In this paper,we firstly find out the unstable periodic orbit of Duffing equation,then control the unstable periodic orbit in bifurcation and chaotic regions by continuous tracing control method.

Identification of determinant dynamics in neurons spiking series by using unstable periodic orbits;

Study of neuron information coding based on theory of unstable periodic orbits;

Numerical simulation results showed that the unstable periodic orbits of the system could be ballasted,the chaos could be eliminated via choosing proper delayed time and gain coefficient,and the system could be changed from unstable to s.

The stabilization problem of unstable periodic orbits embedded in chaotic discrete-time systems is discussed.

The theoretical results on the limitation and controllability of delayed feedback control with respect to the stabilization of unstable fixed point or unstable periodic orbit and the experimental results of the delayed feedback control s applications in controlling chaos in electrical circuits and magneto-elastic beam are summed up.

The conceptual foundation of this analysis is the abstraction of observed neuronal activities into a dynamical landscape characterized by a hierarchy of "unstable periodic orbits" (UPOs).

A new method of stability analysis for periodic orbits of piecewise linear chaotic systems;

Study on analytic approach for extracting periodic orbits of piecewise linear chaotic systems;

On odd periodic orbits of f(x)=1-ax~2;