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We present sufficient conditions which guarantee that all positive solutions of some higher order rational difference equations are global asymptotically stable. The boundedness of the solutions and the existence of prime period two solutions of such equations are also investigated.

A discrete-time prey–predator model with Holling type II is investigated. For this model, the existence and stability of three fixed points are analyzed. The bifurcation diagrams, phase portraits and Lyapunov exponents are obtained for different parameters of the model. The fractal dimension of a strange attractor of the model was also calculated. Numerical simulations show that the discrete model exhibits rich dynamics compared with the continuous model, which means that the present model is a chaotic, and complex one.

We study the asymptotic behavior of some higher order extension forms of some known population models. We establish that every solution of the considered difference equations is bounded from above and bounded from below by positive constants. We also provide sufficient conditions for the global asymptotically stable of all solutions of that higher order difference equations.

The objective of this paper is to investigate some qualitative behavior of the solutions of an economic model. This is accomplished by studying a higher order difference equation where we establish some results about the boundedness, the periodicity, and the global attractivity of the solutions of this higher order difference equation and then apply the obtained results to give a complete description of global stability and the periodic character of the solutions of the model.

Consider the system of neutral delay differential equations d d t ( x (t)+p x (t−τ))+Q(t) x (t−σ)= 0 , where p∈ R ,τ∈(0,∞),σ∈[0,∞] and Q is continuous matrix, and the system d d t ( x (t)+B x (t−τ))+Q(t) x (t−σ)= 0 , where B is a matrix. We obtain the sufficient condition for the existence of certain types of solutions of the above equation to be ∫ ∞ ||Q(s)|| d s for p≠−1 .

We establish a global convergence result and then apply it to show that under appropriate hypotheses every positive solution of the difference equation x n + 1 = ∑ i = 0 m A i x n − 2 i , n = 0, 1,…, converges to a period two solution.

Epidemiologic and animal studies have linked pancreatic cancer growth with fat intake, especially unsaturated fats. Arachidonic acid release from membrane phospholipids is essential for tumor cell proliferation. Lipoxygenases (LOX) constitute one pathway for arachidonate metabolism. We previously reported that 5-LOX and 12-LOX are upregulated in human pancreatic cancer cells and that blockade of these enzymes abolishes pancreatic cancer cell growth. The present study was aimed at evaluating the effect of LOX inhibition on differentiation and apoptosis in pancreatic cancer cells in parallel with growth inhibition. Four human pancreatic cancer cell lines, PANC-1, MiaPaca2, Capan2, and HPAF, were used. Apoptosis was evaluated by three separate methods, including DNA propidium iodide staining, DNA fragmentation, and the TUNEL assay. Morphological changes and carbonic anhydrase activity were used to determine the effect of LOX inhibitors on differentiation. The general LOX inhibitor NDGA, the 5-LOX inhibitor Rev5901, and the 12-LOX inhibitor baicalein all induced apoptosis in all four pancreatic cancer cell lines, as confirmed by all three methods, suggesting that both the 5-LOX and 12-LOX pathways are important for survival of these cells. Furthermore, NDGA, Rev5901, or baicalein resulted in marked cellular morphological changes in parallel with increased intracellular carbonic anhydrase activity, indicating that LOX blockade induced a more differentiated phenotype in human pancreatic cancer cells. Together with our previous findings, this study suggests that perturbations of LOX activity affect pancreatic cancer cell proliferation and survival. Blockade of LOX enzymes may be valuable for the treatment of human pancreatic cancer.