The exact solutions for stationary responses of one class of the second order and three classes of higher order nonlinear systems to parametric and/or external while noise excitations are constructed by using Fokkcr-P...The exact solutions for stationary responses of one class of the second order and three classes of higher order nonlinear systems to parametric and/or external while noise excitations are constructed by using Fokkcr-Planck-Kolmogorov et/ualion approach. The conditions for the existence and uniqueness and the behavior of the solutions are discussed. All the systems under consideration are characterized by the dependence ofnonconservative fqrces on the first integrals of the corresponding conservative systems and arc catted generalized-energy-dependent f G.E.D.) systems. It is shown taht for each of the four classes of G.E.D. nonlinear stochastic systems there is a family of non-G.E.D. systems which are equivalent to the G.E.D. system in the sense of having identical stationary solution. The way to find the equivalent stochastic systems for a given G.E.D. system is indicated and. as an example, the equivalent stochastic systems for the second order G.E. D. nonlinear stochastic system are given. It is pointed out and illustrated with example that the exact stationary solutions for many non-G.E.D. nonlinear stochastic systems may he found by searching the equivalent G.E.D. systems.展开更多
The spatial synchronization and temporal coherence of FitzHugh-Nagumo （FHN） neurons on complex networks are numerically investigated. When an optimal number of random shortcuts are added to a regular neural chain, t...The spatial synchronization and temporal coherence of FitzHugh-Nagumo （FHN） neurons on complex networks are numerically investigated. When an optimal number of random shortcuts are added to a regular neural chain, the system can reach a state which is nearly periodic in time and almost synchronized in space. More shortcuts do not increase the spatial synchronization too much, but will obviously destroy the temporal regularity.展开更多
This work presents a new design method based on differentialgeometry andthe nonlinear H∞approach which has verified thatthe H∞controlforthe feedback linearization system is equivalentto a nonlinear H∞control fort...This work presents a new design method based on differentialgeometry andthe nonlinear H∞approach which has verified thatthe H∞controlforthe feedback linearization system is equivalentto a nonlinear H∞control forthe primitive nonlinear controlsystem in the sense of differential game theory.In addition,this kind of design methodis usedfornonlinearrobust optimalexcitation controlofa multi machine system .The controllerconstructed isimplemented via purely local measurement. Moreover,itisindependent ofthe parameters of power networks. Simulations are performed on a single infinite system .It has been demonstrated thatthe nonlinear H∞excitation controlleris more effective than the other nonlinear excitation controllerin dynamic performance improvementfor variation of operationalstates and parametersin powersystems.展开更多
基金Project Supported by The National Natural Science Foundation of China
文摘The exact solutions for stationary responses of one class of the second order and three classes of higher order nonlinear systems to parametric and/or external while noise excitations are constructed by using Fokkcr-Planck-Kolmogorov et/ualion approach. The conditions for the existence and uniqueness and the behavior of the solutions are discussed. All the systems under consideration are characterized by the dependence ofnonconservative fqrces on the first integrals of the corresponding conservative systems and arc catted generalized-energy-dependent f G.E.D.) systems. It is shown taht for each of the four classes of G.E.D. nonlinear stochastic systems there is a family of non-G.E.D. systems which are equivalent to the G.E.D. system in the sense of having identical stationary solution. The way to find the equivalent stochastic systems for a given G.E.D. system is indicated and. as an example, the equivalent stochastic systems for the second order G.E. D. nonlinear stochastic system are given. It is pointed out and illustrated with example that the exact stationary solutions for many non-G.E.D. nonlinear stochastic systems may he found by searching the equivalent G.E.D. systems.
基金Supported by the National Natural Science Foundation of China under Grant No 20433050, the Programme for New Century Excellent Talents （NCET） in University, the Fok Ying Dong Education Foundation and the Foundation for the Author of National Excellent Doctoral Dissertation （FANEDD） of China.
文摘The spatial synchronization and temporal coherence of FitzHugh-Nagumo （FHN） neurons on complex networks are numerically investigated. When an optimal number of random shortcuts are added to a regular neural chain, the system can reach a state which is nearly periodic in time and almost synchronized in space. More shortcuts do not increase the spatial synchronization too much, but will obviously destroy the temporal regularity.
文摘This work presents a new design method based on differentialgeometry andthe nonlinear H∞approach which has verified thatthe H∞controlforthe feedback linearization system is equivalentto a nonlinear H∞control forthe primitive nonlinear controlsystem in the sense of differential game theory.In addition,this kind of design methodis usedfornonlinearrobust optimalexcitation controlofa multi machine system .The controllerconstructed isimplemented via purely local measurement. Moreover,itisindependent ofthe parameters of power networks. Simulations are performed on a single infinite system .It has been demonstrated thatthe nonlinear H∞excitation controlleris more effective than the other nonlinear excitation controllerin dynamic performance improvementfor variation of operationalstates and parametersin powersystems.
