local well posedness for a lotka volterra system in besov spaces this paper is devoted to study local existence uniqueness and continuous dependence upon the initial data of mild solutions for a diffusive non autonomous lotka volterra system initial data are taken in the besov space b p q n

traveling wave solutions in a diffusive system with two preys and one predator abstract this paper is concerned with the traveling wave solutions in a diffusive system with two preys and one predator by constructing upper and lower solutions the existence of nontrivial traveling wave solutions is established the asymptotic behavior of traveling wave solutions is also confirmed by combining the asymptotic spreading with the contracting rectangles applying the theory of asymptotic spreading the nonexistence of traveling wave solutions is proved

traveling wave solutions for gause type predator prey systems with density dependence a heteroclinic orbit in r4 abstract this paper investigates the existence of traveling wave solutions for a class of diffusive gause type predator prey systems with linear density dependence for predator using the shooting method we establish the existence of a non negative traveling wave solution connecting a boundary equilibrium point to the coexistence equilibrium point with the help of topological method of wazewski theorem and lasalle s invariance principle

a geometric approach in the study of traveling waves for some classes of non monotone reaction diffusion systems abstract in this paper we further extend a recently developed method to investigate the existence of traveling waves solutions and their minimum wave speed for non monotone reaction diffusion systems our approach consists of two steps first we develop a geometrical shooting argument with the aid of the theorem of homotopy invariance on the fundamental group to obtain the positive semi traveling wave solutions for a large class of reaction diffusion systems including the models of predator prey interaction for both predator independent dependent functional responses the models of combustion belousov zhabotinskii reaction si type of disease transmission and the model of biological flow reactor in chemostat next we apply the results obtained from the first step to some models such as the beddinton deangelis model and the model of biolocal flow reactor to show the convergence of these semi traveling wave solutions to an interior equilibrium point by the construction of a lyapunov type function or the convergence of semi traveling waves to another boundary equilibrium point by the further analysis of the asymptotical behavior of semi traveling wave solutions

some entire solutions to the competitive reaction diffusion system abstract this manuscript focuses on the study of the classical lotka volterra competitive reaction diffusion system morita and tachibana 2009 19 proved the existence of entire solutions of this system they used traveling front solutions the lower bound of the proportion between two components of which is positive to construct these entire solutions in order to reasonably explain this positive lower bound we investigate it based on the eigenvalues of the linearized system and show some sufficient and necessary conditions particularly if the parameters in the system satisfy some conditions then the positive lower bound spontaneously holds when the ratio is zero we also construct new entire solutions based on the super sub solution method the comparison theorem and a pair of exact traveling front solutions in addition another kind of entire solutions is revealed by the combination of traveling front solutions their reflects and the solutions of the diffusion free system

spreading speeds of a lotka volterra predator prey system the role of the predator abstract this paper is concerned with the spreading speeds of a modified lotka volterra predator prey system the intention is to describe the propagation mode whereby the two species coinvade a new habitat under some assumptions it is proved that the spreading speed of the prey is slower than in the case where the predator vanishes and the density of the prey on the coexistence domain is also smaller compared with the case where interspecies actions disappear therefore the predator has a negative effect on the evolution of the prey by slowing the spreading speed and decreasing the population density of the prey

torsion free aluffi algebras abstract a pair of ideals j i r has been called aluffi torsion free if the aluffi algebra of i j is isomorphic to the corresponding rees algebra we give necessary and sufficient conditions for the aluffi torsion free property in terms of the first syzygy module of the form ideal j in the associated graded ring of i for two pairs of ideals j 1 j 2 i such that j 1 j 2 i 2 we prove that if one pair is aluffi torsion free the other one is so if and only if the first syzygy modules of j 1 and j 2 have the same form ideals we introduce the notion of strongly aluffi torsion free ideals and present some results on these ideals

invasion traveling wave solutions of a predator prey system abstract this paper is concerned with the traveling wave solutions of a predator prey system in which intra specific conflictions are involved by using the comparison principle and the asymptotic speed of spreading the existence nonexistence and minimal wave speed of non negative traveling wave solutions are established such a traveling wave solution can model the spatial temporal process where the predator invades the territory of the prey and they eventually coexist

asymptotic spreading in a lotka volterra predator prey system abstract this paper is concerned with the asymptotic spreading of a lotka volterra predator prey system with self limit effect in which the intrinsic growth rates of both species are positive the spreading speeds of both species are estimated which implies the role of nonlinearities in asymptotic spreading biologically our results confirm that the prey may contribute to the asymptotic spreading of the predator

traveling wave solutions of diffusive lotka volterra equations a heteroclinic connection in we establish the existence of traveling wave solutions for a reaction dif fusion system based on the lotka volterra differential equation model of a predator and prey interaction the waves are of transition front type analogous to the solutions discussed by fisher and kolmogorov et al for a scalar reaction diffusion equation the waves discussed here are not necessarily monotone there is a speed c 0 such that for c c there is a traveling wave moving with speed c the proof uses a shooting argument based on the nonequivalence of a simply connected region and a nonsimply connected region together with a liapunov function to guarantee the existence of the traveling wave solution the traveling wave solution is equivalent to a heteroclinic orbit in 4 dimensional phase space

traveling wave solutions for diffusive predator prey type systems with nonlinear density dependence abstract traveling wave solution for a class of diffusive predator prey system with nonlinear density dependence is considered using methods of topological shooting we show the existence of a non negative traveling wave solution connecting a boundary equilibrium to the co existence steady state with the help of a wazewski like set together with lyapunov function constructed elaborately this means that the traveling wave solution established by huang 2012 can be preserved in the presence of the nonlinear density dependence for the predator and the results of huang 2012 are generalized

minimal wave speed for a class of non cooperative reaction diffusion systems of three equations abstract in this paper we study the traveling wave solutions and minimal wave speed for a class of non cooperative reaction diffusion systems consisting of three equations based on the eigenvalues a pair of upper lower solutions connecting only the invasion free equilibrium are constructed and the schauder s fixed point theorem is applied to show the existence of traveling semi fronts for an auxiliary system then the existence of traveling semi fronts of original system is obtained by limit arguments the traveling semi fronts are proved to connect another equilibrium if natural birth and death rates are not considered and to be persistent if these rates are incorporated then non existence of bounded traveling semi fronts is obtained by two sided laplace transform then the above results are applied to some disease transmission models and a predator prey model

traveling wavefronts for delayed reaction diffusion systems via a fixed point theorem abstract by using schauder s fixed point theorem we prove some existence results for traveling wavefronts of reaction diffusion systems with quasimonotonicity reactions more precisely we reduce the existence of traveling wavefronts to the existence of an admissible pair of supersolution and subsolution which are easy to construct in practice finally to illustrate our main results we study the existence of traveling wavefronts for a delayed predator prey model with diffusion as well as the reaction diffusion system with the well known belousov zhabotinskii reaction and the obtained results improve the existing ones

triangular decoupling for a binary distillation column under pressure control the possibility of attaining complete decoupling of a distillation column under pressure control is studied using the state space model it is shown that under the situation where the distillation column is under pressure control by the manipulation of the condenser duty the complete decoupling using constant state feedback may not be attained while the triangular decoupling can be attained with eight measurement variables

asymptotic behavior of traveling fronts and entire solutions for a periodic bistable competition diffusion system abstract this paper is concerned with a time periodic competition diffusion system u t u x x u r 1 t a 1 t u b 1 t v t 0 x r v t d v x x v r 2 t a 2 t u b 2 t v t 0 x r where u t x and v t x denote the densities of two competing species d 0 is some constant r i t a i t and b i t are t periodic continuous functions under suitable conditions it has been confirmed by bao and wang 2013 2 that this system admits periodic traveling fronts connecting two stable semi trivial t periodic solutions p t 0 and 0 q t associated to the corresponding kinetic system in the present work we first investigate the asymptotic behavior of periodic bistable traveling fronts with non zero speeds at infinity by a dynamical approach combined with the two sided laplace transform method with these asymptotic properties we then obtain some key estimates as a result by applying the super and subsolutions techniques as well as the comparison principle we establish the existence and various qualitative properties of the so called entire solutions defined for all time and the whole space which provides some new spreading ways other than periodic traveling waves for two strongly competing species interacting in a heterogeneous environment

intersection theory of linear embeddings we study intersection theoretic properties of subschemes defined by ideal sheaves of linear type in particular their behavior with respect to blowups and segre classes

existence of traveling wave solutions for gause type models of predator prey systems this paper deals with the existence of three types of traveling waves for a general predator prey systems of gause type traveling wave train solution point to point and point to periodic traveling wave solutions applying the methods of wazewski theorem lasalle s invariance principle and hopf bifurcation theorem we obtain the existence results also the minimal wave speed for biological invasion is obtained furthermore some applications are given to illustrate our results

exclusive traveling waves for competitive reaction diffusion systems and their stabilities abstract we study the existence uniqueness and asymptotic behavior as well as the stability of a special kind of traveling wave solutions for competitive pde systems involving intrinsic growth competition crowding effects and diffusion the traveling waves are exclusive in the sense that as the variable goes to positive or negative infinity different species are close to extinction or carrying capacity we perform an appropriate affine transformation of the traveling wave equations into monotone form and construct appropriate upper and lower solutions by this means we reduce the existence proof to application of well known theory about monotone traveling wave systems cf a leung systems of nonlinear partial differential equations applications to biology and engineering mia kluwer boston 1989 j wu x zou traveling wave fronts of reaction diffusion systems with delay j dynam differential equations 13 2001 651 687 and i volpert v volpert v volpert traveling wave solutions of parabolic systems transl math monogr vol 140 amer math soc providence ri 1994 then by using spectral analysis of the linearization over the profile we prove the orbital stability of the traveling wave in some banach spaces with exponentially weighted norm furthermore we show that the introduction of some weight is necessary in the sense that in general traveling wave solutions with initial perturbations in the unweighted space c 0 are unstable cf i volpert v volpert v volpert traveling wave solutions of parabolic systems transl math monogr vol 140 amer math soc providence ri 1994 and d henry geometric theory of semilinear parabolic equations lecture notes in math vol 840 springer verlag new york 1981

traveling wave solutions for reaction diffusion systems abstract this paper is concerned with traveling waves of reaction diffusion systems the definition of coupled quasi upper and quasi lower solutions is introduced for systems with mixed quasimonotone functions and the definition of ordered quasi upper and quasi lower solutions is also given for systems with quasimonotone nondecreasing functions by the monotone iteration method it is shown that if the system has a pair of coupled quasi upper and quasi lower solutions then there exists at least a traveling wave solution moreover if the system has a pair of ordered quasi upper and quasi lower solutions then there exists at least a traveling wavefront as an application we consider the delayed system of a mutualistic model

epidemic waves of a spatial sir model in combination with random dispersal and non local dispersal abstract in this paper a spatial sir model in combination with random dispersal and non local dispersal is proposed we establish the existence and non existence of the traveling wave solutions connecting the disease free equilibrium and the endemic equilibrium for the model the main difficulties lie in the fact that the semiflow generated here does not admit the order preserving property and the solutions lack of regularity we use a proper iteration scheme to construct a pair of upper and lower solutions and then apply the schauder s fixed point theorem polar coordinates transform to study the threshold dynamics of the model that is we show that if the basic reproduction number of the model r 0 1 there is a positive constant critical number c such that for each c c the model admits a non trivial and positive traveling wave with wave speed c and if r 0 1 and 0

a variational approach to symmetry monotonicity and comparison for doubly nonlinear equations abstract we advance a variational method to prove qualitative properties such as symmetries monotonicity upper and lower bounds sign properties and comparison principles for a large class of doubly nonlinear evolutionary problems including gradient flows some nonlocal problems and systems of nonlinear parabolic equations our method is based on the so called weighted energy dissipation wed variational approach this consists in defining a global parameter dependent functional over entire trajectories and proving that its minimizers converge to solutions to the target problem as the parameter goes to zero qualitative properties and comparison principles can be easily proved for minimizers of the wed functional and by passing to the limit for the limiting problem several applications of the abstract results to systems of nonlinear pdes and to fractional nonlocal problems are presented eventually we present some extensions of this approach in order to deal with rate independent systems and hyperbolic problems

asymptotic behavior and uniqueness of traveling wave solutions in ricker competition system abstract the existence of traveling wave solutions connecting two half positive equilibria in ricker competition system can be obtained by the results b li h f weinberger m a lewis spreading speeds as slowest wave speeds for cooperative systems math biosci 196 2005 82 98 in this paper we first prove that any nondecreasing traveling wave solutions have the exponential decay asymptotic behavior at the minus plus infinity by means of ikehara s theorem and then use the strong comparison principle and the sliding method to obtain the uniqueness of the traveling wave solutions for this system

traveling wave solutions in a delayed diffusive competition system abstract in this paper we first investigate the existence of traveling wave fronts in a delayed diffusive competition system by constructing a pair of upper and lower solutions then we consider the asymptotic behavior of traveling wave solutions at the minus plus infinity by means of the bilateral laplace transform finally the monotonicity and uniqueness up to the translation of traveling wave solutions are also obtained by the strong comparison principle and the sliding method

static state feedback triangular block decoupling for arbitrary systems a state space method abstractin this paper the static state feedback triangular block decoupling problem for a general system described by a b c d quadruples is studied necessary and sufficient conditions which are numerically verifiable are obtained and a numerically reliable decoupling method is established in the state space two examples are solved by our method which show the effectiveness

the aluffi algebra of the jacobian of points in projective space torsion freeness abstract the algebra in the title has been introduced by p aluffi let j i be ideals in the commutative ring r the embedded aluffi algebra of i on r j is an intermediate graded algebra between the symmetric algebra and rees algebra of the ideal i j over r j a pair of ideals has been dubbed an aluffi torsion free pair if the surjective map of the aluffi algebra of i j onto the rees algebra of i j is injective in this paper we focus on the situation where j is the ideal of points in general linear position in projective space and i is its jacobian ideal

existence of travelling wave solutions of predator prey systems via the connection index we consider a reaction diffusion system which arises as a model of predator prey interactions in mathematical ecology the system admits four constant equilibria two of which are stable the main result is an existence theorem for travelling wave solutions which connect the two stable equilibria most previous efforts with regard to travelling waves for systems employ singular perturbations to locate the connecting orbit the new aspect of the present discussion lies in devising some novel methods for locating the connecting solution in phase space which do not require that the equations be singularly perturbed in certain cases the main result holds for an arbitrary choice of diffusion coefficients

traveling wavefronts in diffusive and cooperative lotka volterra system with delays existence of traveling wave front solutions is established for diffusive and cooperative lotka volterra system with delays the result is an extension of an existing result for delayed logistic scaler equation to systems and is somewhat parallel to the existing result for diffusive and competitive lotka volterra systems without delay the approach used in this paper is the upper lower solution technique and the monotone iteration recently developed by wu and zou j dynam differential equations 13 2001 651 687 for delayed reaction diffusion systems without the so called quasimonotonicity 2002 elsevier science usa all rights reserved

a maximum principle for diffusive lotka volterra systems of two competing species abstract using an elementary approach we establish a new maximum principle for the diffusive lotka volterra system of two competing species which involves pointwise estimates of an elliptic equation consisting of the second derivative of one function the first derivative of another function and a quadratic nonlinearity this maximum principle gives a priori estimates for the total mass of the two species moreover applying it to the system of three competing species leads to a nonexistence theorem of traveling wave solutions

traveling waves and competitive exclusion in models of resource competition and mating interference abstract in this article we study reaction diffusion models for two closed related biological species u and v under resource competition and mating interference from v species to u species the effect of one sided sexual competition makes the trivial state and u dominance state both unstable while the v dominance state is shown to be asymptotically stable with attraction regions and convergent rates depending on the biological parameters using the upper lower solution method we further prove that for a family of wave speeds there exist traveling wave solutions connecting the u dominance state and the v dominance state at this confirms an earlier conjecture that unbalanced mating interference will lead to competitive exclusion these results can also be obtained on an extended model with instantaneous effects of resource competition and temporal delay on mating interference through a transformation into three equation system we prove that the temporal delay does not affect the stability of the steady states and the existence of the traveling waves but causes changes on the attraction regions and convergence rates finally numerical simulations are also presented to illustrate the theoretical results

the stability of traveling wave solutions for a diffusive competition system of three species abstract in this article we investigate the stability of monotone traveling wave solutions for a diffusive three species competition system by considering the initial perturbations of the traveling waves in some weighted function spaces the monotone three species waves become asymptotically stable further stability will be determined from the asymptotic behavior of the waves this can be achieved by using the method of super and subsolutions

existence of traveling wave solutions for diffusive predator prey type systems abstract in this work we investigate the existence of traveling wave solutions for a class of diffusive predator prey type systems whose each nonlinear term can be separated as a product of suitable smooth functions satisfying some monotonic conditions the profile equations for the above system can be reduced as a four dimensional ode system and the traveling wave solutions which connect two different equilibria or the small amplitude traveling wave train solutions are equivalent to the heteroclinic orbits or small amplitude periodic solutions of the reduced system applying the methods of wazewski theorem lasalle s invariance principle and hopf bifurcation theory we obtain the existence results our results can apply to various kinds of ecological models

aluffi torsion free ideals abstract a special class of algebras which are intermediate between the symmetric and the rees algebras of an ideal was introduced by p aluffi in 2004 to define characteristic cycle of a hypersurface parallel to conormal cycle in intersection theory these algebras are recently investigated by a nasrollah nejad and a simis who named them aluffi algebras for a pair of ideals j i of a commutative ring r the aluffi algebra of i j is called aluffi torsion free if it is isomorphic to the rees algebra of i j in this paper ideals generated by 2 minors of a 2 n matrix of linear forms and also edge ideals of graphs are considered and some conditions are presented which are equivalent to aluffi torsion free property of them

controllability distributions and systems approximations a geometric approach given a nonlinear system we determine a relation at an equilibrium between controllability distributions defined for a nonlinear system and a taylor series approximation of it the value of such a relation is appreciated if we recall that the solvability conditions as well as the solutions to some control synthesis problems can be stated in terms of geometric concepts like controlled invariant controllability distributions the relation between these distributions at the equilibrium will help us to decide when the solvability conditions of this kind of problems are equivalent for the nonlinear system and its approximation