Using least parameters, we expand the step-transition operator of any linear multi-step method （LMSM） up to O（τ^s＋5） with order s = 1 and rewrite the expansion of the steptransition operator for s = 2 （obtained...Using least parameters, we expand the step-transition operator of any linear multi-step method （LMSM） up to O（τ^s＋5） with order s = 1 and rewrite the expansion of the steptransition operator for s = 2 （obtained by the second author in a former paper）. We prove that in the conjugate relation G3^λτ o G1^τ =G2^τ o G3^λτ with G1 being an LMSM,（1） theorder of G2 can not be higher than that of G1; （2） if G3 is also an LMSM and G2 is a symplectic B-series, then the orders of G1, G2 and G3 must be 2, 2 and 1 respectively.展开更多
In this paper,a novel and effective approach to impulsive synchronization analysis excited by parameter white-noise of neural networks is investigated using the nonlinear operator named the generalized Dahlquist const...In this paper,a novel and effective approach to impulsive synchronization analysis excited by parameter white-noise of neural networks is investigated using the nonlinear operator named the generalized Dahlquist constant.The proposed approach offers a design procedure for impulsive synchronization of a large class of neural networks.Numerical simulations,where the theoretical results are applied to typical neural networks with and without delayed item,demonstrate the effectiveness and feasibility of the proposed technique.展开更多
A novel and effective approach to exponentially stable analysis for dynamic systems on time scales is investigated using the nonlinear operator named the generalized Dahlquist constant in this paper, and simple yet ge...A novel and effective approach to exponentially stable analysis for dynamic systems on time scales is investigated using the nonlinear operator named the generalized Dahlquist constant in this paper, and simple yet generic criteria are derived ensuring the robust stability.展开更多
基金This research is supported by the Informatization Construction of Knowledge Innovation Projects of the Chinese Academy of Sciences ＂Supercomputing Environment Construction and Application＂ （INF105-SCE）, and by a grant （No. 10471145） from National Natural Science Foundation of China.
文摘Using least parameters, we expand the step-transition operator of any linear multi-step method （LMSM） up to O（τ^s＋5） with order s = 1 and rewrite the expansion of the steptransition operator for s = 2 （obtained by the second author in a former paper）. We prove that in the conjugate relation G3^λτ o G1^τ =G2^τ o G3^λτ with G1 being an LMSM,（1） theorder of G2 can not be higher than that of G1; （2） if G3 is also an LMSM and G2 is a symplectic B-series, then the orders of G1, G2 and G3 must be 2, 2 and 1 respectively.
基金supported by the Research Foundation Project of Heze University under Grant XY10KZ01 and XY05SX01
文摘In this paper,a novel and effective approach to impulsive synchronization analysis excited by parameter white-noise of neural networks is investigated using the nonlinear operator named the generalized Dahlquist constant.The proposed approach offers a design procedure for impulsive synchronization of a large class of neural networks.Numerical simulations,where the theoretical results are applied to typical neural networks with and without delayed item,demonstrate the effectiveness and feasibility of the proposed technique.
文摘A novel and effective approach to exponentially stable analysis for dynamic systems on time scales is investigated using the nonlinear operator named the generalized Dahlquist constant in this paper, and simple yet generic criteria are derived ensuring the robust stability.
