We use the variational method to extract the short periodic orbits of the Qi system within a certain topological length.The chaotic dynamical behaviors of the Qi system with five equilibria are analyzed by the means o...We use the variational method to extract the short periodic orbits of the Qi system within a certain topological length.The chaotic dynamical behaviors of the Qi system with five equilibria are analyzed by the means of phase portraits,Lyapunov exponents,and Poincarémaps.Based on several periodic orbits with different sizes and shapes,they are encoded systematically with two letters or four letters for two different sets of parameters.The periodic orbits outside the attractor with complex topology are discovered by accident.In addition,the bifurcations of cycles and the bifurcations of equilibria in the Qi system are explored by different methods respectively.In this process,the rule of orbital period changing with parameters is also investigated.The calculation and classification method of periodic orbits in this study can be widely used in other similar low-dimensional dissipative systems.展开更多
了解未来气候变化如何影响河流冰情特征对于研究冰凌洪水灾害、水电生产以及大坝管理运行等问题至关重要。基于黄河流域气象观测数据以及第六次国际耦合模式比较计划(CMIP6)中8种全球气候模式(GCMs)的日均气温数据,评估了各GCMs在分位...了解未来气候变化如何影响河流冰情特征对于研究冰凌洪水灾害、水电生产以及大坝管理运行等问题至关重要。基于黄河流域气象观测数据以及第六次国际耦合模式比较计划(CMIP6)中8种全球气候模式(GCMs)的日均气温数据,评估了各GCMs在分位数增量映射(QDM)偏差校正前后对于黄河流域凌汛期日平均气温的模拟能力,预估了黄河流域未来凌汛期气温变化趋势。建立了最大冰厚以及封冻历时预测模型,并预估了黄河防凌重点区域黄河宁蒙段未来最大冰厚以及封冻历时的变化趋势。研究表明,在SSP1-2.6、SSP2-4.5和SSP5-8.5三种气候情景下预计2015—2100年期间黄河流域凌汛期平均气温升温速率分别为0.014、0.031和0.067℃a,黄河巴彦高勒断面21世纪内最大冰厚值将会分别下降8.5、19.5和39.5 cm。SSP2-4.5情景下,随着未来气温升高,2070年之后河道断面仅存一定宽度岸冰、河道中央存在较大清沟的现象将会频繁出现。未来黄河宁蒙段巴彦高勒、三湖河口以及头道拐断面的封冻历时将会呈现出不同程度的缩短趋势,其中巴彦高勒断面缩短趋势最为明显,三种气候情景下封冻历时分别以0.13、0.28和0.66 d a的速率缩短,三湖河口及头道拐断面封冻历时缩短速率较为接近,分别为0.07、0.15、0.36以及0.08、0.17、0.39 d a。展开更多
A non-autonomous competing system is investigated in this paper,where the species x can diffuse between two patches of a heterogeneous environment with barriers between patches,but for species y,the diffusion does not...A non-autonomous competing system is investigated in this paper,where the species x can diffuse between two patches of a heterogeneous environment with barriers between patches,but for species y,the diffusion does not involve a barrier between patches,further it is assumed that all the parameters are time dependent.It is shown that the system can be made persistent under some appropriate conditions.Moreover,sufficient conditions that guarantee the existence of a unique positive periodic orbit which is globally asymptotic stable are derived.展开更多
Chaos-based encryption schemes have been studied extensively, while the security analysis methods for them are still problems to be resolved. Based on the periodic orbit theory, this paper proposes a novel security an...Chaos-based encryption schemes have been studied extensively, while the security analysis methods for them are still problems to be resolved. Based on the periodic orbit theory, this paper proposes a novel security analysis method. The periodic orbits theory indicates that the fundamental frequency of the spiraling orbits is the natural frequency of associated linearized system, which is decided by the parameters of the chaotic system. Thus, it is possible to recover the plaintext of secure communication systems based on chaotic shift keying by getting the average time on the spiraling orbits. Analysis and simulation results show that the security analysis method can break chaos shift keying secure communication systems, which use the parameters as keys.展开更多
This paper investigates the orbital stability of periodic traveling wave solutions to the generalized Zakharov equations {iu ＋uxx = uv ＋ ｜u｜^2u, vtt-vxx=（｜u｜^2）xx.First, we prove the existence of a smooth c...This paper investigates the orbital stability of periodic traveling wave solutions to the generalized Zakharov equations {iu ＋uxx = uv ＋ ｜u｜^2u, vtt-vxx=（｜u｜^2）xx.First, we prove the existence of a smooth curve of positive traveling wave solutions of dnoidal type with a fixed fundamental period L for the generalized Zakharov equations. Then, by using the classical method proposed by Benjamin, Bona et al., we show that this solution is orbitally stable by perturbations with period L. The results on the orbital stability of periodic traveling wave solutions for the generalized Zakharov equations in this paper can be regarded as a perfect extension of the results of [15, 16, 19].展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12205257,11647085,and11647086)the Shanxi Province Science Foundation for Youths(Grant No.201901D211252)+1 种基金Fundamental Research Program of Shanxi Province(Grant No.202203021221095)the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi of China(Grant Nos.2019L0505,2019L0554,and 2019L0572)。
文摘We use the variational method to extract the short periodic orbits of the Qi system within a certain topological length.The chaotic dynamical behaviors of the Qi system with five equilibria are analyzed by the means of phase portraits,Lyapunov exponents,and Poincarémaps.Based on several periodic orbits with different sizes and shapes,they are encoded systematically with two letters or four letters for two different sets of parameters.The periodic orbits outside the attractor with complex topology are discovered by accident.In addition,the bifurcations of cycles and the bifurcations of equilibria in the Qi system are explored by different methods respectively.In this process,the rule of orbital period changing with parameters is also investigated.The calculation and classification method of periodic orbits in this study can be widely used in other similar low-dimensional dissipative systems.
文摘了解未来气候变化如何影响河流冰情特征对于研究冰凌洪水灾害、水电生产以及大坝管理运行等问题至关重要。基于黄河流域气象观测数据以及第六次国际耦合模式比较计划(CMIP6)中8种全球气候模式(GCMs)的日均气温数据,评估了各GCMs在分位数增量映射(QDM)偏差校正前后对于黄河流域凌汛期日平均气温的模拟能力,预估了黄河流域未来凌汛期气温变化趋势。建立了最大冰厚以及封冻历时预测模型,并预估了黄河防凌重点区域黄河宁蒙段未来最大冰厚以及封冻历时的变化趋势。研究表明,在SSP1-2.6、SSP2-4.5和SSP5-8.5三种气候情景下预计2015—2100年期间黄河流域凌汛期平均气温升温速率分别为0.014、0.031和0.067℃a,黄河巴彦高勒断面21世纪内最大冰厚值将会分别下降8.5、19.5和39.5 cm。SSP2-4.5情景下,随着未来气温升高,2070年之后河道断面仅存一定宽度岸冰、河道中央存在较大清沟的现象将会频繁出现。未来黄河宁蒙段巴彦高勒、三湖河口以及头道拐断面的封冻历时将会呈现出不同程度的缩短趋势,其中巴彦高勒断面缩短趋势最为明显,三种气候情景下封冻历时分别以0.13、0.28和0.66 d a的速率缩短,三湖河口及头道拐断面封冻历时缩短速率较为接近,分别为0.07、0.15、0.36以及0.08、0.17、0.39 d a。
基金the Start- up foundation of Fuzhou University ( 0 0 30 82 4 2 2 8),the Foundation ofDeveloping Science and Technical Developmentof Fuzhou University ( 2 0 0 3- QX- 2 1 ) and the Foundation ofScience and Technology of Fujian Province of PR China for Young
文摘A non-autonomous competing system is investigated in this paper,where the species x can diffuse between two patches of a heterogeneous environment with barriers between patches,but for species y,the diffusion does not involve a barrier between patches,further it is assumed that all the parameters are time dependent.It is shown that the system can be made persistent under some appropriate conditions.Moreover,sufficient conditions that guarantee the existence of a unique positive periodic orbit which is globally asymptotic stable are derived.
文摘Chaos-based encryption schemes have been studied extensively, while the security analysis methods for them are still problems to be resolved. Based on the periodic orbit theory, this paper proposes a novel security analysis method. The periodic orbits theory indicates that the fundamental frequency of the spiraling orbits is the natural frequency of associated linearized system, which is decided by the parameters of the chaotic system. Thus, it is possible to recover the plaintext of secure communication systems based on chaotic shift keying by getting the average time on the spiraling orbits. Analysis and simulation results show that the security analysis method can break chaos shift keying secure communication systems, which use the parameters as keys.
基金supported by the National Natural Science Foundation of China(11401122)Science and technology project of Qufu Normal University(xkj201607)
文摘This paper investigates the orbital stability of periodic traveling wave solutions to the generalized Zakharov equations {iu ＋uxx = uv ＋ ｜u｜^2u, vtt-vxx=（｜u｜^2）xx.First, we prove the existence of a smooth curve of positive traveling wave solutions of dnoidal type with a fixed fundamental period L for the generalized Zakharov equations. Then, by using the classical method proposed by Benjamin, Bona et al., we show that this solution is orbitally stable by perturbations with period L. The results on the orbital stability of periodic traveling wave solutions for the generalized Zakharov equations in this paper can be regarded as a perfect extension of the results of [15, 16, 19].
