This paper aims to study the stochastic period-doubling bifurcation of the three-dimensional Rossler system with an arch-like bounded random parameter. First, we transform the stochastic RSssler system into its equiva...This paper aims to study the stochastic period-doubling bifurcation of the three-dimensional Rossler system with an arch-like bounded random parameter. First, we transform the stochastic RSssler system into its equivalent deterministic one in the sense of minimal residual error by the Chebyshev polynomial approximation method. Then, we explore the dynamical behaviour of the stochastic RSssler system through its equivalent deterministic system by numerical simulations. The numerical results show that some stochastic period-doubling bifurcation, akin to the conventional one in the deterministic case, may also appear in the stochastic Rossler system. In addition, we also examine the influence of the random parameter intensity on bifurcation phenomena in the stochastic Rossler system.展开更多
In this paper, the Chebyshev polynomial approximation is applied to the problem of stochastic period-doubling bifurcation of a stochastic Bonhoeffer-van der Pol （BVP for short） system with a bounded random parameter...In this paper, the Chebyshev polynomial approximation is applied to the problem of stochastic period-doubling bifurcation of a stochastic Bonhoeffer-van der Pol （BVP for short） system with a bounded random parameter. In the analysis, the stochastic BVP system is transformed by the Chebyshev polynomial approximation into an equivalent deterministic system, whose response can be readily obtained by conventional numerical methods. In this way we have explored plenty of stochastic period-doubling bifurcation phenomena of the stochastic BVP system. The numerical simulations show that the behaviour of the stochastic period-doubling bifurcation in the stochastic BVP system is by and large similar to that in the deterministic mean-parameter BVP system, but there are still some featured differences between them. For example, in the stochastic dynamic system the period-doubling bifurcation point diffuses into a critical interval and the location of the critical interval shifts with the variation of intensity of the random parameter. The obtained results show that Chebyshev polynomial approximation is an effective approach to dynamical problems in some typical nonlinear systems with a bounded random parameter of an arch-like probability density function.展开更多
An algorithm for accelerating ray tracing through polygon projection is proposed.Ray tracing,as it is well known,invokes large amount of computation,more than 70 percent of total rendering time is spent in calculating...An algorithm for accelerating ray tracing through polygon projection is proposed.Ray tracing,as it is well known,invokes large amount of computation,more than 70 percent of total rendering time is spent in calculating the intersections between rays and objects.Bounding volume is a commonly used technique for reducing the computation time, but this necessitates intersecting rays with bounding volumes.Our new algorithm avoids the initial intersection tests between primary rays and bounding volumes by polygon projection with little extra overhead.With this technique,the bounding volumes can be constructed as tightly as one wishes.Experiments show that the new algorithm is very efficient.展开更多
Starting from the generalized ambiguity function of bistatic SAR （BSAR）, it is shown that 3-D point target estimation can be carried out in space-surface bistatic SAR （SS-BSAR）. Appropriate analytical equations, b...Starting from the generalized ambiguity function of bistatic SAR （BSAR）, it is shown that 3-D point target estimation can be carried out in space-surface bistatic SAR （SS-BSAR）. Appropriate analytical equations, based on maximum likelihood estimation （MLE）, are derived and confirmed via computer simulation. Furthermore, the performance of the estimate using the Crammer-Rao bound is analyzed for the case in question, thus further revealing the possibility and potential of target 3-D position estimation. Setting the determinant maximum of the information matrix as the criterion, the optimal receiver position and multi-receiver configuration are analytically determined in the SS-BSAR system. Simulation results also validate the correctness of the analytical calculation.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 10872165)
文摘This paper aims to study the stochastic period-doubling bifurcation of the three-dimensional Rossler system with an arch-like bounded random parameter. First, we transform the stochastic RSssler system into its equivalent deterministic one in the sense of minimal residual error by the Chebyshev polynomial approximation method. Then, we explore the dynamical behaviour of the stochastic RSssler system through its equivalent deterministic system by numerical simulations. The numerical results show that some stochastic period-doubling bifurcation, akin to the conventional one in the deterministic case, may also appear in the stochastic Rossler system. In addition, we also examine the influence of the random parameter intensity on bifurcation phenomena in the stochastic Rossler system.
基金Project supported by the Major Program of the National Natural Science Foundation of China, China （Grant No 10332030）, the National Natural Science Foundation of China （Grant No 10472091）, and the Graduate Starting Seed Fund of Northwestern Polytechnical University, China （Grant No Z200655）.
文摘In this paper, the Chebyshev polynomial approximation is applied to the problem of stochastic period-doubling bifurcation of a stochastic Bonhoeffer-van der Pol （BVP for short） system with a bounded random parameter. In the analysis, the stochastic BVP system is transformed by the Chebyshev polynomial approximation into an equivalent deterministic system, whose response can be readily obtained by conventional numerical methods. In this way we have explored plenty of stochastic period-doubling bifurcation phenomena of the stochastic BVP system. The numerical simulations show that the behaviour of the stochastic period-doubling bifurcation in the stochastic BVP system is by and large similar to that in the deterministic mean-parameter BVP system, but there are still some featured differences between them. For example, in the stochastic dynamic system the period-doubling bifurcation point diffuses into a critical interval and the location of the critical interval shifts with the variation of intensity of the random parameter. The obtained results show that Chebyshev polynomial approximation is an effective approach to dynamical problems in some typical nonlinear systems with a bounded random parameter of an arch-like probability density function.
文摘An algorithm for accelerating ray tracing through polygon projection is proposed.Ray tracing,as it is well known,invokes large amount of computation,more than 70 percent of total rendering time is spent in calculating the intersections between rays and objects.Bounding volume is a commonly used technique for reducing the computation time, but this necessitates intersecting rays with bounding volumes.Our new algorithm avoids the initial intersection tests between primary rays and bounding volumes by polygon projection with little extra overhead.With this technique,the bounding volumes can be constructed as tightly as one wishes.Experiments show that the new algorithm is very efficient.
基金Supported by program for new century excellent talents in university (Grant No. NCET-06-0162)
文摘Starting from the generalized ambiguity function of bistatic SAR （BSAR）, it is shown that 3-D point target estimation can be carried out in space-surface bistatic SAR （SS-BSAR）. Appropriate analytical equations, based on maximum likelihood estimation （MLE）, are derived and confirmed via computer simulation. Furthermore, the performance of the estimate using the Crammer-Rao bound is analyzed for the case in question, thus further revealing the possibility and potential of target 3-D position estimation. Setting the determinant maximum of the information matrix as the criterion, the optimal receiver position and multi-receiver configuration are analytically determined in the SS-BSAR system. Simulation results also validate the correctness of the analytical calculation.
