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Some observations are made on the Belousov-Zhabotinskii reaction simulated via the Field-Noyes model, also referred to as the Oregonator, and its modification. The simulation is performed with the aid of a cell-to-cell mapping for global analysis. Regarding the standard Oregonator, a two-dimension-like region in the three-dimensional phase space is detected showing the sensitive dependence of short-term ODE integrations on initial conditions. Trajectories with initial conditions closely located in this region may experience a phase lag if they eventually approach the same stable limit cycle connected with a subcritical Hopf bifurcation. When a flow term is added to the Oregonator, chaos can be brought about to mimic the experimental finding by suitably pleating the slow manifold. Coexistent attractors now may have a chaotic member and a fractal separatrix detected by the global analysis. The above mentioned sensitive region is found to play a significant role in shaping the pleating in order for chaos to happen in a manner analogous to the "screw-type" proposed by [Rössler, 1977] as one of the two prototypes for three-variable systems. Some relevant calculations of Lyapunov exponents, fractal dimensions and power spectra are also included.

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In this paper we consider an anisotropic convection-diffusion (ACD) filter for image denoising and compression simultaneously. The ACD filter is discretized by a tailored finite point method (TFPM), which can tailor some particular properties of the image in an irregular grid structure. A quadtree structure is implemented for the storage in multi-levels for the compression. We compare the performance of the proposed scheme with several well-known filters. The numerical results show that the proposed method is effective for removing a mixture of white Gaussian and salt-and-pepper noises.