Discrete Leslie's model with bifurcations and control

We explored a local stability analysis at fixed points, bifurcations, and a control in a discrete Leslie's prey-predator model in the interior of $\mathbb{R}_+^2$. More specially, it is examined that for all parameters, Leslie's model has boundary and interior equilibria, and the local stability is studied by the linear stability theory at equilibrium. Additionally, the model does not undergo a flip bifurcation at the boundary fixed point, though a Neimark-Sacker bifurcation exists at the interior fixed point, and no other bifurcation exists at this point. Furthermore, the Neimark-Sacker bifurcation is controlled by a hybrid control strategy. Finally, numerical simulations that validate the obtained results are given

On a class of nonlinear rational systems of difference equations

In this paper, we construct and formulate the solutions and periodicity character of the following nonlinear rational systems of difference equations: \begin{equation} S_{n+1} = \dfrac{T_{n} S_{n-2}}{S_{n-2} + T_{n-1}},\quad T_{n+1} = \dfrac{S_{n} T_{n-2}}{\pm T_{n-2} \pm S_{n-1}},\quad \;\;\;\; n = 0,1,2,...., \quad\quad\quad(0.1)\end{equation} where the initial conditions $s_{-2}, s_{-1}, s_0, t_{-2}, t_{-1}, t_0$ are positive real numbers. Moreover, some mathematical programs are used to support our theoretical results of each system in this paper

Complicate dynamical analysis of a discrete predator-prey model with a prey refuge

In this paper, some complicated dynamic characteristics are formulated for a discrete predator-prey model with a prey refuge. After studying the local dynamical properties about fixed points, our main purpose is to investigate condition(s) for the occurrence of flip and hopf bifurcations, respectively. Further, by the bifurcation theory, we have studied flip bifurcation at boundary fixed point, and flip and hopf bifurcations at interior fixed point of the discrete model. We have also studied chaos by state feedback control strategy. Furthermore, theoretical results are numerically verified. Finally, we have also discussed the influence of prey refuge in the discrete model

Phenolic Compounds, Antioxidant Activity, Ascorbic Acid, and Sugars in Honey from Ingenious Hail Province of Saudi Arabia

Bioactive compounds are responsible for biological activities in honey. The botanical and regional sources of honey contribute to the variable concentration of bioactive compounds. This paper reports the analysis of bioactive compounds such as phenolic compounds, vitamin C, total phenolic contents (TPC), radical scavenging activity (RSA), and sugars of five honey samples (Talh, Athel, Sidr, Spring flower, and Langnese) from the ingenious Hail region (Saudi Arabia) using HPLC-RID and DAD. Talh has the highest TPC level of 26.9 mg GAE/100 g, whereas Spring flower has the lowest level of 8.2 mg GAE/100 g. Quercetin levels in all samples ranged from 0.28 to 2.68 mg GAE/100 g. Gallic acid, a phenolic compound, was found in three samples of honey at concentrations ranging from 0.81–1.08 mg/100 g. DPPH radical scavenging activity (RSA) of Talh and Sidr honey sample are found to be high as compared to other samples. The Sidr honey sample had the highest vitamin C content, 2.59 mg/100 g. Fructose and glucose sugar concentrations ranged from 28.35–37.81 g/100 g and 20.21–32.28 g/100 g, respectively, with a higher fructose ratio. Sucrose was not found in any of the five samples. These findings point to the high quality of honey produced in Saudi Arabia’s ingenious Hail province, and therefore may contribute in therapeutic use of these types of honey, such as in complementary and alternative medicine

Phenolic Compounds, Antioxidant Activity, Ascorbic Acid, and Sugars in Honey from Ingenious Hail Province of Saudi Arabia

Bioactive compounds are responsible for biological activities in honey. The botanical and regional sources of honey contribute to the variable concentration of bioactive compounds. This paper reports the analysis of bioactive compounds such as phenolic compounds, vitamin C, total phenolic contents (TPC), radical scavenging activity (RSA), and sugars of five honey samples (Talh, Athel, Sidr, Spring flower, and Langnese) from the ingenious Hail region (Saudi Arabia) using HPLC-RID and DAD. Talh has the highest TPC level of 26.9 mg GAE/100 g, whereas Spring flower has the lowest level of 8.2 mg GAE/100 g. Quercetin levels in all samples ranged from 0.28 to 2.68 mg GAE/100 g. Gallic acid, a phenolic compound, was found in three samples of honey at concentrations ranging from 0.81–1.08 mg/100 g. DPPH radical scavenging activity (RSA) of Talh and Sidr honey sample are found to be high as compared to other samples. The Sidr honey sample had the highest vitamin C content, 2.59 mg/100 g. Fructose and glucose sugar concentrations ranged from 28.35–37.81 g/100 g and 20.21–32.28 g/100 g, respectively, with a higher fructose ratio. Sucrose was not found in any of the five samples. These findings point to the high quality of honey produced in Saudi Arabia’s ingenious Hail province, and therefore may contribute in therapeutic use of these types of honey, such as in complementary and alternative medicine