In recent years, there is a wide interest in Sarkovskii's theorem and related study. According to Sarkov.lkii's theorem, if the continuous self-map f of the closed interval has a 3-periodic orbit, then f must ...In recent years, there is a wide interest in Sarkovskii's theorem and related study. According to Sarkov.lkii's theorem, if the continuous self-map f of the closed interval has a 3-periodic orbit, then f must has an n-periodic orbit for any positive integer n. But f can not have all n-periodic orbits for some n.Example. LetEvidently ,f has only one kind of 3-periodic orbit in the two kinds of 3-periodic orbits, which explains that it isn't far enough to uncover the relation between periodic orbits by the information which Sarkovskii's theorem has offered. In this paper, we raise the concept of type of periodic orbits, and give a feasible algorithm which decides the relation of implication between the two kinds of periodic orbits.展开更多
In recent years, there is a wide interest in Sarkovskii's theorem ami the related study. According to Sarkovskii's theoren if the continuous self-mapf of the closed interval has a 3-pcriodic orbit, then fmust ...In recent years, there is a wide interest in Sarkovskii's theorem ami the related study. According to Sarkovskii's theoren if the continuous self-mapf of the closed interval has a 3-pcriodic orbit, then fmust has an n-pcriodic orbit for any positive integer n. But f can not has all n-periodic orbits for some n.For example, letEvidently, f has only one kind of 3-periodic orbit in the two kinds of 3-periodic orbits. This explains that it isn't far enough to uncover the relation between periodic orbits by information which Sarkovskii's theorem has offered. In this paper, we raise the concept of type of periodic orbits, and give a feasible algorithm which decides the relation of implication between two periodic orbits.展开更多
Cortical spreading depression （CSD） is an important experimental model for diseases such as stroke, epilepsy and migraine. Previous observations indicated that the amplitude and velocity of the typical direct curren...Cortical spreading depression （CSD） is an important experimental model for diseases such as stroke, epilepsy and migraine. Previous observations indicated that the amplitude and velocity of the typical direct current potential shift during repetitive CSD waves were varying. The recovery state of the tissue was found related with the variation of successive CSD waves. A computational model in this paper aimed to investigate the role of relative refractory period of CSD. This model simulated that continuous injection of KCI solution induced repetitive CSD waves. The first CSD wave often had a larger amplitude and faster velocity than those of the succeeding secondary waves. The relative refractory period lasted much longer than the recovery of ions turbulence. If the induction interval was long enough for recovery, a series of CSD waves would have the same profile asthe first one. In the relative refractory period, an early stimulation might lead to a late initiation of CSD, i.e., ＂haste makes waste＂. The amplitude and velocity of CSD waves were found increasing with the initiation interval and asymptotic to those of the first CSD wave. This study verified that the propagation dynamics of CSD waves is modulated by the relative refractory period. It suggested that the refractory period is critical for preventing undesirable CSD waves.展开更多
This paper proposes an efficient design method for nano satellites formation flying near a large space target to perform ultra-close inspection missions.A parametric model for periodic relative motion between two sate...This paper proposes an efficient design method for nano satellites formation flying near a large space target to perform ultra-close inspection missions.A parametric model for periodic relative motion between two satellites is firstly proposed through a detailed analysis of the relative orbital dynamics.It is proved that the existing periodic solutions of satellite relative motion such as in-plane 2:1 elliptic and circular periodic relative orbits both belong to the ellipsoid family of periodic relative orbits.The motion planes and their locations and orientations of the general periodic relative orbits are then determined as the analytic functions of the initial relative states.The maximal and minimal distances from the relative orbit to the origin are further analytically calculated too.A formation design algorithm is then proposed for optimal observation of feature points of the target considering various requirements of collision avoidance and observable distance by using this parametric model.Numerical examples about target inspection are introduced to quantitively evaluate and verify the models and methods.The simulation results are well consistent with the theoretical predictions,showing that the design proposed can be potentially applied for future practical on-orbit service missions.展开更多
文摘In recent years, there is a wide interest in Sarkovskii's theorem and related study. According to Sarkov.lkii's theorem, if the continuous self-map f of the closed interval has a 3-periodic orbit, then f must has an n-periodic orbit for any positive integer n. But f can not have all n-periodic orbits for some n.Example. LetEvidently ,f has only one kind of 3-periodic orbit in the two kinds of 3-periodic orbits, which explains that it isn't far enough to uncover the relation between periodic orbits by the information which Sarkovskii's theorem has offered. In this paper, we raise the concept of type of periodic orbits, and give a feasible algorithm which decides the relation of implication between the two kinds of periodic orbits.
基金Projects Supported by the National Natural Science Foundation of China
文摘In recent years, there is a wide interest in Sarkovskii's theorem ami the related study. According to Sarkovskii's theoren if the continuous self-mapf of the closed interval has a 3-pcriodic orbit, then fmust has an n-pcriodic orbit for any positive integer n. But f can not has all n-periodic orbits for some n.For example, letEvidently, f has only one kind of 3-periodic orbit in the two kinds of 3-periodic orbits. This explains that it isn't far enough to uncover the relation between periodic orbits by information which Sarkovskii's theorem has offered. In this paper, we raise the concept of type of periodic orbits, and give a feasible algorithm which decides the relation of implication between two periodic orbits.
文摘Cortical spreading depression （CSD） is an important experimental model for diseases such as stroke, epilepsy and migraine. Previous observations indicated that the amplitude and velocity of the typical direct current potential shift during repetitive CSD waves were varying. The recovery state of the tissue was found related with the variation of successive CSD waves. A computational model in this paper aimed to investigate the role of relative refractory period of CSD. This model simulated that continuous injection of KCI solution induced repetitive CSD waves. The first CSD wave often had a larger amplitude and faster velocity than those of the succeeding secondary waves. The relative refractory period lasted much longer than the recovery of ions turbulence. If the induction interval was long enough for recovery, a series of CSD waves would have the same profile asthe first one. In the relative refractory period, an early stimulation might lead to a late initiation of CSD, i.e., ＂haste makes waste＂. The amplitude and velocity of CSD waves were found increasing with the initiation interval and asymptotic to those of the first CSD wave. This study verified that the propagation dynamics of CSD waves is modulated by the relative refractory period. It suggested that the refractory period is critical for preventing undesirable CSD waves.
基金the National Natural Science Foundation of China(No.12172288)the National Key R&D Program of China(Nos.2021YFC2202601,2021YFC2202603).
文摘This paper proposes an efficient design method for nano satellites formation flying near a large space target to perform ultra-close inspection missions.A parametric model for periodic relative motion between two satellites is firstly proposed through a detailed analysis of the relative orbital dynamics.It is proved that the existing periodic solutions of satellite relative motion such as in-plane 2:1 elliptic and circular periodic relative orbits both belong to the ellipsoid family of periodic relative orbits.The motion planes and their locations and orientations of the general periodic relative orbits are then determined as the analytic functions of the initial relative states.The maximal and minimal distances from the relative orbit to the origin are further analytically calculated too.A formation design algorithm is then proposed for optimal observation of feature points of the target considering various requirements of collision avoidance and observable distance by using this parametric model.Numerical examples about target inspection are introduced to quantitively evaluate and verify the models and methods.The simulation results are well consistent with the theoretical predictions,showing that the design proposed can be potentially applied for future practical on-orbit service missions.
