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Bifurcations and chaos control in a discrete-time biological model

International Journal of Biomathematics 2020年第4期13卷 1-31页

作者： A.Q.Khan t.khalique Department of Mathematics University of Azad Jammu and Kashmir Muzaffarabad 13100 Pakistan

In this papcr,bifurcations and chaos control in a discrete-time Lotka-Volterra predator-prey model have been studied in *** is shown that for all parametric values,model hus boundary equilibria:P00(0,0),Px0(1,0),and the unique positive equilibrium point:P^+xy(d/c,r(c-d)/bc) if c>*** Linearization method,we explored the local dynamics along with different topological classifications about *** also explored the boundedness of positive solution,global dynamics,and existence of prime-period and periodic points of the *** is explored that flip bifurcation occurs about boundary equilibria:Poo(0,0),P.o(1,0),and also there exists a flip bifurcation when parameters of the discrete-time model vary in a small neighborhood of P^+xy(d/c,r(c-d)/bc).Further,it is also explored that about P^+xy(d/c,r(c-d)/bc) the model undergoes a N-S bifurcation,and meanwhile a stable close invariant curves *** the perspective of biology,these curves imply that betwecn predator and prey populations,there exist periodic or quasi-periodic *** simulations are presented to illustrate not only main results but also reveals the complex dynamics such as the orbits of period-2,3,13,15,17 and *** Maximum Lyapunov exponents as well as fractal dimension are computed numeri-cally to justify the chaotic behaviors in the ***,feedback control method is applied to stabilize chaos existing in the model.

关键词： Lotka-Volterra model bifurcations and chaos center manifold theorem numerical simulation

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EMDEN-FOWLER tYPE SYStEM:NOEtHER SYMMEtRIES AND FIRSt INtEGRALS

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Acta Mathematica Scientia 2012年第5期32卷 1959-1966页

作者： B.Muatjetjeja C.M.khalique International Institute for Symmetry Analysis and Mathematical Modelling Department of Mathematical SciencesNorth-West UniversityMafikeng CampusPrivate Bag X 2046Mmabatho 2735Republic of South Africa

We classify a generalized coupled singular Emden-Fowler type system ＋a（t）vn=0,v＋b（t）um=0 with respect to the standard first-order Lagrangian according to the Noether point symmetries which it *** integrals of the various cases which admit Noether point symmetries are then *** system was discussed in the literature from the view-point of existence and uniqueness of positive solutions.

关键词： Lagrangian Noether symmetry first integrals Emden-Fowler type system Gauge function

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Production of low cost <i>Bacillus thuringiensis</i>based-biopesticide for management of chickpea pod-borer <i>Helicoverpa armigera</i>(Huebn) in Pakistan

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Natural Science 2013年第11期5卷 1139-1144页

作者： Abida Bibi khalique Ahmed Najma Ayub Sadia Alam Department of Microbiology Quaid-i-Azam University Islamabad Pakistan Departmentof Microbiology University of Haripur Haripur Pakistan KarakuramUniversity Gilgit Pakistan

the biopesticide was prepared from locally available low cost ingredients: dried beef blood, molasses and mineral salts (ZnCl2, MgCl2, MnCl2, CaCl2CaCl2, and FeCl3) which were used as medium for the laboratory scale production of Bacillus thuringiensis (B.t.) bio-pesticide by shake flask technique. Indigenous B.t. isolate PA-Sb- 46.3 which produced two crystals—bi-pyramidal and cuboidal was found 73.6 times toxic against H. armigera than reference strain Bacillus thuringiensis var. kurstaki (HD-I-S-1980) used. Medium was fermented for 72 hours at 30℃ ± 2℃ and 160 rpm. 72 h fermented medium showed 95% - 99% sprulation, with spore yield of 3.97 × 109 spores/ml, and LC50 value to 1st instar larvae of H. armigera was 0.53 μg/ml diet. Preservatives and diluents used in the biopesticide were found to be effective to store at room temperature over a period of 30 months. these observations suggested that the biopesticide produced was effective and highly economical for the industrial scale production to manage H. armigera in Pakistan.

关键词： Beef Blood Molasses Indigenous B.t. Isolate PA-Sb-46.3 Sporulation Entomotoxicity Biopesticide

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Probiotic enhanced intestinal immunity in broilers against subclinical necrotic enteritis

Probiotic enhanced intestinal immunity in broilers against s...

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中国畜牧兽医学会动物微生态学分会第五届第十三次全国学术研讨会

作者： Jinge Xin Hesong Wang Xueqin Ni Xiaodan Qing Lei Liu Jing Lai Abdul khalique Guangyao Li Kangcheng Pan Bo Jing Dong Zeng Animal Microecology Institute College of VeterinarySichuan Agricultural University

Along with banning of antibiotics,necrotic enteritis(NE),especially subclinical NE(SNE) whereby no clinical signs are present in chicks,has become one of the most threatening problems in poultry ***,increasing attention has been focused on research and application of effective probiotic strains,as an alternative to antibiotics,to prevent SNE in *** the present study,we evaluated the effects of Lactobacillus johnsonii BS15 on prevention of SNE in ***,assessment determined growth performance and indexes related to intestinal mucosal immunity in the ileum and cecal tonsil of broilers.A total of 300 one-day-old Cobb 500 chicks were randomly distributed into the following five groups:control group(fed with basal diet + de Man,Rogosa,and Sharpe liquid medium[normal diet]),SNE group(normal diet),BS15 group(basal diet + 1 × 10 colony-forming units BS15/g as fed[BS15 diet]),treatment group(normal diet[days 1-28]+ BS15 diet[days 29-42]),and prevention group(BS15 diet[days 1-28]+ normal diet[days 29-42]) throughout a 42-day experimental *** infection was treated for all chicks in the SNE,BS15,treatment,and prevention *** present results demonstrated that BS15 supplementation of feeds in BS15 and prevention groups exerted a positive effect on preventing negative influences on growth performance;these negative influences included low body weight gain and increased feed conversion ratio caused by *** no changes were detected in all determined indexes in cecal tonsils,BS15-treated broilers were free from SNE-caused damage in villi in the ***15 inhibited SNE-caused decrease in immunoglobulins in the *** the lamina propria of ileum,t-cell subsets of lymphocytes influenced by SNE were also controlled by ***15 affected antioxidant abilities of the ileum and controlled SNE-induced mitochondrion-mediated apoptosis by positively changing contents and/or mRNA expression levels of apoptosis-related ***

关键词： Subclinical necrotic enteritis Lactobacillus johnsonii intestinal immunity probiotic broiler

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