The dynamical system on T^2 which is a group extension over an irrational rotation on T^1 is investigated. The criterion when the extension is minimal, a system of order 2 and when the maximal equicontinuous factor is...The dynamical system on T^2 which is a group extension over an irrational rotation on T^1 is investigated. The criterion when the extension is minimal, a system of order 2 and when the maximal equicontinuous factor is the irrational rotation is given. The topological complexity of the extension is computed, and a negative answer to the latter part of an open question raised by Host et al.(2014) is obtained.展开更多
This paper investigates the nonlinear dynamics of network-based dynamical systems where network communication channels of finite data rates are inserted into the closed loops of the control systems. The authors analyz...This paper investigates the nonlinear dynamics of network-based dynamical systems where network communication channels of finite data rates are inserted into the closed loops of the control systems. The authors analyze the bifurcation and chaotic behavior of the non-smooth dynamical systems. The authors first prove that for almost all system parameters there are no periodic orbits. This result distinguishes this type of non-smooth dynamical systems from many others exhibiting border-collision bifurcations. Next, the authors show analytically that the chaotic sets are separated from the region containing the line segment of all fixed points with a finite distance. Finally, the authors employ a simple model to highlight that both the number of clients sharing a common network channel and fluctuations in the available network bandwidth have significant influence on the performance of such dynamical systems.展开更多
The author argues that the population system of human societies, the highest form of lives on the planet, may serve as standard paradigm for study of complex systems. it turned out to be a well investigable, nonlinear...The author argues that the population system of human societies, the highest form of lives on the planet, may serve as standard paradigm for study of complex systems. it turned out to be a well investigable, nonlinearly controllable dynamic system, where census plays pivotal role. The theory has led China to succeed in checking the upsurge of population growth of 1970-80s and remains reliable basis for family-planning policy-making in all countries world-wide. It suggests that statistics could be a powerful tool in studying holistic properties of complex systems.展开更多
基金National Natural Science Foundation of China (Grant Nos. 11225105 and 11371339)
文摘The dynamical system on T^2 which is a group extension over an irrational rotation on T^1 is investigated. The criterion when the extension is minimal, a system of order 2 and when the maximal equicontinuous factor is the irrational rotation is given. The topological complexity of the extension is computed, and a negative answer to the latter part of an open question raised by Host et al.(2014) is obtained.
基金supported by an the National Natural Science Foundation of China under Grant No.60804015,and an NSERC grant to the third author
文摘This paper investigates the nonlinear dynamics of network-based dynamical systems where network communication channels of finite data rates are inserted into the closed loops of the control systems. The authors analyze the bifurcation and chaotic behavior of the non-smooth dynamical systems. The authors first prove that for almost all system parameters there are no periodic orbits. This result distinguishes this type of non-smooth dynamical systems from many others exhibiting border-collision bifurcations. Next, the authors show analytically that the chaotic sets are separated from the region containing the line segment of all fixed points with a finite distance. Finally, the authors employ a simple model to highlight that both the number of clients sharing a common network channel and fluctuations in the available network bandwidth have significant influence on the performance of such dynamical systems.
文摘The author argues that the population system of human societies, the highest form of lives on the planet, may serve as standard paradigm for study of complex systems. it turned out to be a well investigable, nonlinearly controllable dynamic system, where census plays pivotal role. The theory has led China to succeed in checking the upsurge of population growth of 1970-80s and remains reliable basis for family-planning policy-making in all countries world-wide. It suggests that statistics could be a powerful tool in studying holistic properties of complex systems.
