restricted three-body problem is employed, in which the three bodies are Uranus, a satellite and a test particle. Dissipations due to interparticle collisions are also taken into consideration. A mapping system has been obtained based on the differential equation system. Numerical results show that only those particles originally lying in the libration region of the resonance can be shepherded. The size of the libration region depends mainly on the orbital eccentricity and mass of the shepherd satellite. For the outer shepherd Ophelia with larger orbital eccentricity, if its mass is a third of the nominal mass 2.5 × 1019 g, most of the orbits are regular and the outer edge of the ring can be shepherded, but more fuzzy than the inner edge. Thus we infer that Ophelia has a smaller mass.
