Optimized Non-hyperbolic Stack Imaging Based on Interpretation Model

In complex media, especially for seismic prospecting in deep layers in East China and in the mountainous area in West China, due to the complex geological condition, the common-mid-point （CMP） gather of deep reflection event is neither hyperbolic, nor any simple function. If traditional normal move-out （NMO） and stack imaging technology are still used, it is difficult to get a clear stack image. Based on previous techniques on non-hyperbolic stack, it is thought in this paper that no matter how complex the geological condition is, in order to get an optimized stack image, the stack should be non time move-out stack, and any stacking method limited to some kind of curve will be restricted to application conditions. In order to overcome the above-mentioned limit, a new method called optimized non-hyperbolic stack imaging based on interpretation model is presented in this paper. Based on CMP/CRP （Common-Reflection-Point） gather after NMO or pre-stack migration, this method uses the interpretation model of reflectors as constraint, and takes comparability as a distinguishing criterion, and finally forms a residual move-out correction for the gather of constrained model. Numerical simulation indicates that this method could overcome the non hyperbolic problem and get fine stack image.

The Existence of Periodic Orbits to a Higher Dimensional Autonomous System with aNon-hyperbolic Singular Point *

By means of theory of topological degree in nonlinear functional analysiscombining with qualitative analysis in ordinary differential equations, we discuss theexistence of nontrivial periodic orbits to a higher dimensional autonomous system witha non-hyperbolic singular point.

Non-hyperbolic Closed Characteristics on Non-degenerate Star-shaped Hypersurfaces in R2n

In this paper, we prove that for every index perfect non-degenerate compact star-shaped hypersurface E C R2n, there exist at least n non-hyperbolic closed characteristics with even Maslov- type indices on E when n is even. When n is odd, there exist at least n closed characteristics with odd Maslov-type indices on E and at least （n - 1） of them are non-hyperbolic. Here we call a compact star-shaped hypersurfaee E ∈R2 index perfect if it carries only finitely many geometrically distinct prime closed characteristics, and every prime closed characteristic （T, y） on E possesses positive mean index and whose Maslov-type index i（y, m） of its m-th iterate satisfies i（y, m） ≠-1 when n is even, and i（y, rn） ≠2{-1,0} when n is odd for all rn E N.

Qualitative Properties of Equilibrium Point in a Discrete Predator-Prey Model

In this paper, the dynamic properties of a discrete predator-prey model are discussed. The properties of non-hyperbolic fixed points and hyperbolic fixed points of the model are analyzed. First, by using the classic Shengjin formula, we find the existence conditions for fixed points of the model. Then, by using the qualitative theory of ordinary differential equations and matrix theory we indicate which points are hyperbolic and which are non-hyperbolic and the associated conditions.

The Dynamical Properties of a Class of Discrete Smith Diffusion Model

In this paper, the dynamical properties of Smith type diffusion model with Dirichlet boundary conditions are studied. The properties of hyperbolic fixed points and non-hyperbolic fixed points of the model are analyzed. By using the central manifold theorem, the bifurcation phenomenon of the model is studied. The results show that flip, transcritical, pitchfork and Fold-flip bifurcations exist at non-hyperbolic fixed points.

Chaos control of gear system with elastomeric web based on multi-parameter multi-step method

This paper employs a multi-parameter multi-step chaos control method, which is built up on the OGY method, to stabilize desirable UPOs of a gear system with elastomeric web as a high-dimensional and non-hyperbolic chaotic system, and the analyses are carried out. Three types of relations between components of a certain control parameter combination are defined in a certain control process. Special emphasis is put on the comparison of control efficiencies of the multi-parameter multi-step method and single-parameter multi-step method. The numerical experiments show the ability to switch between different orbits and the method can be a good chaos control alternative since it provides a more effective UPOs stabilization of high-dimensional and non-hyperbolic chaotic systems than the single-parameter chaos control, and according to the relation between components of each parameter combination, the best combination for chaos control in a certain UPO stabilization process are obtained.

Minimal rambling sets with codimension one dominated splittings

In this paper, we study the dynamics of minimal rambling sets with codimension one dominatedsplittings.

Projection bias, sophistication, and sub-additive discounting

Behavioral studies have revealed the sub-additive discounting pattern,which is at odds with the prevailing hyperbolic discounting framework that explains intertemporal choices.In this study,we demonstrate that completely and partially sophisticated individuals who are aware of their shifting preferences over time may exhibit sub-additive discounting behaviors.More importantly,these behaviors are not determined by whether an individual has hyperbolic time preferences or not.Instead,we show that the choices of reference points and partial projection bias may be the underlying drivers of the observed sub-additive discounting.