利用Chebyshev多项式逼近法在单边约束条件下将带有随机参数的Duffing-van der Pol系统转化为与之等价的确定性系统,然后利用确定性系统的数值方法,研究了系统在擦边附近的动力学行为。研究表明,随机非光滑动力系统由擦边到混沌运动过程...利用Chebyshev多项式逼近法在单边约束条件下将带有随机参数的Duffing-van der Pol系统转化为与之等价的确定性系统,然后利用确定性系统的数值方法,研究了系统在擦边附近的动力学行为。研究表明,随机非光滑动力系统由擦边到混沌运动过程中,存在一个擦边区间。当控制参数完全经过这个区间时,随机系统才变为和确定性系统类似的混沌运动,而在这个区间内,随机系统经过一个由擦边运动到混沌再到擦边运动的反复过程。同时作者还发现,随机非光滑动力系统在擦边附近存在由随机因素诱发的倍周期分岔现象。展开更多
由于高维非光滑系统的复杂性,准确预测其同宿环和异宿环极其困难。本文针对一类四维非光滑动力系统,分别提出了能够精确检测同宿环和异宿环的判据,并利用数学分析和定性理论对其进行了严格证明。此外,本文还建立了此类特殊环诱导系统混...由于高维非光滑系统的复杂性,准确预测其同宿环和异宿环极其困难。本文针对一类四维非光滑动力系统,分别提出了能够精确检测同宿环和异宿环的判据,并利用数学分析和定性理论对其进行了严格证明。此外,本文还建立了此类特殊环诱导系统混沌的存在条件。最后,通过数值算例验证了结果的有效性。Due to the complexity of high-dimensional non-smooth systems, accurately predicting homoclinic cycles or heteroclinic cycles is extremely difficult. This paper proposes some criterion for precisely detecting homoclinic cycles and heteroclinic cycles in a kind of four-dimensional non-smooth dynamical systems, respectively. By combining mathematical analysis with qualitative theory, this work presents a rigourous proof of that. Further, it establishes existence conditions of chaos induced by such special cycles in the considered system. Finally, the numerical simulation for two designed examples is offered to test the validity of obtained results.展开更多
利用随机光滑动力系统的Chebyshev正交多项式逼近方法,研究了双边约束条件下随机vander Pol系统的分岔现象.数值研究表明,双边约束随机van der Pol系统中不仅存在着丰富的倍周期分岔现象,还存在非光滑系统中所特有的擦边分岔.着重研究...利用随机光滑动力系统的Chebyshev正交多项式逼近方法,研究了双边约束条件下随机vander Pol系统的分岔现象.数值研究表明,双边约束随机van der Pol系统中不仅存在着丰富的倍周期分岔现象,还存在非光滑系统中所特有的擦边分岔.着重研究了随机非光滑系统中的擦边分岔,分析了随机因素对非光滑动力系统中擦边分岔的影响.研究表明,Chebyshev多项式逼近也是研究随机非光滑系统动力学行为的一种有效方法.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
Non-smooth system including impulsive strategies at both fixed and unfixed times are analyzed. For the model with fixed impulsive effects, the global stability of pest eradi- cation periodic solution and the dominance...Non-smooth system including impulsive strategies at both fixed and unfixed times are analyzed. For the model with fixed impulsive effects, the global stability of pest eradi- cation periodic solution and the dominance of dynamic behavior are investigated. This indicates that the model with fixed moments has the potential to protect the natural enemies from extinction, but under some conditions may also serve to extinction of the pest. The second model is constructed according to the practices of IPM, that is, when the pest population reaches the economic injury level, a combination of biological, cultural, and chemical tactics that reduce pests to tolerable levels is used. Numerical investigations imply that there are several different types of periodic solutions and their maximum amplitudes are always less than the given economic threshold. The results also show that the time series at which the IPM strategies are applied are quite complex, which means that the application and realization of IPM in practice are very difficult.展开更多
文摘利用Chebyshev多项式逼近法在单边约束条件下将带有随机参数的Duffing-van der Pol系统转化为与之等价的确定性系统,然后利用确定性系统的数值方法,研究了系统在擦边附近的动力学行为。研究表明,随机非光滑动力系统由擦边到混沌运动过程中,存在一个擦边区间。当控制参数完全经过这个区间时,随机系统才变为和确定性系统类似的混沌运动,而在这个区间内,随机系统经过一个由擦边运动到混沌再到擦边运动的反复过程。同时作者还发现,随机非光滑动力系统在擦边附近存在由随机因素诱发的倍周期分岔现象。
文摘由于高维非光滑系统的复杂性,准确预测其同宿环和异宿环极其困难。本文针对一类四维非光滑动力系统,分别提出了能够精确检测同宿环和异宿环的判据,并利用数学分析和定性理论对其进行了严格证明。此外,本文还建立了此类特殊环诱导系统混沌的存在条件。最后,通过数值算例验证了结果的有效性。Due to the complexity of high-dimensional non-smooth systems, accurately predicting homoclinic cycles or heteroclinic cycles is extremely difficult. This paper proposes some criterion for precisely detecting homoclinic cycles and heteroclinic cycles in a kind of four-dimensional non-smooth dynamical systems, respectively. By combining mathematical analysis with qualitative theory, this work presents a rigourous proof of that. Further, it establishes existence conditions of chaos induced by such special cycles in the considered system. Finally, the numerical simulation for two designed examples is offered to test the validity of obtained results.
文摘利用随机光滑动力系统的Chebyshev正交多项式逼近方法,研究了双边约束条件下随机vander Pol系统的分岔现象.数值研究表明,双边约束随机van der Pol系统中不仅存在着丰富的倍周期分岔现象,还存在非光滑系统中所特有的擦边分岔.着重研究了随机非光滑系统中的擦边分岔,分析了随机因素对非光滑动力系统中擦边分岔的影响.研究表明,Chebyshev多项式逼近也是研究随机非光滑系统动力学行为的一种有效方法.
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Non-smooth system including impulsive strategies at both fixed and unfixed times are analyzed. For the model with fixed impulsive effects, the global stability of pest eradi- cation periodic solution and the dominance of dynamic behavior are investigated. This indicates that the model with fixed moments has the potential to protect the natural enemies from extinction, but under some conditions may also serve to extinction of the pest. The second model is constructed according to the practices of IPM, that is, when the pest population reaches the economic injury level, a combination of biological, cultural, and chemical tactics that reduce pests to tolerable levels is used. Numerical investigations imply that there are several different types of periodic solutions and their maximum amplitudes are always less than the given economic threshold. The results also show that the time series at which the IPM strategies are applied are quite complex, which means that the application and realization of IPM in practice are very difficult.
