Abstract: A stage-structured predator-prey system with two time delays is considered. By analyzing the corresponding characteristic equation, the local stability of a positive equilibrium is investigated and the existence of Hopf bifurcations is established. Formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions by using the normal form theory and center manifold theorem. Numerical simulations are carried out to illustrate the theoretical results. Based on the global Hopf bifurcation theorem for general functional differential equations, the global existence of periodic solutions is established.
Abstract: In this paper, we propose a novel adaptive
spatiotemporal filter that utilizes image sequences in order to remove
noise. The consecutive frames include: current, previous and next
noisy frames. The filter proposed in this paper is based upon the
weighted averaging pixels intensity and noise variance in image
sequences. It utilizes the Appropriate Number of Consecutive Frames
(ANCF) based on the noisy pixels intensity among the frames. The
number of consecutive frames is adaptively calculated for each
region in image and its value may change from one region to another
region depending on the pixels intensity within the region. The
weights are determined by a well-defined mathematical criterion,
which is adaptive to the feature of spatiotemporal pixels of the
consecutive frames. It is experimentally shown that the proposed
filter can preserve image structures and edges under motion while
suppressing noise, and thus can be effectively used in image
sequences filtering. In addition, the AWA filter using ANCF is
particularly well suited for filtering sequences that contain segments
with abruptly changing scene content due to, for example, rapid
zooming and changes in the view of the camera.
Abstract: In this paper, a delayed predator–prey system with stage
structure is investigated. Sufficient conditions for the system to have
multiple periodic solutions are obtained when the delay is sufficiently
large by applying Bendixson-s criterion. Further, some numerical
examples are given.