We study the qualitative behavior of a class of predator-prey models with Beddington-DeAngelis-type functional response, primarily from the viewpoint of permanence (uniform persistence). The Beddington-DeAngelis functional response is similar to the Holling type-II functional response but contains a term describing mutual interference by predators. We establish criteria under which we have boundedness of solutions, existence of an attracting set, and global stability of the coexisting interior equilibrium via Lyapunov function.
{"title":"Boundedness and Global Stability for a Predator-Prey System with the Beddington-DeAngelis Functional Response","authors":"Wahiba Khellaf, N. Hamri","doi":"10.1155/2010/813289","DOIUrl":"https://doi.org/10.1155/2010/813289","url":null,"abstract":"We study the qualitative behavior of a class of predator-prey models with Beddington-DeAngelis-type functional response, primarily from the viewpoint of permanence (uniform persistence). The Beddington-DeAngelis functional response is similar to the Holling type-II functional response but contains a term describing mutual interference by predators. We establish criteria under which we have boundedness of solutions, existence of an attracting set, and global stability of the coexisting interior equilibrium via Lyapunov function.","PeriodicalId":30100,"journal":{"name":"Differential Equations and Nonlinear Mechanics","volume":"2010 1","pages":"1-24"},"PeriodicalIF":0.0,"publicationDate":"2010-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2010/813289","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64248296","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We provide an alternate representation to the result that the Lie algebra of generators of the system of n differential equations, (ya)″=0, is isomorphic to the Lie algebra of the special linear group of order (n
{"title":"Another Representation for the Maximal Lie Algebra of sl(n","authors":"T. Feroze, A. Qadir","doi":"10.1155/2009/152698","DOIUrl":"https://doi.org/10.1155/2009/152698","url":null,"abstract":"We provide an alternate representation to the result that the Lie algebra of generators of the system of n differential equations, (ya)″=0, is isomorphic to the Lie algebra \u0000of the special linear group of order (n","PeriodicalId":30100,"journal":{"name":"Differential Equations and Nonlinear Mechanics","volume":"2009 1","pages":"1-3"},"PeriodicalIF":0.0,"publicationDate":"2009-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2009/152698","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64186798","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The oscillation susceptibility of the ADMIRE aircraft along the path of longitudinal flight equilibriums is analyzed numerically in the general and in a simplified flight model. More precisely, the longitudinal flight equilibriums, the stability of these equilibriums, and the existence of bifurcations along the path of these equilibriums are researched in both models. Maneuvers and appropriate piloting tasks for the touch-down moment are simulated in both models. The computed results obtained in the models are compared in order to see if the movement concerning the landing phase computed in the simplified model is similar to that computed in the general model. The similarity we find is not a proof of the structural stability of the simplified system, what as far we know never been made, but can increase the confidence that the simplified system correctly describes the real phenomenon.
{"title":"Oscillation Susceptibility Analysis of the ADMIRE Aircraft along the Path of Longitudinal Flight Equilibriums in Two Different Mathematical Models","authors":"S. Balint, A. Balint, A. Ionita","doi":"10.1155/2009/842656","DOIUrl":"https://doi.org/10.1155/2009/842656","url":null,"abstract":"The oscillation susceptibility of the ADMIRE aircraft along the path of longitudinal flight equilibriums is analyzed numerically in the general and in a simplified flight model. More precisely, the longitudinal flight equilibriums, the stability of these equilibriums, and the existence of bifurcations along the path of these equilibriums are researched in both models. Maneuvers and appropriate piloting tasks for the touch-down moment are simulated in both models. The computed results obtained in the models are compared in order to see if the movement concerning the landing phase computed in the simplified model is similar to that computed in the general model. The similarity we find is not a proof of the structural stability of the simplified system, what as far we know never been made, but can increase the confidence that the simplified system correctly describes the real phenomenon.","PeriodicalId":30100,"journal":{"name":"Differential Equations and Nonlinear Mechanics","volume":"9 1","pages":"1-26"},"PeriodicalIF":0.0,"publicationDate":"2009-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2009/842656","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64209399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A perturbing nonlinear Schrodinger equation is studied under general complex nonhomogeneities and complex initial conditions for zero boundary conditions. The perturbation method together with the eigenfunction expansion and variational parameters methods are used to introduce an approximate solution for the perturbative nonlinear case for which a power series solution is proved to exist. Using Mathematica, the symbolic solution algorithm is tested through computing the possible approximations under truncation procedures. The method of solution is illustrated through case studies and figures.
{"title":"On Perturbative Cubic Nonlinear Schrodinger Equations under Complex Nonhomogeneities and Complex Initial Conditions","authors":"M. El-Tawil, Maha A. El-Hazmy","doi":"10.1155/2009/395894","DOIUrl":"https://doi.org/10.1155/2009/395894","url":null,"abstract":"A perturbing nonlinear Schrodinger equation is studied under general complex nonhomogeneities and complex initial conditions for zero boundary conditions. The perturbation method together with the eigenfunction expansion and variational parameters methods are used to introduce an approximate solution for the perturbative nonlinear case for which a power series solution is proved to exist. Using Mathematica, the symbolic solution algorithm is tested through computing the possible approximations under truncation procedures. The method of solution is illustrated through case studies and figures.","PeriodicalId":30100,"journal":{"name":"Differential Equations and Nonlinear Mechanics","volume":"2009 1","pages":"1-29"},"PeriodicalIF":0.0,"publicationDate":"2009-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2009/395894","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64195536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Direct solution of a class of -order initial value problems (IVPs) is considered based on the homotopy analysis method (HAM). The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of the series solutions. The HAM gives approximate analytical solutions which are of comparable accuracy to the seven- and eight-order Runge-Kutta method (RK78).
{"title":"Direct Solution of -Order IVPs by Homotopy Analysis Method","authors":"A. Bataineh, M. Noorani, I. Hashim","doi":"10.1155/2009/842094","DOIUrl":"https://doi.org/10.1155/2009/842094","url":null,"abstract":"Direct solution of a class of -order initial value problems (IVPs) is considered based on the homotopy analysis method (HAM). The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of the series solutions. The HAM gives approximate analytical solutions which are of comparable accuracy to the seven- and eight-order Runge-Kutta method (RK78).","PeriodicalId":30100,"journal":{"name":"Differential Equations and Nonlinear Mechanics","volume":"2009 1","pages":"842094"},"PeriodicalIF":0.0,"publicationDate":"2009-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2009/842094","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64209385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The combined effects of a uniform vertical magnetic field and a nonuniform basic temperature profile on the onset of steady Marangoni convection in a horizontal layer of micropolar fluid are studied. The closed-form expression for the Marangoni number for the onset of convection, valid for polynomial-type basic temperature profiles upto a third order, is obtained by the use of the single-term Galerkin technique. The critical conditions for the onset of convection have been presented graphically.
{"title":"Effects of Magnetic Field and Nonlinear Temperature Profile on Marangoni Convection in Micropolar Fluid","authors":"M. Mahmud, Ruwaidiah Idris, I. Hashim","doi":"10.1155/2009/748794","DOIUrl":"https://doi.org/10.1155/2009/748794","url":null,"abstract":"The combined effects of a uniform vertical magnetic field and a nonuniform basic temperature profile on the onset of steady Marangoni convection in a horizontal layer of micropolar fluid are studied. The closed-form expression for the Marangoni number for the onset of convection, valid for polynomial-type basic temperature profiles upto a third order, is obtained by the use of the single-term Galerkin technique. The critical conditions for the onset of convection have been presented graphically.","PeriodicalId":30100,"journal":{"name":"Differential Equations and Nonlinear Mechanics","volume":"2009 1","pages":"748794"},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2009/748794","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64206180","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This work is interested in the study of the passage of a long gravity wave above an immersed vertical barrier. The latter is placed at a right angle in the middle of the occupied fluid domain which is limited vertically by both a free surface and an impermeable horizontal bottom. We want to determine the field velocity and the local disturbances in the vicinity of the barrier. For this, we use the generalized theory of shallow water and complex variables method. For illustration, we consider a solitary wave as an emitted long wave.
{"title":"Numerical Simulation of the Field Velocities and Local Disturbances of a Long Gravity Wave Passing above an Immersed Vertical Barrier","authors":"Laouar Abdelhamid, Guerziz Allaoua","doi":"10.1155/2008/135982","DOIUrl":"https://doi.org/10.1155/2008/135982","url":null,"abstract":"This work is interested in the study of the passage of a long gravity wave above an immersed vertical barrier. The latter is placed at a right angle in the middle of the occupied fluid domain which is limited vertically by both a free surface and an impermeable horizontal bottom. We want to determine the field velocity and the local disturbances in the vicinity of the barrier. For this, we use the generalized theory of shallow water and complex variables method. For illustration, we consider a solitary wave as an emitted long wave.","PeriodicalId":30100,"journal":{"name":"Differential Equations and Nonlinear Mechanics","volume":"2008 1","pages":"1-11"},"PeriodicalIF":0.0,"publicationDate":"2008-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2008/135982","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64161627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The least-squares finite element method (LSFEM) has received increasing attention in recent years due to advantages over the Galerkin finite element method (GFEM). The method leads to a minimization problem in the -norm and thus results in a symmetric and positive definite matrix, even for first-order differential equations. In addition, the method contains an implicit streamline upwinding mechanism that prevents the appearance of oscillations that are characteristic of the Galerkin method. Thus, the least-squares approach does not require explicit stabilization and the associated stabilization parameters required by the Galerkin method. A new approach, the bubble enriched least-squares finite element method (BELSFEM), is presented and compared with the classical LSFEM. The BELSFEM requires a space-time element formulation and employs bubble functions in space and time to increase the accuracy of the finite element solution without degrading computational performance. We apply the BELSFEM and classical least-squares finite element methods to benchmark problems for 1D and 2D linear transport. The accuracy and performance are compared.
{"title":"Bubble-Enriched Least-Squares Finite Element Method for Transient Advective Transport","authors":"Rajeev Kumar, B. Dennis","doi":"10.1155/2008/267454","DOIUrl":"https://doi.org/10.1155/2008/267454","url":null,"abstract":"The least-squares finite element method (LSFEM) has received increasing attention in recent years due to advantages over the Galerkin finite element method (GFEM). The method leads to a minimization problem in the -norm and thus results in a symmetric and positive definite matrix, even for first-order differential equations. In addition, the method contains an implicit streamline upwinding mechanism that prevents the appearance of oscillations that are characteristic of the Galerkin method. Thus, the least-squares approach does not require explicit stabilization and the associated stabilization parameters required by the Galerkin method. A new approach, the bubble enriched least-squares finite element method (BELSFEM), is presented and compared with the classical LSFEM. The BELSFEM requires a space-time element formulation and employs bubble functions in space and time to increase the accuracy of the finite element solution without degrading computational performance. We apply the BELSFEM and classical least-squares finite element methods to benchmark problems for 1D and 2D linear transport. The accuracy and performance are compared.","PeriodicalId":30100,"journal":{"name":"Differential Equations and Nonlinear Mechanics","volume":"2008 1","pages":"267454"},"PeriodicalIF":0.0,"publicationDate":"2008-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2008/267454","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64165861","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The time evolution of the multispecies Lotka-Volterra system is investigated by the homotopy analysis method (HAM). The continuous solution for the nonlinear system is given, which provides a convenient and straightforward approach to calculate the dynamics of the system. The HAM continuous solution generated by polynomial base functions is of comparable accuracy to the purely numerical fourth-order Runge-Kutta method. The convergence theorem for the three-dimensional case is also given.
{"title":"Series solution of the multispecies Lotka-Volterra equations by means of the homotopy analysis method","authors":"A. Bataineh, M. Noorani, I. Hashim","doi":"10.1155/2008/816787","DOIUrl":"https://doi.org/10.1155/2008/816787","url":null,"abstract":"The time evolution of the multispecies Lotka-Volterra system is investigated by the homotopy analysis method (HAM). The continuous solution for the nonlinear system is given, which provides a convenient and straightforward approach to calculate the dynamics of the system. The HAM continuous solution generated by polynomial base functions is of comparable accuracy to the purely numerical fourth-order Runge-Kutta method. The convergence theorem for the three-dimensional case is also given.","PeriodicalId":30100,"journal":{"name":"Differential Equations and Nonlinear Mechanics","volume":"103 1","pages":"816787"},"PeriodicalIF":0.0,"publicationDate":"2008-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2008/816787","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64181202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The homotopy analysis method (HAM) is applied to obtain the approximate traveling wave solutions of the coupled Whitham-Broer-Kaup (WBK) equations in shallow water. Comparisons are made between the results of the proposed method and exact solutions. The results show that the homotopy analysis method is an attractive method in solving the systems of nonlinear partial differential equations.
{"title":"Approximate Traveling Wave Solutions of Coupled Whitham-Broer-Kaup Shallow Water Equations by Homotopy Analysis Method","authors":"Mohammad Mehdi Rashidi, D. Ganji, S. Dinarvand","doi":"10.1155/2008/243459","DOIUrl":"https://doi.org/10.1155/2008/243459","url":null,"abstract":"The homotopy analysis method (HAM) is applied to obtain the approximate traveling wave solutions of the coupled Whitham-Broer-Kaup (WBK) equations in shallow water. Comparisons are made between the results of the proposed method and exact solutions. The results show that the homotopy analysis method is an attractive method in solving the systems of nonlinear partial differential equations.","PeriodicalId":30100,"journal":{"name":"Differential Equations and Nonlinear Mechanics","volume":"2008 1","pages":"1-8"},"PeriodicalIF":0.0,"publicationDate":"2008-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2008/243459","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64164997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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