This paper presents two contributions to the stability analysis of periodic systems modeled by a Hill equation: The first is a new method for the computation of the Arnold Tongues associated to a given Hill equation w...This paper presents two contributions to the stability analysis of periodic systems modeled by a Hill equation: The first is a new method for the computation of the Arnold Tongues associated to a given Hill equation which is based on the discretization of the latter. Using the proposed method, a vibrational stabilization is performed by a change in the periodic function which guarantees stability, given that the original equation has unbounded solutions. The results are illustrated by some examples.展开更多
The generalized dynamic Tullock contest model with two homogeneous participants is established, in which both players have the same valuation of winning rewards and losing rewards. Firstly, the unique symmetric equili...The generalized dynamic Tullock contest model with two homogeneous participants is established, in which both players have the same valuation of winning rewards and losing rewards. Firstly, the unique symmetric equilibrium point of the system is obtained by calculation and its local stability condition is given based on the Jury criterion. Then, two paths of the system from stability to chaos, namely flip bifurcation and Neimark-Sacker bifurcation, are analyzed by using the two-dimensional parametric bifurcation diagram. Meanwhile, the abundant Arnold tongues in the two-dimensional parametric bifurcation diagram are analyzed. Finally, the phenomenon of multistability of the system is illustrated through the basin of attraction, and the contact bifurcation occurs during the evolution of the basin of attraction with varying parameters.展开更多
Phase locking dynamics in coupled chaotic oscillators is investigated. For chaotic systems with a poorly coherent phase variable, the imperfect phase locking can be observed before the onset of a complete phase synchr...Phase locking dynamics in coupled chaotic oscillators is investigated. For chaotic systems with a poorly coherent phase variable, the imperfect phase locking can be observed before the onset of a complete phase synchronization. The temporal alternations among phase lockings are found, which originate from an overlap of Arnold tongues.展开更多
文摘This paper presents two contributions to the stability analysis of periodic systems modeled by a Hill equation: The first is a new method for the computation of the Arnold Tongues associated to a given Hill equation which is based on the discretization of the latter. Using the proposed method, a vibrational stabilization is performed by a change in the periodic function which guarantees stability, given that the original equation has unbounded solutions. The results are illustrated by some examples.
基金National Natural Science Foundation of China (No. 61863022)China Postdoctoral Science Foundation,China (No. 2017M623276)。
文摘The generalized dynamic Tullock contest model with two homogeneous participants is established, in which both players have the same valuation of winning rewards and losing rewards. Firstly, the unique symmetric equilibrium point of the system is obtained by calculation and its local stability condition is given based on the Jury criterion. Then, two paths of the system from stability to chaos, namely flip bifurcation and Neimark-Sacker bifurcation, are analyzed by using the two-dimensional parametric bifurcation diagram. Meanwhile, the abundant Arnold tongues in the two-dimensional parametric bifurcation diagram are analyzed. Finally, the phenomenon of multistability of the system is illustrated through the basin of attraction, and the contact bifurcation occurs during the evolution of the basin of attraction with varying parameters.
基金National Natural Science Foundation of China，国家重点基础研究发展计划(973计划)，教育部高校骨干教师资助计划，the TRAPOYT in Higher Education Institutions of MOE，the Fok Ying Tung Educational Funds for Excellent Young Teachers
文摘Phase locking dynamics in coupled chaotic oscillators is investigated. For chaotic systems with a poorly coherent phase variable, the imperfect phase locking can be observed before the onset of a complete phase synchronization. The temporal alternations among phase lockings are found, which originate from an overlap of Arnold tongues.
