The algorithm of singular point quantities for an equilibrium of three-dimensional dynamics system is studied. The explicit algebraic equivalent relation between singular point quantities and Liapunov constants on center manifold is rigorously proved. As an example, the calculation of singular point quantities of the Lü system is applied to illustrate the advantage in investigating Hopf bifurcation of three-dimensional system.

MR (2000) Subject Classification: 34C23, 34C28, 37Gxx.

In this article, we define the fractional differentiation D_δ of order δ, δ > 0, induced by the Laguerre operator L and associated with respect to the Haar measure dm_α. We obtain a characterization of the Bessel potential space using D_δ and different equivalent norms.

In this paper we prove the generalized Hyers-Ulam stability of the system defining general Euler-Lagrange quadratic mappings in non-Archimedean fuzzy normed spaces over a field with valuation using the direct and the fixed point methods.

MSC: 39B82, 39B52, 46H25.

In this article, we deal with the existence, uniqueness, and a variation of solutions of the nonlinear control system with nonlinear monotone hemicontinuous and coercive operator. Moreover, the approximate controllability for the given nonlinear control system is studied.

In this paper, we show that if a -generic diffeomorphism has the weak limit shadowing property on the chain recurrent set, then the diffemorphism satisfies Axiom A and the no-cycle condition.

MSC: 37C50, 37D30.

This paper is concerned with the problem of exponential stabilization for a class of uncertain nonlinear systems with state delay by means of periodically intermittent control. Based on the Lyapunov-Krasovskii functional approach, several sufficient conditions of exponential stabilization for this class of uncertain nonlinear systems with state delay are proposed, which have been expressed in terms of linear matrix inequalities (LMIs) whose feasibility can be easily checked by using the numerically efficient Matlab LMI Toolbox. Further, the control design method is extended to a class of nonlinear systems with state delay. And the new stability criterion is also presented, which guarantees the closed-loop systems are exponentially stable. Finally, two numerical examples are given to show the effectiveness of the proposed approach.

MSC: 93D15, 93C55, 34K20, 34D23.