average rate of downlink heterogeneous cellular networks over generalized fading channels a stochastic geometry approach in this paper we introduce an analytical framework to compute the average rate of downlink heterogeneous cellular networks the framework leverages recent application of stochastic geometry to other cell interference modeling and analysis the heterogeneous cellular network is modeled as the superposition of many tiers of base stations bss having different transmit power density path loss exponent fading parameters and distribution and unequal biasing for flexible tier association a long term averaged maximum biased received power tier association is considered the positions of the bss in each tier are modeled as points of an independent poisson point process ppp under these assumptions we introduce a new analytical methodology to evaluate the average rate which avoids the computation of the coverage probability pcov and needs only the moment generating function mgf of the aggregate interference at the probe mobile terminal the distinguishable characteristic of our analytical methodology consists in providing a tractable and numerically efficient framework that is applicable to general fading distributions including composite fading channels with small and mid scale fluctuations in addition our method can efficiently handle correlated log normal shadowing with little increase of the computational complexity the proposed mgf based approach needs the computation of either a single or a two fold numerical integral thus reducing the complexity of pcov based frameworks which require for general fading distributions the computation of a four fold integral

discrete solitons in nonlinear schrodinger lattices with a power law nonlinearity abstract we study the discrete nonlinear schrodinger lattice model with the onsite nonlinearity of the general form u 2 u we systematically verify the conditions for the existence and stability of discrete solitons in the one dimensional version of the model predicted by means of the variational approximation va and demonstrate the following monostability of fundamental solitons fss in the case of the weak nonlinearity 2 1 3 68 bistability in a finite range of values of the soliton s power for 3 68 2 1 5 and the presence of a threshold minimum norm of the fs for 2 1 5 we also perform systematic numerical simulations to study higher order solitons in the same general model i e bound states of the fss while all in phase bound states are unstable stability regions are identified for antisymmetric double solitons and their triple counterparts these numerical findings are supplemented by an analytical treatment of the stability problem which allows quantitively accurate predictions for the stability features of such multipulses when these waveforms are found to be unstable we show by means of direct simulations that they self trap into a persistent lattice breather or relax into a stable fs or sometimes decay completely

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

an algebraic principle for the stability of difference operators this paper gives necessary and sufficient algebraic criteria for the stability of the difference systemx t ax t r1 bx t r2

qualitative analysis for a ratio dependent predator prey model with disease and diffusion abstract this paper is purported to study a reaction diffusion system arising from a ratio dependent predator prey model with disease we study the dynamical behavior of the predator prey system the conditions for the permanent and existence of steady states and their stability are established we can obtain the bounds for positive steady state of the corresponding elliptic system the non existence results of non constant positive solutions are derived

permanence of periodic holling type predator prey system with stage structure for prey abstract in this paper we study the permanence of the following periodic holling type predator prey system with stage structure for prey x 1 t a t x 2 t b t x 1 t d t x 1 2 t e t x 1 t p t x 1 t y t x 2 t c t x 1 t f t x 2 2 t y t y t g t h t x 1 t p t x 1 t q t y t sufficient and necessary condition which guarantee the predator and the prey species to be permanent is obtained some new results are obtained

existence and global stability of periodic solutions of a discrete predator prey system with delays with the help of continuation theorem in coincidence degree theory and lyapunov functions we derive sufficient and realistic conditions that guarantee the existence of a positive periodic solution for a delayed discrete predator prey system and also obtain sufficient conditions for the global stability of positive periodic solutions

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

diffusive lotka volterra competition models on periodically evolving domains abstract the paper deals with the asymptotic dynamics of a diffusive lotka volterra competition model with periodic coefficients and zero flux boundary conditions acting on a spatially isotropic and temporally periodic evolving domain we determine sufficient conditions for the global stability of the spatially homogeneous positive periodic solution moreover the phenomenon of competitive exclusion is investigated

periodic solutions for a neutral nonlinear dynamical equation on a time scale abstract let t be a periodic time scale we use a fixed point theorem due to krasnosel ski to show that the nonlinear neutral dynamic system with delay x t a t x t c t x t k q t x t x t k t t has a periodic solution we assume that k is a fixed constant if t r and is a multiple of the period of t if t r under a slightly more stringent inequality we show that the periodic solution is unique using the contraction mapping principle

asymptotic analysis for linear difference equations we are concerned with asymptotic analysis for linear difference equations in a locally convex space first we introduce the profile operator which plays a central role in analyzing the asymptotic behaviors of the solutions then factorial asymptotic expansions for the solutions are given quite explicitly finally we obtain gevrey estimates for the solutions in a forthcoming paper we will develop the theory of cohomology groups for recurrence relations the main results in this paper lay analytic foundations of such an algebraic theory while they are of intrinsic interest in the theory of finite differences

breather solutions of the discrete nonlinear schrodinger equations with unbounded potentials in this paper i investigate the existence of nontrivial breather solutions of the discrete nonlinear schrodinger equation with the unbounded potential at infinity first i derive a discrete version of compact embedding theorem then combining the nehari manifold approach and the compact embedding theorem i show the existence of breather solutions without palais smale condition the results on the exponential decay of breather solutions are also provided in this paper

multiplicity of periodic solutions for a delayed ratio dependent predator prey model with monotonic functional response and harvesting terms abstract the existence of four positive periodic solutions for a delayed ratio dependent predator prey model with monotonic functional response x t x t a t b t x t c t g x t y t y t h 1 t y t y t f t g x t t y t t d t h 2 t is established by using the generalized continuation theorem where a t b t c t d t f t t h 1 t and h 2 t are all nonnegative periodic continuous functions with period 0 when h 1 t h 2 t 0 the conditions that guarantee the existence of four positive periodic solutions reduces exactly to that in fan et al 2004 1 and our main result also improves the corresponding results in zhang and hou 2010 2 and fan and wang 2001 3

moments based approach to the performance analysis of equal gain diversity in nakagami m fading in this letter an alternative moments based approach for the performance analysis of an l branch predetection equal gain combiner egc over independent or correlated nakagami m fading channels is presented exact closed form expressions are derived for the moments of the egc output signal to noise ratio snr while the corresponding moment generating function mgf is accurately approximated with the aid of pade spl acute approximants theory important performance criteria are studied the average output snr which is expressed in closed form both for independent and correlative fading and for arbitrary system parameters the average symbol error probability for several coherent noncoherent and multilevel modulation schemes and the outage probability which are both accurately approximated using the well known mgf approach the proposed mathematical analysis is illustrated by various numerical results and computer simulations have been performed to verify the validity and the accuracy of the theoretical approach

on the existence of homoclinic solutions of a class of discrete nonlinear periodic systems abstract in this paper we obtain a new sufficient condition on the existence of homoclinic solutions of a class of discrete nonlinear periodic systems by using critical point theory in combination with periodic approximations we prove that it is also necessary in some special cases

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

uniqueness of periodic solutions of a nonautonomous density dependent predator prey system abstract in this present paper we investigate the uniqueness of periodic solutions of a nonautonomous density dependent and ratio dependent predator prey system where not only the prey density dependence but also the predator density dependence are considered such that the studied predator prey system conforms to the realistically biological environment we start with a sufficient condition for the permanence of the system and then construct a weaker sufficient condition by introducing a specific set denoted as based on this and the brouwer fixed point theorem we obtain the existence condition of positive periodic solutions moreover since the uniqueness of positive periodic solutions can be ensured by global attractiveness we alternatively introduce a sufficient condition for global attractiveness similarly we also provide a sufficient condition for the uniqueness of non negative periodic solutions

permanence for a delayed discrete ratio dependent predator prey system with holling type functional response abstract sufficient conditions are established for the permanence in a delayed discrete predator prey model with holling type iii functional response n 1 k 1 n 1 k exp b 1 k a 1 k n 1 k 1 1 k n 1 k n 2 k n 1 2 k m 2 n 2 2 k n 2 k 1 n 2 k exp b 2 k 2 k n 1 2 k 2 n 1 2 k 2 m 2 n 2 2 k 2 our investigation confirms that when the death rate of the predator is rather small as well as the intrinsic growth rate of the prey is relatively large the species could coexist in the long run

global periodic solutions of a generalized n species gilpin ayala competition model abstract in this paper we investigate a generalized n species gilpin ayala competition system with several deviating arguments in periodic environment which is more general and more realistic than the classical lotka volterra competition systems by using the method of coincidence degree a set of easily verifiable sufficient conditions are derived for the existence of at least one strictly positive componentwise periodic solution some new results are obtained as applications we also apply our main results to some special cases of the system we consider here including the classical n species lotka volterra competition systems and n species gilpin ayala competition model which have been studied extensively in the literature some known results are improved and generalized the examples show that our criteria are new general and easily verifiable

multiple solutions for discrete periodic nonlinear schrodinger equations in this paper we study the existence of multibump solutions for discrete nonlinear schrodinger equations with periodic potentials we first reduce the existence of multibump homoclinic solutions to the existence of an isolated homoclinic solution with a nontrivial critical group then we study the existence of homoclinics with nontrivial critical groups for both superlinear and asymptotically linear discrete periodic nonlinear schrodinger equations and we provide simple sufficient conditions for the existence of homoclinics with nontrivial critical groups in the positive definite case as an application we get without any symmetry assumptions infinitely many geometrically distinct homoclinic solutions with exponential decay at infinity

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

existence and global stability of periodic solutions of a discrete ratio dependent food chain model with delay by using the continuation theorem base on gaines and mawhin s coincidence degree sufficient and realistic conditions are obtained for the global existence of positive periodic solutions for a discrete time nonautonomous food chain model and sufficient conditions for the global stability of positive periodic solutions are also obtained some known results are extended

performance of digital linear modulations on weibull slow fading channels a closed form expression is derived for the moment generating function of the weibull distribution valid when its fading parameter assumes integer values expressions for average signal to noise ratio signal outage and average symbol error rate are derived for single channel reception and independent multichannel diversity reception operating on flat weibull slow fading channels

existence and global attractivity of positive periodic solution for a volterra model with mutual interference and beddington deangelis functional response abstract in this paper a volterra model with mutual interference and beddington deangelis functional response is investigated some sufficient conditions which guarantee the existence and global attractivity of positive periodic solution for the system are obtained furthermore our results improve the main results of paper 1

a predator prey model with ivlev s functional response abstract the uniqueness of limit cycles is proved for a two dimensional predator prey system with a functional response of ivlev type the system of planar autonomous ode s is transformed to a lienard system to which a modified theorem of zhang is applied

periodicity in a food limited population model with toxicants and state dependent delays 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 food limited population model with toxicant and state dependent delays that is du t dt u t r t a t u t j 1 m b j t u t j t u t k t c t u t j 1 m d j t u t j t u t where r t k t a t bj t dj t j 1 2 m are continuous real valued periodic functions with period 0 and r t k t a t 0 bj t dj t 0 j 1 2 m are periodic continuous functions with period 0 j j are periodic with respect to their first arguments some new results are obtained

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

oscillation criteria for second order matrix dynamic equations on a time scale we obtain oscillation criteria for a second order self adjoint matrix differential equation on a measure chain in terms of the eigenvalues of the coefficient matrices and the graininess function we illustrate our results with some nontrivial examples

two parameter bifurcation in a predator prey system of ivlev type abstract our concern is to consider an ecological system with ivlev s functional response 1 e axof predator to prey in addition toa this system contains parametersrandd which represent the intrinsic rate of increase for the prey population and the death rate for the predator population respectively a necessary and sufficient condition for the uniqueness of limit cycles of the predator prey system is presented this result gives the bifurcation curve in the a d plane

positive periodic solutions for neutral delay ratio dependent predator prey model with holling type iii functional response abstract by using a continuation theorem based on coincidence degree theory some new and interesting sufficient conditions are obtained for the existence of positive periodic solutions for neutral delay ratio dependent predator prey model with holling type iii functional response x t x t r t a t x t 1 x t 2 c t x 2 t m 2 y 2 t x 2 t y t y t y t d t h t x 2 t t m 2 y 2 t t x 2 t t an example is represented to illustrate the feasibility of our main results

breathers in nonlinear lattices existence linear stability and quantization abstract it has been proved by the principle of anti integrable limit renamed here anti continuous limit and the implicit function theorem that under rather weak hypotheses there exist spatially localized and time periodic solutions breathers in arrays of nonlinear coupled classical oscillators provided the coupling is not too strong the models can be translationally invariant or not and be of any dimension there are also time periodic solutions corresponding to arbitrary distributions on the lattice of such solutions multibreathers the whole set of these solutions can be labeled by a discrete coding sequence the condition that the frequency of the breather or multibreather solution has no harmonics in the phonon spectrum can be discarded for a large subset of spatially extended time periodic solutions called phonobreather which correspond to special codes which can be also spatially chaotic and where no oscillator is at rest these results extend almost without change to models with coupled rotors the existence of rotobreathers which are exact solutions consisting of a single rotor rotating while the other rotors oscillate is proved there are also multirotobreather solutions and phono rotobreathers etc it is also shown that the phase of the single breathers constituting a multibreather or multirotobreather solution can be submitted to a phase torsion these new dynamical structures carry a nonzero energy flow in models with two dimensions and more the phase torsion of multibreather solutions can generate new dynamical solutions with vortices in the energy flow the dynamics of a quantum electron coupled to a classical lattice is also studied within the same approach from the anti continuous limit the existence of two kinds of polarobreathers which are spatially exponentially localized dynamical solutions is proved for a small enough electronic transfer integral the polarobreathers of the first kind include the standard static polaron the lattice configuration is static time independent when the electron is in an excited state i e the electronic oscillator oscillates periodically they can be spatially chaotic a polarobreather of the second kind corresponds to a localized periodic lattice oscillation associated with a localized quasiperiodic electronic oscillation the most simple of these solutions are those for which both the lattice oscillation and the electron wave function are mostly concentrated close to the same single site the standard floquet analysis of the linear stability of the breather and multibreather solutions is shown to be related with the band spectrum property of the newton operator involved in the implicit function theorem the krein theory of bifurcations is reinterpreted from this point of view the linear stability of the single breather and rotobreather solutions is then proved at least at small enough coupling finally it is shown that in the quantum version of translationally invariant classical models where there cannot exist in principle any strictly localized excitation there are narrow bands of excitations consisting of bound states of many bosons which are the quantum counterpart of the classical breathers the bandwidth of these excitations goes exponentially to zero with the number of bound phonons this theory provides simultaneously existence theorems and a new powerful and accurate numerical method for calculating practically any of the solutions which has been formally predicted to exist these numerical applications are currently written elsewhere

performance analysis of dual selection diversity in correlated weibull fading channels ascertaining the importance of the dual selection combining sc receivers and the suitability of the weibull model to describe mobile fading channels we study the performance of a dual sc receiver over correlated weibull fading channels with arbitrary parameters exact closed form expressions are derived for the probability density function the cumulative distribution function and the moments of the output signal to noise ratio snr important performance criteria such as average output snr amount of fading outage probability and average bit error probability for several modulation schemes are studied furthermore for these performance criteria novel closed form analytical expressions are derived the proposed analysis is complemented by various performance evaluation results including the effects of the input snr s unbalancing fading severity and fading correlation on the overall system s performance computer simulation results have verified the validity and accuracy of the proposed analysis

discrete breathers localization and transfer of energy in discrete hamiltonian nonlinear systems we present a partial review of results concerning the theory of discrete breathers in nonlinear hamiltonian and discrete systems these special time periodic solutions gained much interest during the last decade because they may be involved in numerous and various phenomena in physics and biophysics where they could produce nontrivial effects of energy focusing and transfer we first review the principles which govern their existence and which are used in the existence proofs available up to now next we discuss their linear stability and the interaction of discrete breathers with small amplitude waves showing also how they could grow or decay we also briefly discuss the existence of intraband dbs in systems with a linear discrete spectrum which are not spatially periodic random or otherwise and where linear waves cannot propagate we also show that nonlinearity may restore the existence of solutions that propagate energy we review some results concerning energy transportation by dbs and especially the main features associated with their mobility we briefly discuss new perspectives opened up by the theory for applications that in particular look especially interesting for biophysics

periodic solutions for a delayed predator prey system with stage structured predator on time scales in this paper a modified delayed predator prey system with stage structure for predator is proposed and studied which generalizes and incorporates as special cases some known models with the help of continuation theorem based on the gaines and mawhin coincidence degree theory we investigate the existence of periodic solutions for the proposed delayed predator prey system with stage structured predator and two kinds of functional responses called holling iii functional response and beddington deangelis functional response on time scales in particular when the time scale is chosen as the set of the real numbers or the integers the existence of the periodic solutions of the corresponding continuous time and discrete time models follows

positive periodic solutions for the neutral ratio dependent predator prey model by using a continuation theorem based on coincidence degree theory we obtain some new sufficient conditions for the existence of positive periodic solutions for the neutral ratio dependent predator prey model with holling type ii functional response

periodicity in a generalized semi ratio dependent predator prey system with time delays and impulses abstract with the help of a continuation theorem based on coincidence degree theory we establish necessary and sufficient conditions for the existence of positive periodic solutions in a generalized semi ratio dependent predator prey system with time delays and impulses which covers many models appeared in the literature when the results reduce to the semi ratio dependent predator prey system without impulses they generalize and improve some known ones

dynamics of a stochastic holling ii one predator two prey system with jumps abstract in this paper a stochastic holling ii one predator two prey system with jumps is investigated firstly the properties of the solution such as the existence and uniqueness of the global positive solution stochastic ultimate boundedness and the pathwise estimation are studied then we mainly establish the sufficient conditions for the extinction and persistence in the mean of the solution results show that positive jump noise is advantageous to the system while negative jump noise is disadvantageous finally a numerical example is introduced to illustrate the results

the effect of state dependent delay and harvesting on a stage structured predator prey model we propose and analyze a stage structured predator prey model in which the time from birth to maturity is directly related to the number of individuals present individuals mature more quickly when there are fewer of them around the state dependent time delay is taken to be an increasing differentiable bounded function in this research we study the dynamics of our model analytically we present results on positivity and boundedness of all populations criteria for the existence of all equilibria and uniqueness of a positive equilibrium are given in order to observe the effect of state dependent maturation delay local stability analysis around all equilibria of the proposed model is discussed due to variation of maturation delay also global stability of trivial and the boundary equilibria is investigated using liapunov functional and lasalle invariant principle to investigate the effect of state dependent maturation delay and the harvesting effort of all species we carried out numerical simulations

asymptotic behavior of solutions in nonautonomous predator prey patchy system with beddington type functional response abstract in this paper we study the asymptotic behavior of solutions in nonautonomous predator prey patchy system with beddington type functional response it is proved that the system is permanent under some appropriate conditions furthermore if the system is a n almost periodic one a set of easily verifiable sufficient conditions which guarantee the existence uniqueness and global asymptotic stability of a positive almost periodic solutions of system are obtained

the qualitative analysis of n species nonlinear prey competition systems in this paper we consider an n species nonlinear prey competition system using the differential inequality theorem and the v function method we obtain some sufficient conditions for the permanence and global asymptotic stability of the system

homoclinic solutions of discrete nonlinear schrodinger equations with asymptotically or super linear terms abstract in this paper we study the following periodic discrete nonlinear schrodinger equation u n n u n n g n u n n z where the nonlinearity g n is asymptotically or super linear the sufficient conditions on the existence and on the nonexistence of nontrivial solitons was established by using critical point theory

periodic solution of a delayed predator prey system without dominating instantaneous negative feedback by using the continuation theorem base on gaines and mawhin s coincidence degree sufficient and realistic conditions are obtained for the global existence of positive periodic solution for a delayed predator prey system without dominating instantaneous negative feedback indeed our result are applicable to statedependent delays

existence of gap solitons in periodic discrete nonlinear schrodinger equations in this paper we discuss how to use the critical point theory to study the existence of gap solitons for periodic discrete nonlinear schrodinger equations an open problem proposed by professor alexander pankov is solved

environmental periodicity and time delays in a food limited population model abstract sufficient conditions are obtained for the existence of a globally attracting positive periodic solution of the food limited population system modelled by the equation n t r t k t n t m k t c t r t n t m where m is a nonnegative integer and k r c are continuous positive periodic functions of period

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

permanence and periodicity of a delayed ratio dependent predator prey model with stage structure a periodic ratio dependent predator prey model with time delays and stage structure for both prey and predator is investigated it is assumed that immature individuals and mature individuals of each species are divided by a fixed age and that immature predators do not have the ability to attack prey sufficient conditions are derived for the permanence and existence of positive periodic solutions of the model numerical simulations are presented to illustrate the feasibility of our main results

qualitative analysis of a stochastic ratio dependent predator prey system a stochastic ratio dependent predator prey model is investigated in this paper by the comparison theorem of stochastic equations and ito s formula we obtain the global existence of a positive unique solution of the ratio dependent model besides a condition for species to be extinct is given and a persistent condition is established we also conclude that both the prey population and the ratio dependent function are stable in time average in the end numerical simulations are carried out to confirm our findings

periodic solutions of delayed leslie gower predator prey models with the help of continuation theorem base on gaines and mawhin s coincidence degree sufficient and realistic conditions are obtained for the global existence of positive periodic solutions for both the first and the second leslie gower predator prey models with distributed or state dependent delays

dynamics of a nonautonomous predator prey system with the beddington deangelis functional response abstract in this paper we systematically study the dynamics of a nonautonomous predator prey system with the beddington deangelis functional response the explorations involve the permanence extinction global asymptotic stability general nonautonomous case the existence uniqueness and stability of a positive almost periodic solution and a boundary almost periodic solution for the periodic almost periodic case the paper ends with some interesting numerical simulations that complement our analytical findings

discrete solitons for periodic discrete nonlinear schrodinger equations in this paper we study a class of periodic discrete nonlinear schrodinger equations with superlinear nonlinearities and periodic potential by using the critical point theory we establish results on the existence of discrete solitons our results improve some recent ones

positive periodic solutions of a class of delay differential system with feedback control with the help of continuation theorem based on gaines and mawhin s coincidence degree sufficient and realistic conditions are obtained for the global existence of positive periodic solutions for the delay differential system with feedback control when these results are applied to some special delay population models some new results are obtained and some known results are generalized

discrete nonlinear schrodinger equations with superlinear nonlinearities abstract in this paper we study the discrete nonlinear equation lu n u n n g n u n n z where belongs to a finite spectral gap of the operator l or it is a lower edge of a finite spectral gap by using a variant generalized weak linking theorem for strongly indefinite problem developed by schechter and zou we will study the existence of nontrivial solitons for this equation with gn is super linear

periodicity in a nonlinear predator prey system on time scales with state dependent delays 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 nonlinear state dependent delays predator prey system on time scales

periodic solutions and permanence for a delayed nonautonomous ratio dependent predator prey model with holling type functional response by using the continuation theorem of coincidence degree theory the existence of positive periodic solutions for a delayed ratio dependent predator prey model with holling type iii functional response x t x t a t b t t k t s x s ds c t x2 t y t m2y2 t x2 t y t y t e t x2 t m2y2 t x2 t d t is established where a t b t c t e t and d t are all positive periodic continuous functions with period 0 m 0 and k s is a measurable function with period is a nonnegative constant the permanence of the system is also considered in particular if k s 0 s where 0 s is the dirac delta function at s 0 our results show that the permanence of the above system is equivalent to the existence of positive periodic solution

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

periodicity of scalar dynamic equations and applications to population models easily verifiable sufficient criteria are established for the existence of periodic solutions of a class of nonautonomous scalar dynamic equations on time scales which incorporate as special cases many single species models governed by ordinary differential and difference equations when the time scale is the set of all real and all integer numbers respectively

positive periodic solutions of neutral lotka volterra system with feedback control 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 neutral lotka volterra system with periodic delays and feedback control our results extend and improve existing results and have further applications in population dynamics

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

sufficient conditions for the existence positive periodic solutions of a class of neutral delay models with feedback control 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 neutral model with periodic delays and feedback controldndt n t a t email protected t n t email protected i 1nb i t n email protected i t email protected i 1nc i t n email protected i t email protected t u t email protected i 1nd i t u email protected i t dudt e t u t f t n t email protected i 1ng i t n email protected i t our results extend and improve existing results and have further applications in population dynamics

existence of positive periodic solution of a ratio dependent predator prey model on time scale with monotonic functional response by using gaines and mawhin s continuation theorem the existence of positive periodic solutions of a ratio dependent predator prey model on time scale with monotonic functional response is investigated and some easily verifiable sufficient criteria are established

periodic solutions for hamiltonian systems without ambrosetti rabinowitz condition and spectrum 0 abstract in this paper we consider the superquadratic second order hamiltonian system u t a t u t h t u t 0 t r our main results here allow the classical ambrosetti rabinowitz superlinear condition to be replaced by a general superquadratic condition and 0 lies in a gap of b where b d 2 d t 2 a t we will study the ground state periodic solutions for this problem the main idea here lies in an application of a variant generalized weak linking theorem for strongly indefinite problem developed by schechter and zou

periodic and decaying solutions in discrete nonlinear schrodinger with saturable nonlinearity we demonstrate the existence of solutions in the discrete nonlinear schrodinger equation dnls with saturable nonlinearity we consider two types of solutions to dnls periodic and vanishing at infinity calculus of variations and the nehari manifolds are employed to establish the existence of these solutions we present some extensions of our results combining the nehari manifold approach and the mountain pass argument

existence of multiple positive periodic solutions of delayed predator prey models with functional responses in this paper by applying the continuation theorem of coincidence degree theory we establish some new criteria for the existence of multiple positive periodic solutions for the delayed predator prey model x t x t r t a t x t b t f x t y t y t y t c t f x email protected d t when functional response function f is monotonic or nonmonotonic

standing waves for discrete schrodinger equations in infinite lattices with saturable nonlinearities abstract in this paper we consider the periodic discrete nonlinear equation l u n u n g n u n n z lim n u n 0 where l is a jacobi operator and the nonlinearities g n s are asymptotically linear as s in the two different cases is a spectral endpoint of l or it belongs to a finite spectral gap of l we obtain the existence of nontrivial solitons of this equation by using variational methods in particular a necessary and sufficient condition is obtained for the existence of gap solitons of the nonlinear equation here solitons appear when we look for standing waves of some discrete nonlinear schrodinger equations

periodic solution of a delayed predator prey system with michaelis menten type functional response by using the continuation theorem base on gaines and mawhin s coincidence degree sufficient and realistic conditions are obtained for the global existence of positive periodic solution for a delayed predator prey system with michaelis menten type functional response indeed our results are applicable to state dependent delays

performance of dual maximal ratio combining diversity in nonidentical correlated weibull fading channels using pade spl acute approximation in this letter we evaluate the performance of the dual branch maximal ratio combining mrc diversity scheme in nonidentical correlated weibull fading channels with arbitrary parameters we first use the pade spl acute approximation pa to find closed form rational expressions for the moment generating function mgf of the output signal to noise ratio snr of the mrc receiver different performance measures such as the outage probability and the average symbol error rate for different linear modulations are then presented using the well known mgf approach furthermore the effect of the input snrs unbalancing the severity of fading and the degree of correlation on the system performance are also studied our results are validated by comparing them with computer simulations and we show that the pa technique is indeed a convenient tool for such performance evaluation studies

periodic solutions of a single species discrete population model with periodic harvest stock abstract we discuss a discrete population model describing single species growth with periodic harvest stock the theory of coincidence degree is applied to show that the model equation admits two periodic solutions under minor technical assumptions we show that one of these two periodic solutions is positive and attracts almost all positive solutions

periodic solutions for delay lotka volterra competition systems abstract by using the continuation theorem of coincidence degree theory sufficient and realistic conditions are obtained for the existence of positive periodic solutions for the periodic distributed delay lotka volterra competition system du i t dt u i t r i t a ii t u i t j 1 j i n a ij t 0 t ij k ij s u j t s ds i 1 2 n and the periodic state dependent delay lotka volterra competition system du i t dt u i t r i t a ii t u i t j 1 j i n a ij t u j t j t u 1 t u n t i 1 2 n where ri aii 0 aij 0 j i i j 1 2 n are continuous periodic functions tij 0 j i i j 1 2 n kij c tij 0 0 0 tijkij s ds 1 j i i j 1 2 n i c rn 1 r and i i 1 2 n are periodic with respect to their first arguments respectively

the numerical simulation of periodic solutions for a predator prey system in this article the existence and global stability of periodic solutions for a semi ratio dependent predator prey system with holling iv functional response and time delays are investigated using coincidence degree theory and lyapunov method sufficient conditions for the existence and global stability of periodic solutions are obtained a numerical simulation is given to illustrate the results

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

persistence and global stability of a ratio dependent predator prey model with stage structure a ratio dependent predator prey model with stage structure for prey is investigated first sufficient conditions are derived for the uniform persistence and impermanence of the model next by constructing appropriate lyapunov functions a set of easily verifiable sufficient conditions are obtained for the global asymptotic stability of nonnegative equilibria of the model numerical simulations are presented to illustrate the validity of our main results

existence of positive periodic solutions for an impulsive semi ratio dependent predator prey model with dispersion and time delays in this paper we propose an impulsive semi ratio dependent predator prey model with dispersion and time delays by applying the continuation theorem of coincidence degree theory we establish a set of sufficient conditions on the existence of at least one positive periodic solution the result not only improves but also generalizes that for the case without pulses

higher order dynamic equations on measure chains wronskians disconjugacy and interpolating families of functions this paper introduces generalized zeros and hence disconjugacy of nth order linear dynamic equations which cover simultaneously as special cases among others both differential equations and difference equations we also define markov fekete and descartes interpolating systems of functions the main result of this paper states that disconjugacy is equivalent to the existence of any of the above interpolating systems of solutions and that it is also equivalent to a certain factorization representation of the operator the results in this paper unify the corresponding theories of disconjugacy for nth order linear ordinary differential equations and for nth order linear difference equations

discrete schrodinger equations with sign changing nonlinearities infinitely many homoclinic solutions abstract we obtain infinitely many homoclinic solutions for a class of discrete nonlinear schrodinger equations where nonlinearities are superlinear at infinity and primitive functions of nonlinearities are allowed to be sign changing by using some weaker conditions our results extend and improve some existed results in the literature besides some examples are given to illuminate our results

permanence and periodicity of a delayed ratio dependent predator prey model with holling type functional response and stage structure a periodic and delayed ratio dependent predator prey system with holling type iii functional response and stage structure for both prey and predator is investigated it is assumed that immature predator and mature individuals of each species are divided by a fixed age and immature predator do not have the ability to attack prey sufficient conditions are derived for the permanence and existence of positive periodic solution of the model numerical simulations are presented to illustrate the feasibility of our main results

existence uniqueness and global asymptotic stability of positive solutions of a predator prey system with holling ii functional response with random perturbation abstract this paper discusses a randomized two species predator prey system with holling ii functional response we show that the positive solution of the associated stochastic delay differential equation does not explode to infinity in a finite time in addition the existence uniqueness and global asymptotic stability of the positive solutions are studied