The cross-diffusion competition systems were introduced by Shigesada et al. [J. Theor. Biol. 79, 83-99 (1979)] to describe the population pressure by other species. In this paper, introducing the densities of the active individuals and the less active ones, we show that the cross-diffusion competition system can be approximated by the reaction-diffusion system which only includes the linear diffusion. The linearized stability around the constant equilibrium solution is also studied, which implies that the cross-diffusion induced instability can be regarded as Turing's instability of the corresponding reaction-diffusion system.

A new type of competition-diffusion system with a small parameter is proposed. By singular limit analysis, it is shown that any solution of this system converges to the weak solution of the two-phase Stefan problem with reaction terms. This result exhibits the relation between an ecological population model and water-ice solidification problems.

We investigated the effects of dietary diosgenin (Dio), a plant-derived sapogenin, on indomethacin (Indo)-induced intestinal inflammation and alterations in bile secretion in rats. In anesthetized rats, bile secretion, intestinal inflammation, and blood chemistry were assessed 3 days after two subcutaneous injections of Indo given 24 h apart. Dio (> 80 mg.kg-1.day-1) pretreatment significantly inhibited weight and food intake decreases and intestinal inflammation. This protective effect was confirmed by examination of gross and histological findings and intestinal myeloperoxidase activity. Dio significantly increased biliary cholesterol (Chol) output and prevented the decreases in bile flow, bile acid output, and biliary alpha-muricholic acid and the increases in biliary hyodeoxycholic acid, deoxycholic acid, and hydrophobicity index of bile. Significantly more biliary Chol and phospholipids were present in macromolecules separate from bile acids and Indo in Dio-treated rats. Dio significantly increased the elimination constant of Indo and reduced plasma Indo levels at 3 and 12 h but did not influence biliary secretion of Indo for 3.5 h after injection. Although Dio dose-dependently attenuated subacute intestinal inflammation and normalized bile secretion in this model, it may also compromise the anti-inflammatory action of indo.

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