permanence for a delayed discrete three level food chain model with beddington deangelis functional response a discrete three level food chain model with beddington deangelis functional response is investigated it is shown that the system is permanent under some appropriate conditions

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

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

stability and bifurcation for a delayed predator prey model and the effect of diffusion abstract we consider a predator prey system with one or two delays and a unique positive equilibrium e its dynamics are studied in terms of the local stability of e and of the description of the hopf bifurcation that is proven to exist as one of the delays taken as a parameter crosses some critical values we also consider a reaction diffusion system with neumann conditions resulting from adding one spatial variable and diffusion terms in the previous model the spectral and bifurcation analysis in the neighborhood of e now as a stationary point of this latter system is addressed and the results obtained for the case without diffusion are applied

hopf bifurcation and turing instability in spatial homogeneous and inhomogeneous predator prey models abstract this paper is concerned with two species spatial homogeneous and inhomogeneous predator prey models with beddington deangelis functional response for the spatial homogeneous model the asymptotic behavior of the interior equilibrium and the existence of hopf bifurcation of nonconstant periodic solutions surrounding the interior equilibrium are considered furthermore the direction of hopf bifurcation and the stability of bifurcated periodic solutions are investigated for the model with no flux boundary conditions turing instability of the interior equilibrium solution is studied in particular turing instability region regarding the parameters is established finally to verify our theoretical results some numerical simulations are also included

soliton like phenomena in one dimensional cross diffusion systems a predator prey pursuit and evasion example abstract we have studied properties of non linear waves in a mathematical model of a predator prey system with pursuit and evasion we demonstrate a new type of propagating wave in this system the mechanism of propagation of these waves essentially depends on the taxis represented by non linear cross diffusion terms in the mathematical formulation we have shown that the dependence of the velocity of wave propagation on the taxis has two distinct forms parabolic and linear transition from one form to the other correlates with changes in the shape of the wave profile dependence of the propagation velocity on diffusion in this system differs from the square root dependence typical of reaction diffusion waves we also demonstrate that for systems with negative and positive taxis for example pursuit and evasion there typically exists a large region in the parameter space where the waves demonstrate quasi soliton interaction colliding waves can penetrate through each other and waves can also reflect from impermeable boundaries

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 reaction diffusion equations modelling the effect of fluctuating water levels on prey predator interactions prey predator interactions are influenced by many ecological factors in this paper a prey predator model with spatial diffusion under homogeneous neumann boundary conditions is investigated to study the impact of water level on persistence of two fish populations living in an artificial lake we obtain some important qualitative properties including the existence of the global positive solution the dissipation and permanence of this system the existence of a unique globally stable periodic solution is also presented some numerical examples are presented to verify our results

discrete time dynamics of a system with crowding effect and predator partially dependent on prey in the present study the stability and bifurcation analysis of discrete time predator prey system with predator partially dependent on prey and crowding effect of predator is examined global stability of the system at the fixed points has been discussed the specific conditions for existence of flip bifurcation and hopf bifurcation in the interior of r 2 have been derived by using a center manifold theorem and bifurcation theory numerical simulations have been carried out to show the complex dynamical behavior of the system and to justify our analytic results in case of flip bifurcation numerical simulations presented cascade of period doubling bifurcation in the orbits of period 2 4 8 chaotic orbits and stable window of period 9 orbit whereas in case of hopf bifurcation smooth invariant circle bifurcates from the fixed point the complexity of dynamical behavior is confirmed by computation of lyapunov exponents

the impact of cost uncertainty on cournot oligopoly games abstract in this paper cournot oligopoly model is examined with an uncertain quadratic cost function a random quadratic cost function is introduced in this model the model consists of three competed firms on which each firm in the model wants to maximize its expected profit and also wants to minimize its uncertainty by minimizing the cost to handle this multi objective optimization problem the expectation and worst case approaches are adopted used to study uncertainty the existence and uniqueness of the equilibrium are obtained the asymptotic behavior of the equilibrium point is also investigated complete stability and bifurcation analysis are provided the obtained theoretical results are verified by numerical simulation

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

permanence and global attractivity of a discrete multispecies lotka volterra competition predator prey systems in this paper we propose a discrete multispecies lotka volterra competition predator prey systems for general non autonomous case sufficient conditions which ensure the permanence and the global stability of the system are obtained for periodic case sufficient conditions which ensure the existence of a globally stable positive periodic solution of the system are obtained

turing instability for a ratio dependent predator prey model with diffusion abstract ratio dependent predator prey models have been increasingly favored by field ecologists where predator prey interactions have to be taken into account the process of predation search in this paper we study the conditions of the existence and stability properties of the equilibrium solutions in a reaction diffusion model in which predator mortality is neither a constant nor an unbounded function but it is increasing with the predator abundance we show that analytically at a certain critical value a diffusion driven turing type instability occurs i e the stationary solution stays stable with respect to the kinetic system the system without diffusion we also show that the stationary solution becomes unstable with respect to the system with diffusion and that turing bifurcation takes place a spatially non homogenous non constant solution structure or pattern arises a numerical scheme that preserve the positivity of the numerical solutions and the boundedness of prey solution will be presented numerical examples are also included

stable periodic solution of a discrete periodic lotka volterra competition system abstract this paper discusses a discrete lotka volterra competition system we first obtain the persistence of the system assuming that the coefficients in the system are periodic we obtain the existence of a periodic solution moreover under some additional conditions this periodic solution is globally stable our results not only reduce to those for the scalar equation when there is no coupling but also improve and complement some in the literature

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

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 dynamics of an epidemic model with an unspecified degree in this paper we give the global dynamical behaviors of a reduced sirs epidemic model with a nonlinear incidence rate ki ps q we first discuss the qualitative properties of the equilibria in the interior of the first quadrant and study the bifurcations including saddle node bifurcation transcritical bifurcation hopf bifurcation and bogdanov takens bifurcation then we consider equilibria at infinity determining the number of orbits in exceptional directions for the global tendency in this discussion the unspecified degree p q of polynomials and their high degeneracy prevent us from using the methods of blowing up or normal sectors in some cases we lastly discuss the existence and uniqueness of limit cycles

global analysis in a predator prey system with nonmonotonic functional response a predator prey system with nonmonotonic functional response is considered global qualitative and bifurcation analyses are combined to determine the global dynamics of the model the bifurcation a

global asymptotic stability of almost periodic solution for a multispecies competition predator system with time delays by using the theory of comparison theorem and suitable lyapunov functional a multispecies competition predator system with holling iii functional response and time delays is investigated in this paper some sufficient conditions for the existence and uniqueness and global asymptotic stability of almost periodic solutions of this system is obtained

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

numerical study of an influenza epidemic model with diffusion abstract a diffusive epidemic model is investigated with a view to describe the transmission of influenza as an epidemic the equations are solved numerically using the splitting method under different initial distribution of population density it is shown that the initial population distribution and diffusion play an important role for spread of disease it is also shown that interventions medical and nonmedical significantly slow down the spread of disease stability of equilibria of the numerical solutions are also established

dynamics in a diffusive predator prey system with strong allee effect and ivlev type functional response abstract the dynamics of a kind of reaction diffusion predator prey system with strong allee effect in the prey population is considered we prove the existence and uniqueness of the solution and give a priori bound hopf bifurcation and steady state bifurcation are studied results show that the allee effect has significant impact on the dynamics

existence of multiple sliding segments and bifurcation analysis of filippov prey predator model abstract in a prey predator model an effective management strategy called the threshold policy control tpc is proposed resulting in filippov system considering the limitation of environmental resources filippov system with the weighted sum as the index is put forward in the prey predator model with ivlev s function response firstly the existences of sliding segments in four cases have been discussed completely further the sliding mode dynamics the existences of different types of equilibria and tangent point regular virtual equilibrium and sliding mode bifurcations have been addressed moreover the results obtained in present work indicate that the local sliding bifurcations such as boundary focus boundary node and tangent bifurcations occur sequentially with the threshold value varying finally some global sliding bifurcations including touching and buckling bifurcations are investigated by employing numerical techniques

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

convergence results in a well known delayed predator prey system abstract in this paper we provide a detailed and explicit procedure of obtaining some regions of attraction for the positive steady state assumed to exist of a well known lotka volterra type predator prey system with a single discrete delay our procedure requires the delay length to be small a detailed example is presented the method used here is to construct a proper liapunov functional in a restricted region

rich dynamics of a predator prey model with spatial motion one of the central issues in ecosystem is the influence of space on the stability of the populations as a result a predator prey model with spatial diffusion and cubic growth rate is investigated asymptotical properties of solutions of such spatial model are obtained based on comparison principle what is more we show the global stability of positive equilibrium by constructing lyapunov function we also show how predator diffuses has impact on the pattern dynamics based on numerical simulations the results may well enrich the findings in predator prey systems with spatial motions

dynamic behavior of a discrete modified ricker beverton holt model in this paper a discrete modified ricker beverton holt model with two parameters is investigated the boundedness the persistence and the global asymptotic stability are considered at the same time in the unstable domain the chaotic behavior will be shown for some particular parameters usually chaos can cause the population to run a higher risk of extinction and make the population become out of control due to the unpredictability to control the unpredictability the immigration parameter will be introduced when the immigration constant is larger than a positive number chaos will be controlled and the positive equilibrium is stable furthermore the obtained results show that the reproduction rate of adults plays an important role in the process of the population

optimization of non linear gravity models through generalized simulated annealing abstract in this paper we apply the generalized simulated annealing gsa approach to the inversion of gravity data for 2 d and 3 d density distributions we consider a modeling process where the input is the vector of model parameters m that can be density contrast mass or some coordinates and the output is described by the transformation h m d where d is the vector of data parameters we generally have access in practical problems if the vector d describes the observed actual output of the system the problem is to choose or estimate the parameters m est in order to minimize in some sense in our case in the least squares sense the difference between the observed vector d and the prescribed output of the system h m est the tests with synthetic data show the promising application of gsa in gravity inversion the results obtained suggest us that the gsa approach enables to find quickest optimization machines than the two conventional approaches boltzmann and cauchy machines

dynamics of an epidemic model with spatial diffusion mathematical models are very useful in analyzing the spread and control of infectious diseases which can be used to predict the developing tendency of the infectious disease determine the key factors and to seek the optimum strategies of disease control as a result we investigated the pattern dynamics of a spatial epidemic model with logistic growth by using amplitude equation we found that there were different types of stationary patterns including spotted mixed and stripe patterns which mean that spatial motion of individuals can form high density of diseases the obtained results can be extended in other related fields such as vegetation patterns in ecosystems

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

reaction diffusion predator prey parasite system and spatiotemporal complexity abstract this paper deals with the spatial pattern formation in a diffusive predator prey parasite ppp model where predator feeds on infected prey following type ii response function and infection spreads among prey species through horizontal transmission the study is accomplished with respect to an ecological parameter that quantifies the reproductive gain of predator and two epidemiological parameters which measure the force of infection and virulence of the disease we show analytically that the interior equilibrium loses its stability through hopf bifurcation in the absence of diffusion if the reproductive gain of predator crosses some threshold value in case of diffusive system it is shown that the interior equilibrium which is otherwise stable may lose its stability due to diffusion criteria for the occurrence of various types of instability like turing hopf turing and pure hopf associated with the ppp model are presented with illustrations our simulation results reveal that this diffusion driven instability creates various spatio temporal patterns like spot stripe mixture of spots stripes and spiral patterns depending upon the values of ecological and diffusion parameters turing instability and the corresponding patterns are also observed with the variation of two epidemiological parameters interestingly the epidemiological parameters that measure the infection rate and virulence of the disease show opposite patterns with their increasing values

global stability for infinite delay lotka volterra type systems abstract in this paper sufficient conditions are established for the global stability of the saturated equilibrium of an infinite delay nonautonomous lotka volterra type system the present work is distinguished from previous work principally be allowing the system to be nonautonomous and relaxing the traditional requirement that the undelayed intraspecific competition dominates both the delayed intraspecific competition as well as the interspecific interactions we require the undelayed intraspecific competition to dominate the latter but not the former

stability analysis on a predator prey system with distributed delays abstract this paper concerns the local and global dynamical properties of the nonnegative and positive equilibria of a lotka volterra predator prey system with distributed delays it is shown that while the positive equilibrium does not exist the nonnegative equilibrium is globally asymptotically stable or globally attractive as long as the delays are small enough if the positive equilibrium exists it is shown that it is locally asymptotically stable when the delays are suitably small furthermore an explicit asymptotic stability region for the positive equilibrium is also obtained based on a liapunov functional

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

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

global existence of periodic solutions in a class of delayed gause type predator prey systems where x t y t denote the population density of prey and predator at time t respectively g e p e and z s are assumed to satisfy appropriate conditions v a positive constant stands for the death rate of predator y in the absence of prey x we may think of this system as herbivores y grazing upon vegetation x which take time r to recover in view of the fact that many predator prey systems display sustained fluctuations for examples see freedman l it is thus desirable to construct predator prey models capable of producing nonconstant periodic solutions when r 0 1 1 reduces to the well known undelayed gause type or kolmogorov predator prey systems again see freedman l and the references cited theorein under some assumptions the resulting systems can have a unique limit cycle in the positive cone see kuang and freedman 2 and the references cited therein to the best of our knowledge about delayed population interaction models the existing literature establishes the existence of a periodic solution by hopf bifurcation argument or reduces the delayed systems to undelayed systems of higher dimensions therefore these existence results are generally local most of the existing results on the global existence of nonconstant periodic solutions in delayed equations deal with scalar equations with single discrete delay such as 13 101

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

numerical continuation methods for studying periodic travelling wave wavetrain solutions of partial differential equations abstract periodic travelling waves wavetrains are an important solution type for many partial differential equations in this paper i review the use of numerical continuation for studying these solutions i discuss the calculation of the form and stability of a given periodic travelling wave and the calculation of boundaries in a two dimensional parameter plane for wave existence and stability i also describe the automated implementation of these numerical continuation procedures via the software package wavetrain http www ma hw ac uk wavetrain i conclude by discussing ongoing work on numerical continuation methods for determining the absolute stability of periodic travelling waves

on factorization of matrix polynomials abstract an interrelationship between the numerical range of matrix polynomials and its factorization with linear or nonlinear factors is investigated here also a bound on the number of components of numerical range is given

uniform persistence in functional differential equations abstract in this paper we investigate the question of uniform persistence for retarded functional differential equations by utilizing liapunov like functions razumikhin techniques and differential inequalities we are able to establish criteria for uniform persistence analogous to those obtained by others for ordinary differential equations difference equations and reaction diffusion equations we apply these criteria to some well known biological models with delay our results indicate that the conditions which guarantee the existence of an interior equilibrium are enough to ensure uniform persistence moreover these conditions are equivalent to uniform persistence for the cases without delay as well

factorization of matrix polynomials with multiple roots abstract the concept of a multiple root of matrix polynomial l is introduced and associated spectral properties of l are investigated a statement concerning factorization of l is presented applications are made to factorizations of the matrix polynomial l for any positive integer

on the connectedness of numerical range of matrix polynomials abstract an investigation on nonconnectedness of numerical range for monic matrix polynomials l is undertaking here the distribution of eigenvalues of l to the components of numerical range and some other algebraic properties are also presented

effect of cross diffusion on the stationary problem of a predator prey system with a protection zone abstract this paper is concerned with the steady state problem of a predator prey cross diffusion system with herd effect allee effect and a protection zone some sufficient conditions for the existence of positive steady state solutions are given our proof is based on the local and global bifurcation theory and some a priori estimates some limiting behavior of positive steady states with respect to the allee effect constant or the diffusion coefficient d are discussed

the existence uniqueness and global attractivity of periodic solution for a type of neutral functional differential system with delays in this article by applying the coincidence degree theory and constructing a suitable lyapunov functional the authors study a kind of neutral functional differential system with delays some sufficient conditions which guarantee the existence uniqueness and global attractivity of periodic solution for this system are obtained

a non standard numerical scheme for a generalized gause type predator prey model abstract a non standard finite difference scheme is constructed to simulate a predator prey model of gause type with a functional response using fixed point analysis it is shown that the scheme preserves the physical properties of the model and gives results that are qualitatively equivalent to the real dynamics of the model it is also shown that the scheme undergoes a supercritical hopf bifurcation for a specific value of the bifurcation parameter k0 this leads to the existence of a stable limit cycle created by the scheme when the bifurcation parameter passes through k0 as predicted by the continuous model the scheme is used to simulate the model with the functional responses of holling types ii and iii the simulation results generated by the non standard finite difference scheme are compared with those obtained from the standard methods such as forward euler and runge kutta methods these comparisons show that the standard methods give erroneous results that disagree with the theoretical predictions of the model however it is proved that the proposed non standard finite difference scheme is consistent with the asymptotic dynamics of the model numerical simulations are presented to support these facts

permanence for the michaelis menten type discrete three species ratio dependent food chain model with delay abstract a discrete three trophic level food chain model with ratio dependent michaelis menten type functional response is investigated it is shown that under some appropriate conditions the system is permanent the results indicate that to make the species coexist in the long run it is a surefire strategy to keep the death rate of the predator and top predator rather small and the intrinsic growth rate of the prey relatively large

dynamics in a predator prey model with space and noise in this paper we presented a predator prey model with spatial diffusion and density dependent noise it was found that the spatial model without noise has spotted pattern however combined with density dependent noise the predator prey model exhibits transition from spotted to labyrinth pattern furthermore when noise intensity and temporal correlation are in appropriate levels the populations will extinct the obtained results suggest that stochastic factors may play an important role in populations dynamics which well enrich the findings in predator prey models

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

permanence and stability of equilibrium for a two prey one predator discrete model in this letter a predator prey system of two prey one predator discrete model is investigated it is proved that the system is permanence under some appropriate conditions by jacobian matrix method a sufficient and necessary condition is derived for the local asymptotic stability of a equilibrium of the system meanwhile we give a suitable example for supporting our theoretical result

pattern dynamics of a spatial epidemic model with time delay we presented an epidemic model with delay emergence of spatial pattern is obtained rich dynamics is shown by analysis and numerical results observed data confirms our theoretical results the nonlinear incidence rate can explain the complicated infectious process of disease and time delay describing the latent period widely exists in the process of disease contagion in this paper a spatiotemporal epidemic model with nonlinear incidence rate is investigated in particular we considered that the time delay is relatively small in this case the characteristic equation are derived we obtain two mechanisms of instability of the positive constant stationary state that is one is the diffusion induced instability and the other one is delay induced instability moreover the results of numerical simulation validate our theoretical analyses the obtained results may well catch some major features for epidemic models

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

stability and hopf bifurcation in a delayed ratio dependent holling tanner type model in this study a delayed ratio dependent holling tanner type predator prey model is investigated first the local stability of a positive equilibrium is studied and then the existence of hopf bifurcations is established by using the normal form theory and center manifold theorem the explicit algorithm determining the stability direction of the bifurcating periodic solutions are derived finally we perform the numerical simulations for justifying the theoretical results

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

stability and bifurcation analysis for a delayed lotka volterra predator prey system the present paper deals with a delayed lotka volterra predator prey system by linearizing the equations and by analyzing the locations on the complex plane of the roots of the characteristic equation we find the necessary conditions that the parameters should verify in order to have the oscillations in the system in addition the normal form of the hopf bifurcation arising in the system is determined to investigate the direction and the stability of periodic solutions bifurcating from these hopf bifurcations to verify the obtained conditions a special numerical example is also included

measure for the resolving power and bias effect in the nonlinear inverse analysis of geophysical potential fields several measures are proposed for the power of resolution and the bias effect of nonlinearity in the inverse analysis of geophysical potential fields they are the power of complete resolution for the entire system of both data and parameters the power of partial resolution for individual data prediction and parameter estimation and the bias for the effect of linearization of a nonlinear function relations between the measures for the resolution power and bias are derived the tradeoff relations between the resolving power and estimation variance are also demonstrated all these measures are tested on a synthetic gravity data set a two dimensional 2 d forward gravity model is employed to demonstrate the use of the measures proposed in this study the selection of the reference depth z0 and the number of nonzero eigenvalues q is highlighted based on the 2 d prism forward model the best z0 is that value that produces the least curvature in the plot of singular values versus q the choice of q i

coexistence of limit cycles and homoclinic loops in a sirs model with a nonlinear incidence rate recently ruan and wang j differential equations 188 2003 pp 135 163 studied the global dynamics of a sirs epidemic model with vital dynamics and a nonlinear saturated incidence rate under certain conditions they showed that the model undergoes a bogdanov takens bifurcation i e it exhibits saddle node hopf and homoclinic bifurcations they also considered the existence of none one or two limit cycles in this paper we investigate the coexistence of a limit cycle and a homoclinic loop in this model one of the difficulties is to determine the multiplicity of the weak focus we first prove that the maximal multiplicity of the weak focus is 2 then feasible conditions are given for the uniqueness of limit cycles the coexistence of a limit cycle and a homoclinic loop is obtained by reducing the model to a universal unfolding for a cusp of codimension 3 and studying degenerate hopf bifurcations and degenerate bogdanov takens bifurcations of limit cycles and homoclinic loops of order 2

bifurcation analysis of a predator prey system with nonmonotonic functional response we consider a predator prey system with nonmonotonic functional response p x frac mx ax 2 bx 1 by allowing b to be negative b 2 sqrt a p x is concave up for small values of x 0 a

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

stability and delays in a predator prey system abstract sufficient conditions for both local and global stability of the positive equilibrium in a predator prey system with time delays are obtained by constructing suitable lyapunov functionals a remark on the mistake by k n murty and m a s srinivas j math anal appl 158 1991 333 341 is also included

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

permanence and global attractivity of the discrete gilpin ayala type population model in this paper we propose a discrete gilpin ayala competition model and a discrete gilpin ayala type multispecies competition predator model for general nonautonomous case sufficient conditions which ensure the permanence and the global stability of the system are obtained for periodic case sufficient conditions which ensure the existence of an unique globally stable positive periodic solution of the system are obtained an example together with its numeric simulations shows the feasibility of the main 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

ecological chaos and the choice of optimal harvesting policy abstract harvested populations fluctuate because of two primary reasons the inherent nonlinearity contained in the interactions among the constituent species and the forces of harvesting acting on the oscillatory dynamics resulting from species interactions during the course of these fluctuations population densities make excursions to low densities when the ecological system executes chaotic motion extinction sized densities are common thus it is imperative to design harvesting strategies which aim at maximizing economic gains giving due consideration to the ecological health of the concerned ecological system the present study was designed and performed to figure out how to set harvesting strategies which optimize the economic gain the choice of optimal harvesting policy can be made only if dynamical features of the concerned ecological system are well understood in this paper we have consider the temporal and spatiotemporal interactions among phytoplankton zooplankton and fish population with holling type ii and holling type iii functional responses we have calculated stability analysis of the model system and performed the numerical simulations for both non spatial and spatial models to figure out the parameters that are responsible for chaotic dynamics of the model system the temporal model system shows rich dynamics including limit cycles and chaos whereas spatial model shows different types of patterns for population distribution in this work we have taken the case study of sundarban wetland ecosystem we have carried out the analysis of maximum sustainable yield and identified the parameters that are responsible for good health of wetland ecosystem through numerical simulation results

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

matrix polynomials with spectral radius equal to the numerical radius in this paper we study a class of matrix polynomials with the property that spectral radius and numerical radius coincide special attention is paid to the spectrum on the boundary of the numerical range

versal unfoldings of predator prey systems with ratio dependent functional response abstract in this paper we study the versal unfolding of a predator prey system with ratio dependent functional response near a degenerate equilibrium in order to obtain all possible phase portraits for its perturbations we first construct the unfolding and prove its versality and degeneracy of codimension 2 then we discuss all its possible bifurcations including transcritical bifurcation hopf bifurcation and heteroclinic bifurcation give conditions of parameters for the appearance of closed orbits and heteroclinic loops and describe the bifurcation curves phase portraits for all possible cases are presented

permanence of a discrete n species food chain system with time delays in this paper a discrete n species food chain system with time delays is considered by applying the comparison theorem of difference equation sufficient conditions are obtained for the permanence of the system

bifurcation and chaos in a discrete physiological control system in this paper we introduce a new method to discrete a physiological control system with delay and investigate the dynamical behavior of the discrete model basic properties of the discrete system are analyzed by means of lyapunov exponent spectrum and bifurcation diagrams analysis results show that this system has complex dynamics with some interesting characteristics which may provide some new knowledge for us in fields of physiology

periodic traveling wave train and point to periodic traveling wave for a diffusive predator prey system with ivlev type functional response abstract a diffusive predator prey system with ivlev type scheme is investigated in this article the existences of a small amplitude periodic traveling wave train p and the traveling wave solution connecting the boundary equilibrium e u 1 0 to the periodic traveling wave p are obtained the existence of this point to periodic solution reveals that the predator invasion leads to the periodic population densities in the coexistence domain and thus plays a mild role in the evolution of predator prey communities the techniques used here are the hopf bifurcation theorem the improved shooting method combining with the geometric singular perturbation method

global stability in delay differential systems without dominating instantaneous negative feedbacks abstract most of the global stability or convergence results appearing so far for delayed lotka volterra type systems or other delay differential systems require that the instantaneous negative feedbacks dominate both delayed feedback and interspecific interactions such a requirement is rarely met in real systems since feedbacks are generally delayed this leads to the long standing question under what conditions will the global stability of a nonnegative steady state of a differential delay system persist when time delays involved in some part of the negative feedbacks are small enough this paper presents a partial answer to this open question roughly our results show that if the delay differential system remains dissipative when delays are introduced then the above open question has an affirmative answer our results also improve some recent findings

stability and bifurcation of a predator prey model with disease in the prey and temporal spatial nonlocal effect in this paper we consider the dynamics of a predator prey model with disease in the prey and ratio dependent michaelis menten functional response the model is a reaction diffusion system with a nonlocal term representing the temporal spatial weighted average for the prey density the limiting case of the system reduces to the lotka volterra diffusive system with logistic growth of the prey we study the linear stability of the two non trivial steady states either with or without nonlocal term the bifurcations to three types of periodic solutions occurring from the coexistence steady state are investigated for two particular kernels which reveal the important significance of temporal spatial nonlocal effects