bifurcation analysis of a generalized gause model with prey harvesting and a generalized holling response function of type iii abstract in this paper we study a generalized gause model with prey harvesting and a generalized holling response function of type iii p x m x 2 a x 2 b x 1 the goal of our study is to give the bifurcation diagram of the model for this we need to study saddle node bifurcations hopf bifurcation of codimension 1 and 2 heteroclinic bifurcation and nilpotent saddle bifurcation of codimension 2 and 3 the nilpotent saddle of codimension 3 is the organizing center for the bifurcation diagram the hopf bifurcation is studied by means of a generalized lienard system and for b 0 we discuss the potential integrability of the system the nilpotent point of multiplicity 3 occurs with an invariant line and can have a codimension up to 4 but because it occurs with an invariant line the effective highest codimension is 3 we develop normal forms in which the invariant line is preserved for studying of the nilpotent saddle bifurcation for b 0 the reversibility of the nilpotent saddle is discussed we study the type of the heteroclinic loop and its cyclicity the phase portraits of the bifurcations diagram partially conjectured via the results obtained allow us to give a biological interpretation of the behavior of the two species

entropy dissipation and long range interactions we study boltzmann s collision operator for long range interactions i e without grad s angular cut off assumption we establish a functional inequality showing that the entropy dissipation controls smoothness of the distribution function in a precise sense our estimate is optimal and gives a unified treatment of both the linear and the nonlinear cases we also give simple and self contained proofs of several useful results that were scattered in previous works as an application we obtain several helpful estimates for the cauchy problem and for the landau approximation in plasma physics

periodicity in a delayed ratio dependent predator prey system abstract with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of a delayed ratio dependent predator prey system in a periodic environment

rich dynamics in a spatial predator prey model with delay in this paper we study the spatiotemporal dynamics of a diffusive holling tanner predator prey model with discrete time delay via analytically and numerically analysis we unveil six types of patterns with and without time delay among them of particular novel is the observation of linear pattern consisting of a series of parallel lines whose formation is closely related with the temporal hopf bifurcation threshold moreover we also find that larger time delay or diffusion of predator may induce the extinction of both prey and predator theoretical analysis and numerical simulations validate the well known conclusion diffusion is usually beneficial for stabilizing pattern formation yet discrete time delay plays a destabilizing role in the generation of pattern

nonexistence of limit cycles in two classes of predator prey systems abstract this paper deals with the question of nonexistence of limit cycles in two famous classes of predator prey systems we present some sufficient conditions for the nonexistence of limit cycles in these systems our results extend and improve the results presented by moghadas

dynamics of a predator prey model we describe the bifurcation diagram of limit cycles that appear in the first realistic quadrant of the predator prey model proposed by r m may stability and complexity in model ecosystems princeton university press princeton nj 1974 in particular we give a qualitative description of the bifurcation curve when two limit cycles collapse on a semistable limit cycle and disappear moreover we show that locally asymptotic stability of a positive equilibrium point does not imply global stability for this class of predator prey models

positive steady states of the holling tanner prey predator model with diffusion this paper is concerned with the holling tanner prey predator model with diffusion subject to the homogeneous neumann boundary condition we obtain the existence and non existence of positive non constant steady states

dynamics in a diffusive predator prey system with ratio dependent predator influence abstract a diffusive predator prey system with predator functional response subject to neumann boundary conditions is considered existence nonexistence and boundedness of positive steady state solutions are shown to identify the ranges of parameters of spatial pattern formation hopf and steady state bifurcation analyses are carried out in detail these results provide theoretical evidences to the complex spatio temporal dynamics found by numerical simulation

effect of a protection zone in the diffusive leslie predator prey model abstract in this paper we consider the diffusive leslie predator prey model with large intrinsic predator growth rate and investigate the change of behavior of the model when a simple protection zone 0 for the prey is introduced as in earlier work y du j shi a diffusive predator prey model with a protection zone j differential equations 229 2006 63 91 y du x liang a diffusive competition model with a protection zone j differential equations 244 2008 61 86 we show the existence of a critical patch size of the protection zone determined by the first dirichlet eigenvalue of the laplacian over 0 and the intrinsic growth rate of the prey so that there is fundamental change of the dynamical behavior of the model only when 0 is above the critical patch size however our research here reveals significant difference of the model s behavior from the predator prey model studied in y du j shi a diffusive predator prey model with a protection zone j differential equations 229 2006 63 91 with the same kind of protection zone we show that the asymptotic profile of the population distribution of the leslie model is governed by a standard boundary blow up problem and classical or degenerate logistic equations

ultimate approximation and its application in nonmonotonic knowledge representation systems in this paper we study fixpoints of operators on lattices and bilattices in a systematic and principled way the key concept is that of an approximating operator a monotone operator on the product bilattice which gives approximate information on the original operator in an intuitive and well defined way with any given approximating operator our theory associates several different types of fixpoints including the kripke kleene fixpoint stable fixpoints and the well founded fixpoint and relates them to fixpoints of operator being approximated compared to our earlier work on approximation theory the contribution of this paper is that we provide an alternative more intuitive and better motivated construction of the well founded and stable fixpoints in addition we study the space of approximating operators by means of a precision ordering and show that each lattice operator o has a unique most precise we call it ultimale approximation we demonstrate that fixpoints of this ultimate approximation provide useful insights into fixpoints of the operator o we then discuss applications of these results in logic programming

global dynamics of a ratio dependent holling tanner predator prey system abstract a ratio dependent holling tanner predator prey model is studied by investigating the local stability properties of equilibrium points and periodic solutions of a transformed system and by applying the poincare bendixson theorem we are able to give a complete classification of the global dynamics of the ratio dependent holling tanner predator prey model

global stability for a class of predator prey systems this paper deals with the question of global stability of the positive locally asymptotically stable equilibrium in a class of predator prey systems the dulac s criterion is applied and liapunov functions are constructed to establish the global stability

regularizing effect and local existence for the non cutoff boltzmann equation the boltzmann equation without grad s angular cutoff assumption is believed to have a regularizing effect on the solutions because of the non integrable angular singularity of the cross section however even though this has been justified satisfactorily for the spatially homogeneous boltzmann equation it is still basically unsolved for the spatially inhomogeneous boltzmann equation in this paper by sharpening the coercivity and upper bound estimates for the collision operator establishing the hypo ellipticity of the boltzmann operator based on a generalized version of the uncertainty principle and analyzing the commutators between the collision operator and some weighted pseudo differential operators we prove the regularizing effect in all time space and velocity variables on the solutions when some mild regularity is imposed on these solutions for completeness we also show that when the initial data has this mild regularity and a maxwellian type decay in the velocity variable there exists a unique local solution with the same regularity so that this solution acquires the c regularity for any positive time

non constant positive steady states of a predator prey system with non monotonic functional response and diffusion this paper deals with non constant positive steady state solutions of a predator prey system with non monotonic functional response also called holling type iv interaction terms and diffusion under the homogeneous neumann boundary condition we first establish positive upper and lower bounds for such solutions and then study their non existence global existence and bifurcation

stochastic persistence and stationary distribution in a holling tanner type prey predator model abstract in this paper we study a stochastic predator prey model with beddington deangelis type functional response and logistic growth for predators the deterministic model is already well studied and we recall some important results here we construct the stochastic model from the deterministic model by introducing multiplicative noise terms into the growth equations of prey and predator populations for the stochastic model we show that the system admits unique positive global solution starting from the positive initial value then we prove that the system is strongly persistent in mean when the intensity of environmental forcing is less than some threshold magnitudes finally we show that the system has a stationary distribution under certain parametric restrictions numerical simulations are carried out to substantiate the analytical results

periodicity and attractivity of a ratio dependent leslie system with impulses a ratio dependent leslie system with impulses is studied by using a comparison theorem continuation theorem base on coincidence degree and constructing a suitable lyapunov function we establish sufficient and necessary conditions for the existence and global attractivity of periodic solution examples show that the obtained criteria are easily verifiable

hopf bifurcation analysis of a predator prey system with holling type iv functional response and time delay this paper is concerned with a predator prey system with holling type iv functional response and time delay our aim is to investigate how the time delay affects the dynamics of the predator prey system by choosing the delay as a bifurcation parameter the local asymptotic stability of the positive equilibrium and existence of local hopf bifurcations are analyzed based on the normal form and the center manifold theory the formulaes for determining the properties of hopf bifurcation of the predator prey system are derived finally to support these theoretical results some numerical simulations are given to illustrate the results

pattern formation of a spatial predator prey system abstract there are random and directed movements of predator and prey populations in many natural systems which are strongly influenced and modified by spatial factors to investigate how these migration directed movement and diffusion random movement affect predator prey systems we have studied the spatiotemporal complexity in a predator prey system with holling tanner form a theoretical analysis of emerging spatial pattern is presented and wavelength and pattern speed are calculated at the same time we present the properties of pattern solutions the results of numerical simulations show that migration has prominent effect on the pattern formation of the population i e changing turing pattern into traveling pattern this study suggests that modelling by migration and diffusion in predator prey systems can account for the dynamical complexity of ecosystems

steady state bifurcation and hopf bifurcation for a diffusive leslie gower predator prey model we consider a diffusive leslie gower predator prey model subject to the homogeneous neumann boundary condition treating the diffusion coefficient d as a parameter the hopf bifurcation and steady state bifurcation from the positive constant solution branch are investigated moreover the global structure of the steady state bifurcations from simple eigenvalues is established by bifurcation theory in particular the local structure of the steady state bifurcations from double eigenvalues is also obtained by the techniques of space decomposition and implicit function theorem

global weak solutions of the vlasov maxwell system with boundary conditions boundaries occur naturally in physucal systems which satisfy the vlasov maxwell system assume perfect conductor boundary conditions for maxwell and either specular reflection or partial absorption for vlasov then weak solutions with finite energy exist for all time

dynamics of a class of nonautonomous semi ratio dependent predator prey systems with functional responses abstract in this paper we investigate the dynamics of a class of the so called semi ratio dependent predator prey interaction models with functional responses based on systems of nonautonomous differential equations with time dependent parameters the functional responses are classified into five types and typical examples of each type are provided then we establish sufficient criteria for the boundedness of solutions the permanence of system and the existence uniqueness and globally asymptotic stability of positive periodic solution and positive almost periodic solution some conclusive discussion is presented at the end of this paper

abstract time dependent transport equations abstract we consider the abstract time dependent linear transport equation as an initial boundary value evolution problem in the banach spaces lp 1 p

traveling wave solutions for a continuous and discrete diffusive predator prey model abstract we study a diffusive predator prey model of lotka volterra type functional response in which both species obey the logistic growth such that the carrying capacity of the predator is proportional to the prey population and the one for prey is a constant both continuous and discrete diffusion are addressed our aim is to see whether both species can survive eventually if an alien invading predator is introduced to the habitat of an existing prey the answer to this question is positive under certain restriction on the parameter applying schauder s fixed point theory with the help of suitable upper and lower solutions the existence of traveling wave solutions for this model is proven furthermore by deriving the non existence of traveling wave solutions we also determine the minimal speed of traveling waves for this model this provides an estimation of the invasion speed

stability and hopf bifurcation analysis of a ratio dependent predator prey model with two time delays and holling type iii functional response in this paper a delayed ratio dependent predator prey model with holling type iii functional response and stage structure for the predator is considered by analyzing the corresponding characteristic equations the local stability of each of the feasible equilibria of the system is addressed and the existence of hopf bifurcations at the coexistence equilibrium is established by utilizing normal form method and center manifold theorem the explicit formulas which determine the direction of hopf bifurcation and the stability of bifurcating period solutions are derived finally numerical simulations supporting the theoretical analysis are given

analyzing the computational complexity of abstract dialectical frameworks via approximation fixpoint theory abstract dialectical frameworks adfs have recently been proposed as a versatile generalization of dung s abstract argumentation frameworks afs in this paper we present a comprehensive analysis of the computational complexity of adfs our results show that while adfs are one level up in the polynomial hierarchy compared to afs there is a useful subclass of adfs which is as complex as afs while arguably offering more modeling capacities as a technical vehicle we employ the approximation fixpoint theory of denecker marek and truszczynski thus showing that it is also a useful tool for complexity analysis of operator based semantics

a strongly coupled predator prey system with modified holling tanner functional response in this paper a strongly coupled system of partial differential equations in a bounded domain with the homogeneous neumann boundary condition which models a predator prey system with modified holling tanner functional response is considered first the authors study the stability of the positive constant solution sufficient conditions are derived for the global stability of the positive equilibrium by constructing a suitable lyapunov function by using the leray schauder theorem the authors prove a number of existence and non existence results about the non constant steady states of the system

combined analytical and numerical approaches in dynamic stability analyses of engineering systems abstract dynamic stability is a widely studied area that has attracted many researchers from various disciplines although dynamic stability is usually associated with mechanics theoretical physics or other natural and technical disciplines it is also relevant to social economic and philosophical areas of our lives therefore it is useful to occasionally highlight the general aspects of this amazing area to present some relevant examples and to evaluate its position among the various branches of rational mechanics from this perspective the aim of this study is to present a brief review concerning the dynamic stability problem its basic definitions and principles important phenomena research motivations and applications in engineering the relationships with relevant systems that are prone to stability loss encountered in other areas such as physics other natural sciences and engineering are also noted the theoretical background which is applicable to many disciplines is presented in this paper the most frequently used dynamic stability analysis methods are presented in relation to individual dynamic systems that are widely discussed in various engineering branches in particular the lyapunov function and exponent procedures routh hurwitz lienard and other theorems are outlined together with demonstrations the possibilities for analytical and numerical procedures are mentioned together with possible feedback from experimental research and testing the strengths and shortcomings of these approaches are evaluated together with examples of their effective complementing of each other the systems that are widely encountered in engineering are presented in the form of mathematical models the analyses of their dynamic stability and post critical behaviour are also presented the stability limits bifurcation points quasi periodic response processes and chaotic regimes are discussed the limit cycle existence and stability are examined together with their separating roles as attractors and repulsers two levels of stability loss recovery of the system is possible or final collapse is inevitable as can be observed in softening systems are noted time limited excitation and relevant transition effects e g seismic excitation are also discussed together with the evaluation of possible system reliability improvement the dynamic stability investigation of two degrees of freedom aero elastic systems in a linear formulation using several approaches is briefly highlighted further systems modelling problems that arise in transport engineering are also outlined a few hints for applications are given some open problems and possible future research strategies are outlined

spatial patterns of a fractional type cross diffusion holling tanner model abstract in this paper a fractional type cross diffusion holling tanner model under homogeneous neumann boundary condition is considered using the maximum principle and the harnack inequality we obtain a priori estimates of the positive stationary solution nonexistence and existence of nonconstant positive stationary solution are obtained which reveal that fractional type cross diffusion can create spatial patterns but the random diffusion fails

on the relation between default and autoepistemic logic abstract default logic is a formal means of reasoning about defaults what normally is the case in the absence of contradicting information autoepistemic logic on the other hand is meant to describe the consequences of reasoning about ignorance what must be true if a certain fact is not known although the motivation and formal character of these two systems are different a closer analysis shows that they share a common trait which is the indexical nature of certain elements in the theory in this paper we compare the expressive power of the two systems first we give an effective translation of default logic into autoepistemic logic default theories can thus be embedded into autoepistemic logic we also present a more surprising result the reverse translation is also possible so that every set of sentences in autoepistemic logic can be effectively rewritten as a default theory the formal equivalence of these two differing systems is thus established this analysis gives an interpretive semantics to default logic and yields insight into the nature of defaults in autoepistemic reasoning

spatiotemporal dynamics in a delayed diffusive predator model in this paper we investigate the spatiotemporal dynamics of a delayed reaction diffusion leslie gower model based on the stability analysis we demonstrate that delayed feedback may generate hopf and turing instability under some conditions resulting in spatial patterns one of the most interesting findings is that the model exhibits complex pattern replication pure turing instability gives birth to spots spots stripes mixture stripes stripes holes mixture and holes patterns pure hopf instability to spiral wave pattern and hopf turing instability to chaotic wave pattern our results well extend the findings of spatiotemporal dynamics in the delayed reaction diffusion predator prey model and indicate that time delay play an important roles in pattern formation

uniform persistence for a discrete predator prey system with delays abstract in this paper we deal with a discrete predator prey model with monotonic functional responses and give a sufficient condition of uniform persistence for the system

non constant positive steady state of one resource and two consumers model with diffusion abstract in this paper a predator prey reaction diffusion system with one resource and two consumers is considered assume that one consumer species exhibits holling ii functional response while the other consumer species exhibits beddington deangelis functional response and they compete for the common resource first it is proved that the unique positive constant steady state is stable for the ode system and the reaction diffusion system second a prior estimates of positive steady state is given finally the non existence of non constant positive steady state the existence and bifurcation of non constant positive steady state are studied

steady states of a leslie gower model with diffusion and advection abstract this paper focuses on a stationary leslie gower model with diffusion and advection firstly some existence conditions of nonconstant positive solutions are obtained by means of the leray schauder degree theory as diffusion and advection of one of the species both tend to infinity we obtain a limiting system which is a semi linear elliptic equation with nonlocal constraint in the simplified 1d case the global bifurcation structure of nonconstant solutions of the limiting system is classified

qualitative analysis for a diffusive predator prey model in this paper we study the qualitative properties of a diffusive predator prey model subject to the homogeneous neumann boundary condition by a comparison argument and iteration technique under some hypotheses we prove that the positive constant steady state is globally asymptotically stable we also establish the existence and non existence of non constant positive steady states stationary patterns by use of the degree theory and the a priori estimates

qualitative analysis of a lotka volterra predator prey system with migration abstract two species lotka volterra predator prey models are analyzed we study some qualitative criteria such as stability the existence of a coexistence equilibrium for the models for system with migration criteria are derived for the asymptotic behaviors with 0 or

three valued semantics for hybrid mknf knowledge bases revisited abstract knorr et al 2011 9 formulated a three valued formalism for the logic of minimal knowledge and negation as failure mknf and proposed a well founded semantics for hybrid mknf knowledge bases the main results state that if a hybrid mknf knowledge base has a three valued mknf model its well founded mknf model exists which is unique and can be computed by an alternating fixpoint construction however we show that these claims are erroneous the goal of this paper is two fold first we provide insight into why these claims fail to hold this leads to a classification of hybrid mknf knowledge bases into a hierarchy of four classes of which the smallest one is what works for the well founded semantics proposed by knorr et al after that we characterize three valued mknf models into what we call stable partitions which are similar to partial stable models in logic programming the intuitive notion of stable partitions allows us to discover a new proof theoretic method to determine whether a three valued mknf model exists for a given hybrid mknf knowledge base we can guess partial partitions and verify their stability by computing alternating fixpoints and by performing a consistency check this algorithm can be applied to compute all three valued mknf models as well as all two valued ones originally formulated by motik and rosati for query answering as a result our work provides a uniform characterization of well founded two valued and all three valued mknf models in terms of stable partitions and the alternating fixpoint construction

on a periodic predator prey system with time delays abstract this paper deals with discuss the global existence of positive periodic solutions for a predator prey system with time delays based on the theory of coincidence degree

uncertainty principle and kinetic equations abstract a large number of mathematical studies on the boltzmann equation are based on the grad s angular cutoff assumption however for particle interaction with inverse power law potentials the associated cross sections have a non integrable singularity corresponding to the grazing collisions smoothing properties of solutions are then expected on the other hand the uncertainty principle established by heisenberg in 1927 has been developed so far in various situations and it has been applied to the study of the existence and smoothness of solutions to partial differential equations this paper is the first one to apply this celebrated principle to the study of the singularity in the cross sections for kinetic equations precisely we will first prove a generalized version of the uncertainty principle and then apply it to justify rigorously the smoothing properties of solutions to some kinetic equations in particular we give some estimates on the regularity of solutions in sobolev spaces w r t all variables for both linearized and nonlinear space inhomogeneous boltzmann equations without angular cutoff as well as the linearized space inhomogeneous landau equation

a diffusive predator prey model in heterogeneous environment abstract in this paper we demonstrate some special behavior of steady state solutions to a predator prey model due to the introduction of spatial heterogeneity we show that positive steady state solutions with certain prescribed spatial patterns can be obtained when the spatial environment is designed suitably moreover we observe some essential differences of the behavior of our model from that of the classical lotka volterra model that seem to arise only in the heterogeneous case

qualitative analysis of a ratio dependent holling tanner model abstract in this paper we consider a holling tanner system with ratio dependence first we establish the sufficient conditions for the global stability of positive equilibrium by constructing lyapunov function second through a simple change of variables we transform the ratio dependent holling tanner model into a better studied lienard equation as a result the uniqueness of limit cycle can be solved

grounded fixpoints and their applications in knowledge representation in various domains of logic researchers have made use of a similar intuition that facts or models can be derived from the ground up they typically phrase this intuition by saying e g that the facts should be grounded or that they should not be unfounded or that they should be supported by cycle free arguments et cetera in this paper we formalise this intuition in the context of algebraical fixpoint theory we define when a lattice element x l is grounded for lattice operator o l l on the algebraical level we investigate the relationship between grounded fixpoints and the various classes of fixpoints of approximation fixpoint theory including supported minimal kripke kleene stable and well founded fixpoints on the logical level we investigate groundedness in the context of logic programming autoepistemic logic default logic and argumentation frameworks we explain what grounded points and fixpoints mean in these logics and show that this concept indeed formalises intuitions that existed in these fields we investigate which existing semantics are grounded we study the novel semantics for these logics that is induced by grounded fixpoints which has some very appealing properties not in the least its mathematical simplicity and generality our results unveil a remarkable uniformity in intuitions and mathematics in these fields

travelling waves in the holling tanner model with weak diffusion for a wide range of parameters we study travelling waves in a diffusive version of the holling tanner predator prey model from population dynamics fronts are constructed using geometric singular perturbation theory and the theory of rotated vector fields we focus on the appearance of the fronts in various singular limits in addition periodic travelling waves of relaxation oscillation type are constructed using a recent generalization of the entry exit function

existence of almost periodic solution in a ratio dependent leslie system with feedback controls a ratio dependent leslie system with feedback controls is studied by using a comparison theorem and constructing a suitable lyapunov function some sufficient conditions for the existence of a unique almost periodic solution periodic solution and the global attractivity of the solutions are obtained examples show that the obtained criteria are new general and easily verifiable

non constant positive steady states of a diffusive predator prey system in homogeneous environment abstract in this paper we investigate the existence and non existence of non constant positive steady states of a diffusive predator prey interaction system under homogeneous neumann boundary condition in homogeneous environment we show that the predator prey model with leslie gower functional response has no non constant positive solution but the system with a general functional response may have at least one non constant positive steady state under some conditions

qualitative analysis of a ratio dependent predator prey system with diffusion ratio dependent predator prey models are favoured by many animal ecologists recently as they better describe predator prey interactions where predation involves a searching process when densities of prey and predator are spatially homogeneous the so called michaelis menten ratio dependent predator prey system which is an ordinary differential system has been studied by many authors the present paper deals with the case where densities of prey and predator are spatially inhomogeneous in a bounded domain subject to the homogeneous neumann boundary condition its main purpose is to study qualitative properties of solutions to this reaction diffusion partial differential system in particular we will show that even though the unique positive constant steady state is globally asymptotically stable for the ordinary differential equation dynamics non constant positive steady states exist for the partial differential equation model this demonstrates that stationary patterns arise as a result of diffusion

a logic for default reasoning the need to make default assumptions is frequently encountered in reasoning about incompletely specified worlds inferences sanctioned by default are best viewed as beliefs which may well be modified or rejected by subsequent observations it is this property which leads to the non monotonicity of any logic of defaults in this paper we propose a logic for default reasoning we then specialize our treatment to a very large class of commonly occuring defaults for this class we develop a complete proof theory and show how to interface it with a top down resolution theorem prover finally we provide criteria under which the revision of derived beliefs must be effected

stationary patterns of the holling tanner prey predator model with diffusion and cross diffusion this paper is concerned with the holling tanner prey predator model subject to the homogeneous neumann boundary condition we will show that under certain hypotheses even though the unique positive constant steady state is uniformly asymptotically stable for the dynamics with diffusion non constant positive steady states can exist due to the emergence of cross diffusion the biological implication of cross diffusion means that the prey species exercise a self defense mechanism to protect themselves from the attack of the predator our result also demonstrates that cross diffusion can create stationary patterns

canards heteroclinic and homoclinic orbits for a slow fast predator prey model of generalized holling type iii abstract for a classical ratio dependent predator prey model with the generalized holling type iii functional response it was previously investigated in 20 by hsu and huang for global stability of an equilibrium and in 21 by huang ruan and song for subcritical hopf and bogdanov takens bifurcations here in this model when prey reproduces much faster than predator by using geometric singular perturbation theory we achieve much richer new dynamical phenomena than the existing ones such as the existence of canard cycles canard explosion and relaxation oscillations heteroclinic and homoclinic orbits cyclicity of slow fast cycles and the coexistence of the hopf cycle and the relaxation oscillation on global stability of the equilibrium we also provide less restricted conditions than the existing ones

bifurcations in a predator prey system of leslie type with generalized holling type iii functional response abstract we consider a predator prey system of leslie type with generalized holling type iii functional response p x m x 2 a x 2 b x 1 by allowing b to be negative b 2 a p x is monotonic for b 0 and nonmonotonic for b 0 when x 0 the model has two non hyperbolic positive equilibria one is a multiple focus of multiplicity one and the other is a cusp of codimension 2 for some values of parameters and a degenerate bogdanov takens singularity focus or center case of codimension 3 for other values of parameters when there exist a multiple focus of multiplicity one and a cusp of codimension 2 we show that the model exhibits subcritical hopf bifurcation and bogdanov takens bifurcation simultaneously in the corresponding small neighborhoods of the two degenerate equilibria respectively different phase portraits of the model are obtained by computer numerical simulations which demonstrate that the model can have i a stable limit cycle enclosing two non hyperbolic positive equilibria ii a stable limit cycle enclosing an unstable homoclinic loop iii two limit cycles enclosing a hyperbolic positive equilibrium iv one stable limit cycle enclosing three hyperbolic positive equilibria or v the coexistence of three stable states two stable equilibria and a stable limit cycle when the model has a bogdanov takens singularity of codimension 3 we prove that the model exhibits degenerate focus type bogdanov takens bifurcation of codimension 3 these results not only demonstrate that the dynamics of this model when b 2 a are much more complex and far richer than the case when b 0 but also provide new bifurcation phenomena for predator prey systems

uniqueness of the limit cycle for gause type predator prey systems abstract in this paper we derive some results to ensure that the number of the limit cycle of a generalized gause type predator prey system does not exceed one two examples are presented in the final section

asymptotic behavior and multiplicity for a diffusive leslie gower predator prey system with crowley martin functional response abstract a diffusive predator prey system with modified leslie gower and crowley martin functional response is considered the extinction and permanence of the time dependent system are determined by virtue of the comparison principle then the sufficient and necessary conditions for the existence of coexistence states are obtained furthermore the stability uniqueness and exact multiplicity of coexistence states are investigated by means of the combination of the perturbation theory bifurcation theory and degree theory our results indicate that c 1 have an effect on the stability and exact multiplicity of coexistence states finally some numerical simulations are presented to verify and complement the theoretical results

regularity of the boltzmann equation in convex domains a basic question about regularity of boltzmann solutions in the presence of physical boundary conditions has been open due to characteristic nature of the boundary as well as the non local mixing of the collision operator consider the boltzmann equation in a strictly convex domain with the specular bounce back and diffuse boundary condition with the aid of a distance function toward the grazing set we construct weighted classical c 1 solutions away from the grazing set for all boundary conditions for the diffuse boundary condition we construct w 1 p solutions for 1 p 2 and weighted w 1 p solutions for 2 le p le infty as well

stationary distribution and periodic solutions for stochastic holling leslie predator prey systems abstract the stochastic autonomous and periodic predator prey systems with holling and leslie type functional response are investigated for the autonomous system we prove that there exists a unique stationary distribution which is ergodic by constructing a suitable lyapunov function under relatively small white noise the result shows that stationary distribution doesn t rely on the existence and the stability of the positive equilibrium in the undisturbed system furthermore for the corresponding non autonomous system we show that there exists a positive periodic markov process under relatively weaker condition finally numerical simulations illustrate our theoretical results

diffusion self diffusion and cross diffusion u1 x 0 u 1 0 x u2 x 0 u 2 0 x i n 0 where 2 n 1 2 x 2 is the laplace operator 0 is a bounded smooth domain of r n with n1 0 and 0 are the boundary and the closure of 0 respectively 0t 0 0 t and 0t 0 0 t for some t 0 is the outward unit normal vector on 0 di ai bi ci i 1 2 are all positive constants while ij i j 1 2 denote non negative constants the initial values u1 0 and u2 0 are non negative smooth func tions which are not identically zero the mathematical model 1 1 was proposed by shigesada et al 27 in their study of spatial segregation of interacting species where u1 and u2 represent the densities of two competing species d1 and d2 are their diffu sion rates a1 and a2 denote the intrinsic growth rates b1 and c2 account for intra specific competitions b2 and c1 are the coefficients of inter specific competitions 11 and 22 are usually referred as self diffusion pressures and 12 and 21 are cross diffusion pressures an interesting feature of 1 1 is that the movements of these two competing species are affected by the population pressures due to the mutual interference between the individuals and it was hoped that the nonlinear dispersive force due to the

retracted stability and hopf bifurcations in a delayed leslie gower predator prey system in this paper we consider the following delayed leslie gower predator prey system x t r 1 x t 1 x t k mx t y t y t r 2 y t 1 y t x t by choosing the delay as a bifurcation parameter we show that hopf bifurcations can occur as the delay crosses some critical values by deriving the equation describing the flow on the center manifold we can determine the direction of the hopf bifurcations and the stability of the bifurcating periodic solutions in addition special attention is paid to the global continuation of local hopf bifurcations using a global hopf bifurcation result of wu j wu symmetric functional differential equations and neural networks with memory trans amer math soc 350 1998 4799 4838 for functional differential equations we may show the global existence of periodic solutions computer simulations illustrate the results

global existence and full regularity of the boltzmann equation without angular cutoff we prove the global existence and uniqueness of classical solutions around an equilibrium to the boltzmann equation without angular cutoff in some sobolev spaces in addition the solutions thus obtained are shown to be non negative and c in all variables for any positive time in this paper we study the maxwellian molecule type collision operator with mild singularity one of the key observations is the introduction of a new important norm related to the singular behavior of the cross section in the collision operator this norm captures the essential properties of the singularity and yields precisely the dissipation of the linearized collision operator through the celebrated h theorem

limit cycles for two families of cubic systems abstract in this paper we study the number of limit cycles of two families of cubic systems introduced in previous papers to model real phenomena the first one is motivated by a model of star formation histories in giant spiral galaxies and the second one comes from a model of volterra type to prove our results we develop a new criterion on the non existence of periodic orbits and we extend a well known criterion on the uniqueness of limit cycles due to kuang and freedman both results allow to reduce the problem to the control of the sign of certain functions that are treated by algebraic tools moreover in both cases we prove that when the limit cycles exist they are non algebraic

on a delayed nonautonomous ratio dependent predator prey model with holling type functional response and diffusion abstract a two species periodic ratio dependent predator prey model with holling type functional response and diffusion is investigated three different sets of sufficient conditions one set is diffusive independent and the other two sets are diffusive dependent which ensure the permanence of the system and a set of sufficient condition which ensure the extinction of the predator species are obtained examples together with their numeric simulations show the feasibility of the main results

positive periodic solutions in delayed gause type predator prey systems abstract by using a continuation theorem based on coincidence degree theory we establish easily verifiable criteria for the existence of positive periodic solutions in delayed gause type predator prey systems some known results are shown to be special cases of the presented paper

autoepistemic logic autoepistemic logic is one of the principal modes of nonmonotonic reasoning it unifies several other modes of nonmonotonic reasoning and has important application in logic programming in the paper a theory of autoepistemic logic is developed this paper starts with a brief survey of some of the previously known results then the nature of nonmonotonicity is studied by investigating how membership of autoepistemic statements in autoepistemic theories depends on the underlying objective theory a notion similar to set theoretic forcing is introduced expansions of autoepistemic theories are also investigated expansions serve as sets of consequences of an autoepistemic theory and they can also be used to define semantics for logic programs with negation theories that have expansions are characterized and a normal form that allows the description of all expansions of a theory is introduced our results imply algorithms to determine whether a theory has a unique expansion sufficient conditions stratification that imply existence of a unique expansion are discussed the definition of stratified theories is extended and under some additional assumptions efficient algorithms for testing whether a theory is stratified are proposed the theorem characterizing expansions is applied to two classes of theories k1 theories and ae programs in each case simple hypergraph characterization of expansions of theories from each of these classes is given finally connections with stable model semantics for logic programs with negation is discussed in particular it is proven that the problem of existence of stable models is np complete authors abstract

permanence and extinction of a three species ratio dependent food chain model with delay and prey diffusion abstract in this paper we study a diffusive three species ratio dependent food chain model using differential inequality to obtain sufficient conditions that ensure the permanence of the system and the extinction of predator species our results reinforce the main result of sun wen shihua chen and huihai mei positive periodic solution of a more realistic three species lotka volterra model with delay and density regulation chaos solitons and fractals in press

on the boltzmann equation for long range interactions we study the boltzmann equation without grad s angular cutoff assumption we introduce a suitable renormalized formulation that allows the cross section to be singular in both the angular and the relative velocity variables angular singularities occur as soon as one is interested in long range interactions while singularities in the relative velocity variable occur in the study of soft potentials in particular coulomb interaction together with several new estimates this new formulation enables us to prove existence of weak solutions and to give a proof of a conjecture by lions appearance of strong compactness under general fully realistic assumptions 2001 john wiley sons inc

approximating operators and semantics for abstract dialectical frameworks we provide a systematic in depth study of the semantics of abstract dialectical frameworks adfs a recent generalisation of dung s abstract argumentation frameworks this is done by associating with an adf its characteristic one step consequence operator and defining various semantics for adfs as different fixpoints of this operator we first show that several existing semantical notions are faithfully captured by our definition then proceed to define new adf semantics and show that they are proper generalisations of existing argumentation semantics from the literature most remarkably this operator based approach allows us to compare adfs to related nonmonotonic formalisms like dung argumentation frameworks and propositional logic programs we use polynomial faithful and modular translations to relate the formalisms and our results show that both abstract argumentation frameworks and abstract dialectical frameworks are at most as expressive as propositional normal logic programs

the bifurcation structure of the holling tanner model for predator prey interactions using two timing the holling tanner model for predator prey systems has two hopf bifurcation points for certain parameters the dependence of the environmental parameters on the underlying bifurcation structure is uncovered using two timing emphasis is on how the bifurcation diagram changes as the hopf bifurcation points separate two degenerate cases require a modification of conventional two timing when the two hopf bifurcation points nearly coalesce the two stable periodic solution branches are shown to be connected as a ratio of linear growth rates varies the hopf bifurcation points separate further and one limit cycle becomes unstable this situation can correspond to an outbreak in populations the modified two timing analysis analytically captures the unstable and stable limit cycles of the new branch

permanence for nonautonomous predator prey kolmogorov systems with impulses and its applications in this paper the general impulsive non autonomous predator prey kolmogorov system is studied some new criteria on the permanence and ultimate boundedness are established as applications of these results some special models are studied such as a class of impulsive non autonomous lotka volterra systems impulsive holling i type functional response systems impulsive holling m n type functional response systems impulsive beddington deangelis functional response systems leslie gower functional response systems and chemostat type systems

stationary patterns of a predator prey model with spatial effect abstract in this paper spatial patterns of predator prey model with cross diffusion are investigated the hopf and turing bifurcation critical line in a spatial domain are obtained by using mathematical theory moreover exact turing space is given in two parameters space our results reveal that cross diffusion can induce stationary patterns which may be useful to help us better understand the dynamics of the real ecosystems

dynamics of a diffusive predator prey model with modified leslie gower and holling type iii schemes abstract the diffusive predator prey system with modified leslie gower and holling type iii schemes is considered here firstly stability analysis of the equilibrium for a reduced ode system is discussed secondly we obtain that the system is permanent thirdly sufficient conditions for the global asymptotical stability of the unique positive equilibrium of the system are derived by using the method of lyapunov function finally we establish the existence and nonexistence of nonconstant positive steady states of this reaction diffusion system which indicates the effect of large diffusivity

non isothermal boundary in the boltzmann theory and fourier law in the study of the heat transfer in the boltzmann theory the basic problem is to construct solutions to the following steady problem v cdot nabla x f frac 1 rm k rm n q f f qquad x v in omega times mathbf r 3 quad quad 0 1 f x v n x cdot v 0 f x v prime n x cdot v prime dv prime quad x in partial omega quad quad 0 2 where is a bounded domain in mathbf r d 1 leq d leq 3 kn is the knudsen number and mu theta frac 1 2 pi theta 2 x rm exp frac v 2 2 theta x is a maxwellian with non constant non isothermal wall temperature x based on new constructive coercivity estimates for both steady and dynamic cases for theta theta 0 leq delta ll 1 and any fixed value of kn we construct a unique non negative solution fs to 0 1 and 0 2 continuous away from the grazing set and exponentially asymptotically stable this solution is a genuine non equilibrium stationary solution differing from a local equilibrium maxwellian as an application of our results we establish the expansion f s mu theta 0 delta f 1 o delta 2 and we prove that if the fourier law holds the temperature contribution associated to f1 must be linear in the slab geometry

existence and global stability of positive periodic solutions of a predator prey system with delays this paper studies the existence global stability and uniform persistence of positive periodic solutions of a periodic predator prey system with holling type iii functional response by using the continuation theorem of coincidence degree theory and liapunov functional some sufficient conditions are obtained

l2 solution of linear non cutoff boltzmann equation with boundary conditions abstract in this paper we are concerned about the existence of solution to linear non cutoff boltzmann equation with boundary conditions in 9 and 18 the existence of the solutions to the kinetic equation and linear boltzmann equation were obtained by characteristic line and iteration methods however their methods are not applicable in the context of non cutoff linear operators to overcome this difficulty we cut off the non cutoff linear operator l to l r the latter is compatible with the method in 9 via this process we are able to use the sequence of solutions associated to l r to approximate the solution associated to l which is corresponding to the original equation in turn obtain the weak solutions of linear non cutoff boltzmann equation with specular and diffusion reflection boundary conditions

uniform semantic treatment of default and autoepistemic logics we revisit the issue of epistemological and semantic foundations for autoepistemic and default logics two leading formalisms in nonmonotonic reasoning we develop a general semantic approach to autoepistemic and default logics that is based on the notion of a belief pair and that exploits the lattice structure of the collection of all belief pairs for each logic we introduce a monotone operator on the lattice of belief pairs we then show that a whole family of semantics can be defined in a systematic and principled way in terms of fixpoints of this operator or as fixpoints of certain closely related operators our approach elucidates fundamental constructive principles in which agents form their belief sets and leads to approximation semantics for autoepistemic and default logics it also allows us to establish a precise one to one correspondence between the family of semantics for default logic and the family of semantics for autoepistemic logic the correspondence exploits the modal interpretation of a default proposed by konolige our results establish conclusively that default logic can be viewed as a fragment of autoepistemic logic a result that has been long anticipated at the same time they explain the source of the difficulty to formally relate the semantics of default extensions by reiter and autoepistemic expansions by moore these two semantics occupy different locations in the corresponding families of semantics for default and autoepistemic logics