Based on passive theory, this paper studies a hybrid chaotic dynamical system from the mathematics perspective to implement the control of system stabilization. According to the Jacobian matrix of the nonlinear system...Based on passive theory, this paper studies a hybrid chaotic dynamical system from the mathematics perspective to implement the control of system stabilization. According to the Jacobian matrix of the nonlinear system, the stabilization control region is gotten. The controller is designed to stabilize fast the minimum phase Lorenz-Chen chaotic system after equivalently transforming from chaotic system to passive system. The simulation results show that the system not only can be controlled at the different equilibria, but also can be transformed between the different chaotic attractors.展开更多
In this paper, using the characteristic analysis method, we study the relativistic Euler equations of conservation laws in energy and momentum in special relativity. The interactions of elementary waves for the relati...In this paper, using the characteristic analysis method, we study the relativistic Euler equations of conservation laws in energy and momentum in special relativity. The interactions of elementary waves for the relativistic Euler equations are shown. The collision of two shocks, two centered rarefaction waves, a shock and a rarefaction wave yield corresponding ransmitted waves. The overtaking of two shocks appears a transmitted shock wave, together with a reflected centered rarefaction wave.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No60702023)Natural Science Foundation of Zhejiang Province,China(Grant No Y104414)
文摘Based on passive theory, this paper studies a hybrid chaotic dynamical system from the mathematics perspective to implement the control of system stabilization. According to the Jacobian matrix of the nonlinear system, the stabilization control region is gotten. The controller is designed to stabilize fast the minimum phase Lorenz-Chen chaotic system after equivalently transforming from chaotic system to passive system. The simulation results show that the system not only can be controlled at the different equilibria, but also can be transformed between the different chaotic attractors.
基金Project supported by the National Natural Science Foundation of China (Grant No.10671120)
文摘In this paper, using the characteristic analysis method, we study the relativistic Euler equations of conservation laws in energy and momentum in special relativity. The interactions of elementary waves for the relativistic Euler equations are shown. The collision of two shocks, two centered rarefaction waves, a shock and a rarefaction wave yield corresponding ransmitted waves. The overtaking of two shocks appears a transmitted shock wave, together with a reflected centered rarefaction wave.
