Competition of spatial and temporal instabilities under time delay near codimension-two Turing-Hopf bifurcations

Competition of spatial and temporal instabilities under time delay near the codimension-two Turing-Hopf bifurcations is studied in a reaction-diffusion equation. The time delay changes remarkably the oscillation frequency, the intrinsic wave vector, and the intensities of both Turing and Hopf modes. The application of appropriate time delay can control the competition between the Turing and Hopf modes. Analysis shows that individual or both feedbacks can realize the control of the transformation between the Turing and Hopf patterns. Two dimensional numerical simulations validate the analytical results.Comment: 13 pages, 6 figure

The diffuse gamma-ray emission toward the Galactic mini starburst W43

In this paper we report the Fermi Large Area Telescope (LAT) detection of the gamma-ray emission toward the young star forming region W43. Using the latest source catalog and diffuse background models, the extended gamma-ray excess is detected with a significance of about 16 $\sigma$. The gamma-ray emission has a spectrum with a photon index of $2.3 \pm 0.1$. We also performed a detailed analysis of the gas content in this region by taking into account the opacity correction to the HI gas column density. The total cosmic-ray (CR) proton energy is estimated to be on the order of $10^{48}\ \rm erg,$ assuming the gamma-ray are produced from the interaction of the accelerated protons and nuclei with the ambient gas. Comparing this region to the other star formation regions in our Galaxy, we find that the CR luminosity is better correlated with the wind power than the star formation rate (SFR). This result suggests that CRs are primarily accelerated by stellar wind in these systemsComment: accepted for publications in A&