The Poincaré Bifurcation of a Class of Planar Hamiltonian Systems

In this paper, we discuss the Poincaré bifurcation of a class of Hamiltonian systems having a region consisting of periodic cycles bounded by a parabola and a straight line. We prove that the system can generate at most two limit cycles and may generate two limit cycles after a small cubic polynomial perturbation.

THE POINCAR BIFURCATION OF QUADRATIC SYSTEMS HAVING A REGION CONSISTING OF PERIODIC CYCLES BOUNDED BY A HYPERBOLA AND AN ARC OF EQUATOR

In this paper, we discuss the Poincare bifurcation for a class of quadratic systems having a region consisting of periodic cycles bounded by a hyperbola and an arc of equator. We prove that the system can at most generate two limit cycles after a small perturbation.

Detecting P2P bots by mining the regional periodicity

Peer-to-peer (P2P) botnets outperform the traditional Internet relay chat (IRC) botnets in evading detection and they have become a prevailing type of threat to the Internet nowadays.Current methods for detecting P2P botnets,such as similarity analysis of network behavior and machine-learning based classification,cannot handle the challenges brought about by different network scenarios and botnet variants.We noticed that one important but neglected characteristic of P2P bots is that they periodically send requests to update their peer lists or receive commands from botmasters in the command-and-control (C&C) phase.In this paper,we propose a novel detection model named detection by mining regional periodicity (DMRP),including capturing the event time series,mining the hidden periodicity of host behaviors,and evaluating the mined periodic patterns to identify P2P bot traffic.As our detection model is built based on the basic properties of P2P protocols,it is difficult for P2P bots to avoid being detected as long as P2P protocols are employed in their C&C.For hidden periodicity mining,we introduce the so-called regional periodic pattern mining in a time series and present our algorithms to solve the mining problem.The experimental evaluation on public datasets demonstrates that the algorithms are promising for efficient P2P bot detection in the C&C phase.

Evolution of the “f” Family Orbits in the Photo Gravitational Sun-Saturn System with Oblateness

We analyze the periodic orbits of “f” family (simply symmetric retrograde periodic orbits) and the regions of quasi-periodic motion around Saturn in the photo gravitational Sun-Saturn system in the framework of planar circular restricted three-body problem with oblateness. The location, nature and size of these orbits are studied using the numerical technique of Poincare surface of sections (PSS). In this paper we analyze these orbits for different solar radiation pressure (q) and actual oblateness coefficient of Sun Saturn system. It is observed that as Jacobi constant (C) increases, the number of islands in the PSS and consequently the number of periodic and quasi-periodic orbits increase. The periodic orbits around Saturn move towards the Sun with decrease in solar radiation pressure for given value of “C”. It is observed that as the perturbation due to solar radiation pressure decreases, the two separatrices come closer to each other and also come closer to Saturn. It is found that the eccentricity and semi major axis of periodic orbits at both separatrices are increased by perturbation due to solar radiation pressure.

The spatio-temporal variations of frost-free period in China from 1951 to 2012

The frost-free period（FFP）first frost date（FFD） and last frost date（LFD） have been regard as the important climate variables for agricultural production. Understanding the spatio-temporal variations of the FFPFFD and LFD is beneficial to reduce the harmful impacts of climate change on agricultural production and enhance the agricultural adaptation. This study examined daily minimum temperatures for 823 national-level meteorological stationscalculated the values of FFDLFD and FFP for station-specific and region-specific from 1951 to 2012estimated the gradients of linear regression for station-specific moving averages of FFDLFD and FFPand assessed station-specific time series of FFP and detected the abrupt change. The results as follows： at both the station level and the regional levelthe FFP across China decreases with the increase of latitude from south to northand with the increase of altitude from east to west generally. At the station levelthe inter-annual fluctuations of FFDLFD and FFP in south and west agricultural regions are greater than those in north and east. At the regional levelexcluding the QT regiontemporal changes of FFP are relatively small in both the low-latitude and the high-latitude regionsbut for the mid-latitude regions. According to the linear trend gradients of the moving average values of station-specific FFDLFD and FFPFFD was delayedLFD advancedand FFP extended gradually over the 80% of China. Furthermorethe change magnitudes for FFDLFD and FFP in the north and east agricultural regions are higher than that in the southern and western. Among the 659 station-specific time series of FFP examined by the Mann-Kendall test341 stationslocated mainly in the north regionhave one identifiable and significant abrupt change. And at the 341 stations with identified abrupt changesmost（57%） abrupt changes occurred during 1991–2012followed by the periods of 1981–1990（28%）1971–1980（12%）and 1951–1970（3%）. The spatio-temporal variations of FFDLFD and FFP would provide important guidance to agricultural practices.