global stability of an hiv 1 infection model with saturation infection and intracellular delay in this paper an hiv 1 infection model with a saturation infection rate and an intracellular delay accounting for the time between viral entry into a target cell and the production of new virus particles is investigated by analyzing the characteristic equations the local stability of an infection free equilibrium and a chronic infection equilibrium of the model is established by using suitable lyapunov functionals and the lasalle invariant principle it is proved that if the basic reproduction ratio is less than unity the infection free equilibrium is globally asymptotically stable if the basic reproduction ratio is greater than unity the chronic infection equilibrium is globally asymptotically stable

analysis of the dynamics of a delayed hiv pathogenesis model in this paper considering full logistic proliferation of cd4 t cells we study an hiv pathogenesis model with antiretroviral therapy and hiv replication time we first analyze the existence and stability of the equilibrium and then investigate the effect of the time delay on the stability of the infected steady state sufficient conditions are given to ensure that the infected steady state is asymptotically stable for all delay furthermore we apply the nyquist criterion to estimate the length of delay for which stability continues to hold and investigate the existence of hopf bifurcation by using a delay t as a bifurcation parameter finally numerical simulations are presented to illustrate the main results

dynamics of virus infection models with density dependent diffusion abstract density dependent diffusion plays an important role in the process of viral infection in this paper we construct mathematical models to investigate the dynamics of the viruses and their control single strain and multi strain viral infections are both considered in this work using the method proposed by pao and ruan 2013 we prove the well posedness of the models by constructing appropriate lyapunov functions we proved the global asymptotical stabilities of the models for the multi strain model we show that when the basic reproduction number for each strain is greater than one all viral strains coexist since the effect of different treatments may result in competitive exclusion it is essential to employ the treatment with combined therapy we find with surprise that the density dependent diffusion of the virus does not influence the global stabilities of the model with homogeneous neumann boundary conditions

principal component analysis based on l1 norm maximization a method of principal component analysis pca based on a new l1 norm optimization technique is proposed unlike conventional pca which is based on l2 norm the proposed method is robust to outliers because it utilizes l1 norm which is less sensitive to outliers it is invariant to rotations as well the proposed l1 norm optimization technique is intuitive simple and easy to implement it is also proven to find a locally maximal solution the proposed method is applied to several datasets and the performances are compared with those of other conventional methods

global qualitative analysis for a ratio dependent predator prey model with delay abstract a ratio dependent predator prey model with time lag for predator is proposed and analyzed mathematical analyses of the model equations with regard to boundedness of solutions nature of equilibria permanence and stability are analyzed we note that for a ratio dependent system local asymptotic stability of the positive steady state does not even guarantee the so called persistence of the system and therefore does not imply global asymptotic stability it is found that an orbitally asymptotically stable periodic orbit exists in that model some sufficient conditions which guarantee the global stability of positive equilibrium are given

threshold dynamics of a delayed nonlocal reaction diffusion hiv infection model with both cell free and cell to cell transmissions abstract in this paper we derive and analyze an hiv infection model containing a fixed latent period and both cell free and cell to cell transmissions the model is described by a spatially non local reaction diffusion system with the zero flux condition on the boundary we first show that the model admits global solutions and possesses a global attractor following the definition of the next infection operator we obtain the expression of the basic reproduction number 0 which is shown as a threshold parameter for the model dynamics our results indicate that the clearance persistence of hiv is governed by the sign of 0 1 in particular an explicit formula of 0 is given in the homogeneous case

a stochastic model for internal hiv dynamics in this paper we analyse a stochastic model representing hiv internal virus dynamics the stochasticity in the model is introduced by parameter perturbation which is a standard technique in stochastic population modelling we show that the model established in this paper possesses non negative solutions as this is essential in any population dynamics model we also carry out analysis on the asymptotic behaviour of the model we approximate one of the variables by a mean reverting process and find out the mean and variance of this process numerical simulations conclude the paper

a differential equation model of hiv infection of cd4 t cells with cure rate abstract a differential equation model of hiv infection of cd4 t cells with cure rate is studied we prove that if the basic reproduction number r 0 1 the hiv infection is cleared from the t cell population and the disease dies out if r 0 1 the hiv infection persists in the host we find that the chronic disease steady state is globally asymptotically stable if r 0 1 furthermore we also obtain the conditions for which the system exists an orbitally asymptotically stable periodic solution numerical simulations are presented to illustrate the results

classification of integrable hydrodynamic chains and generating functions of conservation laws a new approach to classification of integrable hydrodynamic chains is established generating functions of conservation laws are classified by the method of hydrodynamic reductions the n parametric family of explicit hydrodynamic reductions allows us to reconstruct corresponding hydrodynamic chains many new hydrodynamic chains are found

hydrodynamic chains and the classification of their poisson brackets infinite component poisson brackets of the dubrovin novikov type sov math dokl 27 665 669 1983 are considered the corresponding jacobi identity is significantly simplified in the liouville coordinates since the skew symmetry condition is automatically satisfied the concept of m poisson bracket connected with hydrodynamic chains is introduced then the jacobi identity is a nonlinear system of equations in partial derivatives which can be completely integrated in such a case a classification of infinite component poisson brackets of the dubrovin novikov type can be obtained two simplest examples m 0 and m 1 are considered also infinite component poisson brackets of the ferapontov am math soc transl 170 38 58 1995 type can be simplified in the liouville coordinates the jacobi identity for infinite component poisson brackets of the ferapontov mokhov type russ math surveys 45 218 219 1990 is presented in the liouville coordinates

asymptotic behaviors of a cell to cell hiv 1 infection model perturbed by white noise abstract in this paper we analyze a mathematical model of cell to cell hiv 1 infection to c d 4 t cells perturbed by stochastic perturbations first of all we investigate that there exists a unique global positive solution of the system for any positive initial value then by using lyapunov analysis methods we study the asymptotic property of this solution moreover we discuss whether there is a stationary distribution for this system and if it owns the ergodic property numerical simulations are presented to illustrate the theoretical results

reductions and hodograph solutions of the dispersionless kp hierarchy a general scheme for analysing reductions of dispersionless integrable hierarchies is presented it is based on a method for determining the s function by means of a system of first order differential equations compatibility systems of nonlinear partial differential equations of bourlet type characterizing both reductions and hodograph solutions of the dkp hierarchy are obtained wide classes of illustrative explicit examples are exhibited

classical r matrix theory for bi hamiltonian field systems this is a survey of the application of the classical r matrix formalism to the construction of infinite dimensional integrable hamiltonian field systems the main point is the study of bi hamiltonian structures appropriate constructions on poisson noncommutative and loop algebras as well as the central extension procedure are presented the theory is developed for 1 1 and 2 1 dimensional field and lattice soliton systems as well as hydrodynamic systems the formalism presented contains sufficiently many proofs and important details to make it self contained and complete the general theory is applied to several infinite dimensional lie algebras in order to construct both dispersionless and dispersive soliton integrable field systems

on the integrability of 2 1 dimensional quasilinear systems a 2 1 dimensional quasilinear system is said to be integrable if it can be decoupled in infinitely many ways into a pair of compatible n component one dimensional systems in riemann invariants exact solutions described by these reductions known as nonlinear interactions of planar simple waves can be viewed as natural dispersionless analogues of n gap solutions it is demonstrated that the requirement of the existence of sufficiently many n component reductions provides the effective classification criterion as an example of this approach we classify integrable 2 1 dimensional systems of conservation laws possessing a convex quadratic entropy

efficient computation of robust weighted low rank matrix approximations using the l_1 norm the calculation of a low rank approximation to a matrix is fundamental to many algorithms in computer vision and other fields one of the primary tools used for calculating such low rank approximations is the singular value decomposition but this method is not applicable in the case where there are outliers or missing elements in the data unfortunately this is often the case in practice we present a method for low rank matrix approximation which is a generalization of the wiberg algorithm our method calculates the rank constrained factorization which minimizes the l1 norm and does so in the presence of missing data this is achieved by exploiting the differentiability of linear programs and results in an algorithm can be efficiently implemented using existing optimization software we show the results of experiments on synthetic and real data

limit cycles for competitor competitor mutualist lotka volterra systems abstract it is known that a limit cycle or periodic coexistence can occur in a competitor competitor mutualist lotka volterra system x 1 x 1 r 1 a 11 x 1 a 12 x 2 a 13 x 3 x 2 x 2 r 2 a 21 x 1 a 22 x 2 a 23 x 3 x 3 x 3 r 3 a 31 x 1 a 32 x 2 a 33 x 3 where r i a i j are positive real constants x liang j jiang the dynamical behavior of type k competitive kolmogorov systems and its applications to 3 dimensional type k competitive lotka volterra systems nonlinearity 16 2003 785 801 in this paper we shall construct an example with at least two limit cycles and furthermore we will show that the number of periodic orbits and hence a fortiori of limit cycles is finite it is also shown that contrary to three dimensional competitive lotka volterra systems nontrivial periodic coexistence does occur even if none of the three species can resist invasion from either of the others in this case new amenable conditions are given on the coefficients under which the system has no nontrivial periodic orbits these conditions imply that the positive equilibrium if it exists is globally asymptotically stable

dynamics of the modified michaelis menten system abstract the theory of cooperative and competitive systems is used to study the dynamical behaviour of the modified michaelis menten system conditions for convergence to equilibria and existence of stable closed orbits are given improving previous results obtained in r a smith some modified michaelis menten equations having stable closed orbits proc roy soc edinburgh sect a 109 1988 341 359

differential geometric approach to the integrability of hydrodynamic chains the haantjes tensor the integrability of an m component system of hydrodynamic type u t v u u x by the generalized hodograph method requires the diagonalizability of the m m matrix v u this condition is known to be equivalent to the vanishing of the corresponding haantjes tensor we generalize this approach to hydrodynamic chains infinite component systems of hydrodynamic type for which the matrix v u is sufficiently sparse for such systems the haantjes tensor is well defined and the calculation of its components involves finite summations only we illustrate our approach by classifying broad classes of conservative and hamiltonian hydrodynamic chains with the zero haantjes tensor we prove that the vanishing of the haantjes tensor is a necessary condition for a hydrodynamic chain to possess an infinity of semi hamiltonian hydrodynamic reductions thus providing an easy to verify necessary condition for the integrability

asymptotic properties of a hiv 1 infection model with time delay based on some important biological meanings a class of more general hiv 1 infection models with time delay is proposed in the paper in the hiv 1 infection model time delay is used to describe the time between infection of uninfected target cells and the emission of viral particles on a cellular level as proposed by herz et al a v m herz s bonhoeffer r m anderson r m may m a nowak viral dynamics in vivo limitations on estimates of intracellular delay and virus decay proc natl acad sci usa 93 1996 7247 7251 then the effect of time delay on stability of the equilibria of the hiv 1 infection model has been studied and sufficient criteria for local asymptotic stability of the infected equilibrium and global asymptotic stability of the viral free equilibrium are given

global properties for virus dynamics model with mitotic transmission and intracellular delay abstract in this paper we study the basic model of viral infections with mitotic transmission and intracellular delay discrete the delay corresponds to the time between infection of uninfected cells and the emission of virus on a cellular level by means of volterra type lyapunov functionals we provide the global stability for this model let be the number of virus produced per infected cell if crit the critical number satisfies crit then the virus free steady state is globally asymptotically stable on the contrary if crit then the infected steady state is globally asymptotically stable if a sufficient condition is satisfied

robust matrix factorization by majorization minimization l 1 norm based low rank matrix factorization in the presence of missing data and outliers remains a hot topic in computer vision due to non convexity and non smoothness all the existing methods either lack scalability or robustness or have no theoretical guarantee on convergence in this paper we apply the majorization minimization technique to solve this problem at each iteration we upper bound the original function with a strongly convex surrogate by minimizing the surrogate and updating the iterates accordingly the objective function has sufficient decrease which is stronger than just being non increasing that other methods could offer as a consequence without extra assumptions we prove that any limit point of the iterates is a stationary point of the objective function in comparison other methods either do not have such a convergence guarantee or require extra critical assumptions extensive experiments on both synthetic and real data sets testify to the effectiveness of our algorithm the speed of our method is also highly competitive

hamiltonian formalism of whitham type hierarchies and topological landau ginsburg models we show that the bi hamiltonian structure of the averaged gelfand dikii hierarchy is involved in the landau ginsburg topological models fora n series the casimirs for the first p b give the correct coupling parameters for the perturbed topological minimal model the correspondence coupling parameters primary fields is determined by the second p b the partition function at the tree level and the chiral algebra for lg models are calculated for any genusg

s functions reductions and hodograph solutions of the rth dispersionless modified kp and dym hierarchies we introduce an s function formulation for the recently found rth dispersionless modified kp and rth dispersionless dym hierarchies giving also a connection of these s functions with the orlov functions of the hierarchies then we discuss a reduction scheme for the hierarchies that together with the s function formulation leads to hodograph systems for the associated solutions we consider also the connection of these reductions with those of the dispersionless kp hierarchy and with hydrodynamic type systems in particular for the one component and two component reduction we derive for both hierarchies ample sets of examples of explicit solutions

global stability and periodic solution of a model for hiv infection of cd4 t cells abstract it is well known that the mathematical models provide very important information for the research of human immunodeficiency virus type 1 and hepatitis c virus hcv however the infection rate of almost all mathematical models is linear the linearity shows the simple interaction between the t cells and the viral particles in this paper we consider the classical mathematical model with non linear infection rate the global dynamics of this model is rigorously established we prove that if the basic reproduction number r 0 1 the hiv infection is cleared from the t cells population if r 0 1 the hiv infection persists further the existence of a non trivial periodic solution is also studied by means of numerical simulation

robust dlpp with nongreedy ell _1 norm minimization and maximization recently discriminant locality preserving projection based on l1 norm dlpp l1 was developed for robust subspace learning and image classification it obtains projection vectors by greedy strategy i e all projection vectors are optimized individually through maximizing the objective function thus the obtained solution does not necessarily best optimize the corresponding trace ratio optimization algorithm which is the essential objective function for general dimensionality reduction it results in insufficient recognition accuracy to tackle this problem we propose a nongreedy algorithm to solve the trace ratio formula of dlpp l1 and analyze its convergence experimental results on three databases illustrate the effectiveness of our proposed algorithm

robust l1 principal component analysis and its bayesian variational inference we introduce a robust probabilistic l1 pca model in which the conventional gaussian distribution for the noise in the observed data was replaced by the laplacian distribution or l1 distribution due to the heavy tail characteristics of the l1 distribution the proposed model is supposed to be more robust against data outliers in this letter we demonstrate how a variational approximation scheme enables effective inference of key parameters in the probabilistic l1 pca model as the l1 density can be expanded as a superposition of infinite number of gaussian densities we express the l1 pca model as a marginalized model over the superpositions by doing so a tractable bayesian inference can be achieved based on the variational expectation maximization type algorithm

the approach to the dispersionless kp hierarchy the dispersionless limit of the scalar nonlocal problem is derived it is given by a special class of nonlinear first order equations a quasiclassical version of the dressing method is presented it is shown that the algebraic formulation of dispersionless hierarchies can be expressed in terms of properties of beltrami type equations the universal whitham hierarchy and in particular the dispersionless kp hierarchy turn out to be rings of symmetries for the quasiclassical problem pacs number 02 30 uk

global stability and hopf bifurcation of an hiv 1 infection model with saturation incidence and delayed ctl immune response abstract in this paper an hiv 1 infection model with saturation incidence and time delay due to the ctl immune response is investigated by analyzing corresponding characteristic equations the local stability of each of feasible equilibria and the existence of hopf bifurcation at the ctl activated infection equilibrium are established respectively by means of lyapunov functionals and lasalle s invariance principle it is shown that the infection free equilibrium is globally asymptotically stable when the basic reproduction ratio is less than unity when the immune response reproductive ratio is less than unity and the basic reproductive ratio is greater than unity the ctl inactivated infection equilibrium of the system is globally asymptotically stable

threshold dynamics of hiv 1 virus model with cell to cell transmission cell mediated immune responses and distributed delay we study the problem of global asymptotic stability for equilibria of a hiv 1 virus model we broaden the construction method into the viral model with infinite distributed delay and cell to cell transmission respectively numerical examples are given to illustrate the effectiveness of the theoretical results for sharp threshold property the goal of this paper is to study the threshold dynamics of an hiv 1 viral infection model with cell mediated immune responses and direct cell to cell transmission mechanism the model demonstrates global threshold dynamics with respect to the reproductive numbers for viral infection 0 and for ctl immune response 1 the proofs of main results come from suitable uses of analyzing the characteristic equation and constructing lyapunov functionals specifically if 0 1 the ctl activated equilibrium e2 is locally and globally asymptotically stable and the infection is chronic with persistent ctls response numerical simulations are performed to support our results

the dispersionless lax equations and topological minimal models it is shown that perturbed rings of the primary chiral fields of the topological minimal models coincide with some particular solutions of the dispersionless lax equations the exact formulae for the tree level partition functions of an topological minimal models are found the virasoro constraints for the analogue of the function of the dispersionless lax equation correspond ing to these models are proved

dynamics of a diffusive virus model with general incidence function cell to cell transmission and time delay abstract in this paper we revisit a diffusive virus dynamics model with general incidence function and time delay one novelty of our model is that we introduce cell to cell transmission via formation of virological synapses to reflect the fact that it may play a more important role in virus spreading in addition to virus to cell infection we justify the well posedness of the model and identify the basic reproduction number 0 for the model to be a sharp threshold value the global stability of equilibria is determined by constructing suitable lyapunov functionals in the sense that the infection free equilibrium is globally asymptotically stable if 0 1 and when 0 1 the global asymptotic stability of infection equilibrium implies that the infection will persist a significant impact of the cell to cell transmission is that they increase the basic reproduction number if one neglects either the cell to cell transmission or virus to cell infection the basic reproduction number of the model that is under evaluated last we perform numerical simulation to support our theoretic results we set the domain of the viruses to be a two dimensional square domain with the homogeneous neumann boundary conditions to reflect the spatial spreading

stability in a predator prey model with crowley martin function and stage structure for prey abstract this paper is concerned with a stage structured predator prey system with crowley martin functional response by analyzing the characteristic equation the local stability of the equilibria is investigated the persistence of system and global asymptotic stability of the positive equilibrium are carried out finally several numerical simulations to illustrate the theoretical analysis are also given

global stability of a diffusive and delayed virus dynamics model with beddington deangelis incidence function and ctl immune response in this paper we study a diffusive and delayed virus dynamics model with beddington deangelis incidence and ctl immune response by constructing lyapunov functionals we show that if the basic reproductive number is less than or equal to one then the infection free equilibrium is globally asymptotically stable if the immune reproductive number is less than or equal to one and the basic reproductive number is greater than one then the immune free equilibrium is globally asymptotically stable if the immune reproductive number is greater than one then the interior equilibrium is globally asymptotically stable

on local description of two dimensional geodesic flows with a polynomial first integral in this paper we present a construction of multiparametric families of two dimensional metrics with a polynomial first integral of arbitrary degree in momenta such integrable geodesic flows are described by solutions of some semi hamiltonian hydrodynamic type system we give a constructive algorithm for the solution of the derived hydrodynamic type system i e we found infinitely many conservation laws and commuting flows thus we were able to find infinitely many particular solutions of this hydrodynamic type system by the generalized hodograph method therefore infinitely many particular two dimensional metrics equipped with first integrals polynomial in momenta were constructed

global stability for a delayed hiv 1 infection model with nonlinear incidence of infection abstract in this paper a delayed hiv 1 infection model with nonlinear incidence of infection is reinvestigated it is shown that if the reproduction number r 1 then the system is permanent and the infective equilibrium of the system is globally asymptotically stable thus the global dynamics of the system is completely determined by the reproduction number r the results obtained enrich and improve the corresponding results given by wang et al x wang y tao x song a delayed hiv 1 infection model with beddington deangelis functional response nonlinear dynamics 62 2010 67 72 the conclusions we established also verify the numerical simulation results on the global asymptotic stability of the infective equilibrium in the paper d li w ma asymptotic properties of an hiv 1 infection model with time delay j math anal appl 335 2007 683 691

efficient l_ 1 norm based low rank matrix approximations for large scale problems using alternating rectified gradient method low rank matrix approximation plays an important role in the area of computer vision and image processing most of the conventional low rank matrix approximation methods are based on the l 2 norm frobenius norm with principal component analysis pca being the most popular among them however this can give a poor approximation for data contaminated by outliers including missing data because the l 2 norm exaggerates the negative effect of outliers recently to overcome this problem various methods based on the l 1 norm such as robust pca methods have been proposed for low rank matrix approximation despite the robustness of the methods they require heavy computational effort and substantial memory for high dimensional data which is impractical for real world problems in this paper we propose two efficient low rank factorization methods based on the l 1 norm that find proper projection and coefficient matrices using the alternating rectified gradient method the proposed methods are applied to a number of low rank matrix approximation problems to demonstrate their efficiency and robustness the experimental results show that our proposals are efficient in both execution time and reconstruction performance unlike other state of the art methods

on jack hale s problem for impulsive systems abstract an interesting problem of jack hale deals with the existence of a maximal compact invariant set in discrete dynamical systems a solution for this problem is known for locally bounded dynamical systems following this line of research we consider in this paper a class of systems whose continuous dynamics are interrupted by abrupt changes of state and we present sufficient conditions to obtain the existence of a maximal compact invariant set for a system in this class we use the theory of asymptotic compactness to get the results

classification of integrable hamiltonian hydrodynamic chains associated with kupershmidt s brackets we characterize a class of integrable hamiltonian hydrodynamic chains based on the necessary condition for the integrability provided by the vanishing of the haantjes tensor we prove that the vanishing of the first few components of the haantjes tensor is already sufficiently restrictive and allows a complete description of the corresponding hamiltonian densities in each of the cases we were able to explicitly construct a generating function for conservation laws thus establishing the integrability

asymptotic behavior of a stochastic delayed hiv 1 infection model with nonlinear incidence abstract in this paper a stochastic delayed hiv 1 infection model with nonlinear incidence is proposed and investigated first of all we prove that there is a unique global positive solution as desired in any population dynamics then by constructing some suitable lyapunov functions we show that if the basic reproduction number r 0 1 then the solution of the stochastic system oscillates around the infection free equilibrium e 0 while if r 0 1 then the solution of the stochastic system fluctuates around the infective equilibrium e sufficient conditions of these results are established finally we give some examples and a series of numerical simulations to illustrate the analytical results

the τ function of the universal whitham hierarchy matrix models and topological field theories the universal witham hierarchy is considered from the point of view of topological field theories the function for this hierarchy is defined it is proved that the algebraic orbits of whitham hierarchy can be identified with various topological matter models coupled with topological gravity

bayesian robust principal component analysis a hierarchical bayesian model is considered for decomposing a matrix into low rank and sparse components assuming the observed matrix is a superposition of the two the matrix is assumed noisy with unknown and possibly non stationary noise statistics the bayesian framework infers an approximate representation for the noise statistics while simultaneously inferring the low rank and sparse outlier contributions the model is robust to a broad range of noise levels without having to change model hyperparameter settings in addition the bayesian framework allows exploitation of additional structure in the matrix for example in video applications each row or column corresponds to a video frame and we introduce a markov dependency between consecutive rows in the matrix corresponding to consecutive frames in the video the properties of this markov process are also inferred based on the observed matrix while simultaneously denoising and recovering the low rank and sparse components we compare the bayesian model to a state of the art optimization based implementation of robust pca considering several examples we demonstrate competitive performance of the proposed model

robust elastic net subspace representation recently finding the low dimensional structure of high dimensional data has gained much attention given a set of data points sampled from a single subspace or a union of subspaces the goal is to learn or capture the underlying subspace structure of the data set in this paper we propose elastic net subspace representation a new subspace representation framework using elastic net regularization of singular values due to the strong convexity enforced by elastic net the proposed method is more stable and robust in the presence of heavy corruptions compared with existing lasso type rank minimization approaches for discovering a single low dimensional subspace we propose a computationally efficient low rank factorization algorithm called facten using a property of the nuclear norm and the augmented lagrangian method then clusten is proposed to handle the general case in which the data samples are drawn from a union of multiple subspaces for joint subspace clustering and estimation the proposed algorithms are applied to a number of subspace representation problems to evaluate the robustness and efficiency under various noisy conditions and experimental results show the benefits of the proposed method compared with existing methods

ordinary differential equations which linearize on differentiation in this paper we discuss ordinary differential equations odes which linearize upon one or more differentiations although the subject is fairly elementary equations of this type arise naturally in the context of integrable systems

the russo smereka kinetic equation conservation laws reductions and numerical solutions abstract the one dimension russo smereka kinetic equation describing the propagation of nonlinear concentration waves in a rarefied bubbly fluid is considered stability of the bubbly flow in terms of hyperbolicity of the kinetic equation is studied it is proved that a hydrodynamical chain associated with the russo smereka kinetic equation possesses infinitely many conservation laws reductions of the model to finite component systems are derived conservative form of the kinetic model is proposed and numerical solution of the cauchy problem with discontinuous initial data is obtained

stable periodic orbits for a predator prey model with delay abstract in this paper we consider a predator prey model with time lag which improves upon that proposed by cavani and farkas 1994 acta math hungar 63 3 213 229 we show that when the model has exactly one non trivial unstable and hyperbolic equilibrium there exists a stable periodic orbit

a model of partial differential equations for hiv propagation in lymph nodes abstract a system of partial differential equations is used to model the dissemination of the human immunodeficiency virus hiv in cd 4 t cells within lymph nodes besides diffusion terms the model also includes a time delay dependence to describe the time lag required by the immunologic system to provide defenses to new virus strains the resulting dynamics strongly depends on the properties of the invariant sets of the model consisting of three fixed points related to the time independent and spatial homogeneous tissue configurations in healthy and infected states a region in the parameter space is considered for which the time dependence of the space averaged model variables follows the clinical pattern reported for infected patients a short scale primary infection followed by a long latency period of almost complete recovery and third phase characterized by damped oscillations around a value with large hiv counting depending on the value of the diffusion coefficient the latency time increases with respect to that one obtained for the space homogeneous version of the model it is found that same initial conditions lead to quite different spatial patterns which depend strongly on the latency interval

associated integrable systems new class of integrable hamiltonian systems is obtained as systems directly defined over jacobi varieties this approach enables one to establish a link between associated discrete and continuous systems in particular regular procedure is found for the discretization of the integrable continuous systems hierarchies of the continuous systems associated with toda lattices relativistic toda lattices and volterra lattices are found and studied

the haantjes tensor and double waves for multi dimensional systems of hydrodynamic type a necessary condition for integrability an invariant differential geometric approach to the integrability of 2 1 dimensional systems of hydrodynamic type is developed we prove that the existence of special solutions known as double waves is equivalent to the diagonalizability of an arbitrary matrix of the two parameter familysince the diagonalizability can be effectively verified by calculating the haantjes tensor this provides a simple necessary condition for integrability

global stability and periodic solution of the viral dynamics it is well known that the mathematical models provide very important information for the research of human immunodeficiency virus type 1 and hepatitis c virus hcv however the infection rate of almost all mathematical models is linear the linearity shows the simple interaction between the t cells and the viral particles in this paper we consider the classical mathematical model with saturation response of the infection rate by stability analysis we obtain sufficient conditions on the parameters for the global stability of the infected steady state and the infection free steady state we also obtain the conditions for the existence of an orbitally asymptotically stable periodic solution numerical simulations are presented to illustrate the results

stability analysis of a virus dynamics model with general incidence rate and two delays the aim of this work is to study the dynamical behavior of a virus dynamics model with general incidence rate and two delays the first delay represents the time from the virus entry to the production of new viruses and the second delay corresponds to the time necessary for a newly produced virus to become infectious lyapunov functionals are constructed and lasalle invariance principle for delay differential equations is used to establish the global asymptotic stability of the disease free and the chronic infection equilibria the results obtained show that the global dynamics are completely determined by the value of a certain threshold parameter called the basic reproduction number r 0 and under some assumptions on the general incidence function our results extend the known results on delay virus dynamics considered in the other papers and suggest useful methods to control virus infection these results can be applied to a variety of possible incidence functions that could be used in virus dynamics model as well as epidemic models

algebro geometric approach in the theory of integrable hydrodynamic type systems the algebro geometric approach for integrability of semi hamiltonian hydrodynamic type systems is presented the class of symmetric hydrodynamic type systems is defined and the calculation of the associated riemann surfaces is greatly simplified for this class many interesting and physically motivated examples are investigated

stable periodic orbits for a class of three dimensional competitive systems abstract it is shown that for a dissipative three dimensional competitive and irreducible system of ordinary differential equations having a unique equilibrium point at which point the jacobian matrix has negative determinant either the equilibrium point is stable or there exists an orbitally stable periodic orbit if in addition the system is analytic then there exists an orbitally asymptotically stable periodic orbit when the equilibrium is unstable the additional assumption of analyticity can be replaced by the assumption that the equilibrium point and every periodic orbit are hyperbolic in this case the morse smale conditions hold and the flow is structurally stable

stability properties and hopf bifurcation of a delayed viral infection model with lytic immune response a class of more general delayed viral infection model with lytic immune response is proposed based on some important biological meanings the effect of time delay on stabilities of the equilibria is given the sufficient criteria for local and global asymptotic stabilities of the viral free equilibrium and the local asymptotic stabilities of the no immune response equilibrium are given we also get the sufficient criteria for stability switch of the positive equilibrium numerical simulations are carried out to explain the mathematical conclusions

a predator prey system with stage structure for predator abstract this paper studies the asymptotoc behavior of a predator prey model with stage structure it is found that an orbitally asymptotically stable periodic orbit exists in that model when time delay due to gestation of predator and time delay from crowding effect of prey are incorporated we establish the condition for the permanence of populations and sufficient conditions under which positive equilibrium of the model is globally stable

the characterization of two component 2 1 dimensional integrable systems of hydrodynamic type we obtain the necessary and sufficient conditions for a two component 2 1 dimensional system of hydrodynamic type to possess infinitely many hydrodynamic reductions these conditions are in involution implying that the systems in question are locally parametrized by 15 arbitrary constants it is proved that all such systems possess three conservation laws of hydrodynamic type and therefore are symmetrizable in godunov s sense moreover all such systems are proved to possess a scalar pseudopotential which plays the role of the dispersionless lax pair we demonstrate that the class of two component systems possessing a scalar pseudopotential is in fact identical with the class of systems possessing infinitely many hydrodynamic reductions thus establishing the equivalence of the two possible definitions of integrability explicit linearly degenerate examples are constructed

four limit cycles for a three dimensional competitive lotka volterra system with a heteroclinic cycle abstract for three dimensional competitive lotka volterra systems zeeman m l zeeman hopf bifurcations in competitive three dimensional lotka volterra systems dynamics and stability of systems 8 1993 189 217 identified 33 stable equivalence classes among these only classes 26 31 may have limit cycles it is known that all these classes may possess two limit cycles and in classes 27 and 29 three limit cycles have been constructed it has been conjectured that the maximum number of limit cycles is three in this paper we disprove the conjecture by constructing four limit cycles in the three dimensional competitive lotka volterra system with a heteroclinic cycle class 27 in zeeman s classification furthermore in the case of a heteroclinic cycle on the boundary of the carrying simplex of three dimensional competitive lotka volterra systems we show that i the conditions a there is a pair of purely imaginary eigenvalues at a positive equilibrium b the first focal values vanishes and c the second focal values vanishes do not imply that the heteroclinic cycle is neutrally stable and hence they do not imply that the interior equilibrium is a center ii the conditions a there is a pair of purely imaginary eigenvalues at a positive equilibrium b the first focal value vanishes and c the heteroclinic cycle is neutrally stable do not imply the second focal value vanishes and hence they do not imply that the interior equilibrium is a center this refutes a conjecture by hofbauer and so j hofbauer j w h so multiple limit cycles for three dimensional lotka volterra equations appl math lett 7 1994 65 70

global dynamics for a class of age infection hiv models with nonlinear infection rate abstract in this paper we study the global stability of a class of hiv viral infection models with continuous age structure using the direct lyapunov method in each of the cases where the incidence rates are given by nonlinear infection rate f t g v holling type ii functional response and crowley martin functional response we define the basic reproduction number and prove that it is a sharp threshold determining whether the infection dies out or not we give a rigorous mathematical analysis on technical materials and necessary arguments including relative compactness of the orbit and uniform persistence of system by reformulating the system as a system of volterra integral equations we further investigate global behaviors of hiv viral infection models with holling type ii functional response and crowley martin functional response through numerical simulations

global dynamics of a predator prey model with stage structure for the predator the global properties of a predator prey model with nonlinear functional response and stage structure for the predator are studied using lyapunov functions and lasalle s invariance principle it is found that under hypotheses which ensure the uniform persistence of the system and the existence of a unique positive steady state a feasible a priori lower bound condition on the abundance of the prey population ensures the global asymptotic stability of the positive steady state a condition which leads to the extinction of the predators is indicated we also obtain results on the existence and stability of periodic solutions in particular when 4 2 fails to hold and the unique positive steady state e becomes unstable the coexistence of prey and predator populations is ensured for initial populations not on the one dimensional stable manifold of e albeit with fluctuating population sizes

existence of periodic orbits for high dimensional autonomous systems abstract we give a result on existence of periodic orbits for autonomous differential systems with arbitrary finite dimension it is based on a poincare bendixson property enjoyed by a new class of monotone systems introduced in l a sanchez cones of rank 2 and the poincare bendixson property for a new class of monotone systems j differential equations 216 2009 1170 1190 a concrete application is done to a scalar differential equation of order 4

global dynamics of a viral infection model with a latent period and beddington deangelis response in this paper we study the global dynamics of a viral infection model with a latent period the model has a nonlinear function which denotes the incidence rate of the virus infection in vivo the basic reproduction number of the virus is identified and it is shown that the uninfected equilibrium is globally asymptotically stable if the basic reproduction number is equal to or less than unity moreover the virus and infected cells eventually persist and there exists a unique infected equilibrium which is globally asymptotically stable if the basic reproduction number is greater than unity the basic reproduction number determines the equilibrium that is globally asymptotically stable even if there is a time delay in the infection

stability analysis of delay differential equation models of hiv 1 therapy for fighting a virus with another virus considering two kinds of delays accounting respectively for i a latent period between the time target cells are contacted by the virus particles and the time the virions enter the cells and ii a virus production period for new virions to be produced within and released from the infected cells we develop and analyze a mathematical model for hiv 1 therapy by fighting a virus with another virus for the different values of the basic reproduction number and the second basic reproduction number we investigate the stability of the infection free equilibrium the single infection equilibrium and the double infection equilibrium we conclude that increasing delays will decrease the values of the basic reproduction number and the second basic reproduction number our results have potential applications in hiv 1 therapy the approach we use here is a combination of analysis of characteristic equations fluctuation lemma and lyapunov function

global stability in a viral infection model with lytic and nonlytic immune responses this paper investigates the global stability of a viral infection model with lytic and nonlytic immune responses if the basic reproductive ratio of the virus is less than or equal to one by the lasalle s invariance principle and center manifold theorem the disease free steady state is globally asymptotically stable if the basic reproductive ratio of the virus is greater than one then the virus persists in the host and the disease steady state is locally asymptotically stable furthermore by the method of lyapunov function the global stability of the disease steady state is established at the same time if we neglect the efficacy of the lytic component using a geometrical approach we obtain a different type of conditions for the global stability of the disease steady state

analysis of stability and hopf bifurcation for an hiv infection model with time delay a class of more general hiv infection models with time delay is proposed based on some important biological meanings the effect of time delay on stability of the equilibria of the infection model has been studied and the sufficient criteria for stability switch of the infected equilibrium and the local and global asymptotic stability of the viral free equilibrium are given using the normal form theory and center manifold argument the explicit formulaes which determine the stability the direction and the periodic of bifurcating period solutions are derived numerical simulations are carried out to explain the mathematical conclusions

modeling and mathematical analysis of an initial boundary value problem for hepatitis b virus infection abstract in this work we investigate the hepatitis b virus infection we first derive a nonlinear pde model for the studied biological phenomenon the obtained initial boundary value problem is completely analyzed to begin with the analysis of the model we use lou and zhao lemma concerning globally attractive steady states to prove boundedness of potential solutions then we prove global existence uniqueness and positivity of the solution by a variational method combined with semigroups theory and some other useful tools from functional analysis moreover the basic reproduction number r 0 determining the extinction or the persistence of the hbv infection is thoroughly computed via a new method based on spectral properties of differential operators the residue theorem and some arguments from numerical analysis also the global asymptotical properties of the hbv free equilibrium of the model are derived via a skillful construction of a suitable lyapunov function local stability of the endemic equilibrium of the model is studied as well finally numerical simulations are performed to support the theoretical results obtained

invariants of a family of third order ordinary differential equations we consider a family of third order ordinary differential equations odes with the cubic nonlinearity in second order derivative which is closed with respect to contact transformations using lie s infinitesimal method we construct the basis of differential invariants for this family of equations and the operators of invariant differentiation invariants provide a simple way of finding the equations which may be equivalent to a given nonlinear ode and the transformation connecting two equivalent equations some examples are given to illustrate the results obtained in the paper

global dynamics of a cell mediated immunity in viral infection models with distributed delays abstract in this paper we investigate global dynamics for a system of delay differential equations which describes a virus immune interaction in vivo the model has two distributed time delays describing time needed for infection of cell and virus replication our model admits three possible equilibria an uninfected equilibrium and infected equilibrium with or without immune response depending on the basic reproduction number for viral infection r 0 and for ctl response r 1 such that r 1 r 0 it is shown that there always exists one equilibrium which is globally asymptotically stable by employing the method of lyapunov functional more specifically the uninfected equilibrium is globally asymptotically stable if r 0 1 an infected equilibrium without immune response is globally asymptotically stable if r 1 1 r 0 and an infected equilibrium with immune response is globally asymptotically stable if r 1 1 the immune activation has a positive role in the reduction of the infection cells and the increasing of the uninfected cells if r 1 1

integrable hydrodynamic chains a new approach for derivation of benney type moment chains and integrable hydrodynamic type systems is presented new integrable hydrodynamic chains are constructed all their hydrodynamical reductions are described and integrated new 2 1 integrable hydrodynamic type systems are found

stability and hopf bifurcation in a delayed viral infection model with mitosis transmission in this paper we study a model of hcv with saturation and delay we stablish the local and global stability of system also we stablish the occurrence of a hopf bifurcation we will determine conditions for the permanence of model and the length of delay to preserve stability we present a sensitivity analysis for the basic reproductive number

global properties of delayed hiv dynamics models with differential drug efficacy in cocirculating target cells the objective of this work is to investigate the qualitative behaviors of three hiv dynamical models with two types of cocirculating target cells and intracellular discrete time delay in the two types of target cells the drug efficacy is assumed to be different the models take into account both short lived infected cells and long lived chronically infected cells the incidence rate of infection is given by bilinear and saturation functional response in the first and second model respectively while it is given by a general function in the third model lyapunov functionals are constructed and lasalle s invariance principle is applied to prove the global asymptotic stability of all equilibria of the models in the first two models we have derived the basic reproduction number r0 it has been proven that the disease free equilibrium is globally asymptotically stable gas when r0 1 and the endemic equilibrium is gas when r0 1 for the third model we have derived r0 and established a set of sufficient conditions for global stability of both disease free and endemic equilibria of the model at the end theoretical results have been checked by numerical simulations