effect of weak prey in leslie gower predator prey model a leslie gower prey predator model incorporating partial prey protection is proposed prey densities are divided into two groups strong and weak the special dynamic of each group is considered the condition of existence and uniqueness of the equilibrium point in the positive octant is determined and by constructing a suitable lyapunov function it is shown that the unique equilibrium point is stable in the positive octant the effects of strong prey becoming weak prey is studied and it is shown that it has no influence on the persistent property of the system and can enhance the co existence of the prey predator

optimal harvesting control problem for linear periodic age dependent population dynamics in this paper we investigate an optimal harvesting problem for linear periodic age dependent population dynamics namely we consider the lotka mckendrick model with periodic vital rates and a periodic forcing term that sustains oscillations by mazur s theorem we demonstrate existence of solutions of the optimal control problem oh and by the conception of normal cone we also obtain the first order necessary conditions of optimality for problem oh finally under suitable assumptions we give uniqueness of solutions of the optimal control problem oh our results extend some known criteria

dynamics of a nonlocal multi type sis epidemic model with seasonality abstract in this paper we propose and study a multi type sis nonlocal epidemic model with seasonality we first establish the existence of the spreading speed c and the non existence of periodic traveling waves with wave speed c c then we prove the existence and asymptotic behavior of the periodic traveling fronts with speed c c finally the existence of the critical periodic traveling wave fronts is established by using a limiting argument to overcome the difficulty of lack of compactness of solution maps of the nonlocal system with respect to compact open topology we show that the solution sequence is pre compact in l loc r 2 r m

approximation by chlodowsky type jakimovski leviatan operators we introduce a generalization of the jakimovski leviatan operators constructed by a jakimovski and d leviatan 1969 in 1 and the theorems on convergence and the degree of convergence are established we also give a voronovskaya type theorem furthermore we study the convergence of these operators in a weighted space of functions on a positive semi axis and estimate the approximation by using a new type of weighted modulus of continuity introduced by a d gadjiev and a aral 2007 in 9

asymptotic speeds of spread and traveling waves for integral equations and delayed reaction diffusion models abstract the theory of asymptotic speeds of spread and monotone traveling waves is generalized to a large class of scalar nonlinear integral equations and is applied to some time delayed reaction and diffusion population models

electronic properties of the tight binding fibonacci hamiltonian the analysis of the electronic properties of the tight binding fibonacci hamiltonian is carried out using dynamical systems techniques two classes of fibonacci sequences are considered corresponding to the cases when there are two types of building blocks and also when there are three types of building blocks the recursion relations for the traces of the transfer matrices are determined and studied for various extensions of the fibonacci case with the golden mean some differences are obtained between the various types of second order fibonacci sequences and are most likely due to long range order applications of this work to the transmission of light through a multilayered medium and the electrical resistance of a one dimensional quasicrystal as determined by the landauer formula are presented

the landauer conductance of generalised fibonacci superlattices numerical results abstract the quantum model for quasi one dimensional generalised fibonacci superlattices gfs is formulated the landauer electrical conductance l of gfs is studied numerically it is shown that l as a function of incident particle energy e oscillates strongly and exhibits resonant character we have verified numerically that l e reaches its local maximum for e corresponding to energy eigenenvalues of charge in superlattices

modeling and analysis in a prey predator system with commercial harvesting and double time delays both maturation delay for prey and gestation delay for predator are considered positivity of solutions and uniform persistence of system are investigated combined dynamic effects of double time delays and economic interest are studied existence and control for singularity induced bifurcation are investigated local stability analysis and properties of hopf bifurcation are studied a differential algebraic prey predator system with commercial harvesting on predator is proposed where maturation delay for prey and gestation delay for predator are considered since commercial harvesting is dynamically influenced by variation of economic interest we will investigate combined dynamic effects of double time delays and economic interest on population dynamics positivity of solutions and uniform persistence of system are studied in the absence of time delay by taking economic interest as bifurcation parameter existence of singularity induced bifurcation is investigated based on differential algebraic system theory state feedback controllers are designed to eliminate singularity induced bifurcation and stabilize the proposed system around corresponding interior equilibrium in the presence of double time delays by analyzing associated characteristic transcendental equation it is found that interior equilibrium loses local stability when double time delays cross corresponding critical values according to hopf bifurcation theorem for functional differential equation existence of hopf bifurcation is investigated as local stability switches based on normal form theory and center manifold theorem directions of hopf bifurcation and stability of the bifurcating periodic solutions are studied numerical simulations are carried out to show consistency with theoretical analysis

a sequence of positive linear operators associated with an approximation process considering a general class of discrete linear positive operators by using a one to one function we associate to the class mentioned above a new sequence of operators our aim is to establish the transfer of approximation properties on this construction the study is carried out in a weighted space and our results are materialized in obtaining both a convergence theorem of korovkin type and an inequality for the approximation error expressed in terms of a certain weighted modulus of smoothness two particular cases are analyzed

localization problem in one dimension mapping and escape a one dimensional schr odinger equation in a discontinuous quasiperiodic potential is reduced to a recursion relation for transfer matrices and then to one for traces of these matrices when the potential is periodic the bandwidth goes to zero as an algebraic function of the period with a critical index which depends upon the potential strength this critical index is also evaluated as the solution to an escape rate problem for the recursion relations

effect of harvesting delay and diffusion in a generalist predator prey model in compared with specialist predators which feed almost exclusively on a specific species of prey generalist predators feed on many types of species consequently their dynamics is not coupled to the dynamics of a specific prey population and the generalist predators has itself growth function which be extended a well known logistic growth term we develop a generalist predator prey model with diffusion and study the effect of harvesting and delay under neumann conditions the stability of the equilibria is firstly investigated and the existence of traveling wave solutions is then established by constructing a pair of upper lower solutions and using the cross iteration method and schauder s fixed point theorem

optimal harvesting of a stochastic delay tri trophic food chain model with levy jumps abstract in this paper the optimal harvesting of a stochastic delay tri trophic food chain model with levy jumps is considered we introduce two kinds of environmental perturbations in this model one is called white noise which is continuous and is described by a stochastic integral with respect to the standard brownian motion and the other one is jumping noise which is modeled by a levy process under some mild assumptions the critical values between extinction and persistent in the mean of each species are established the sufficient and necessary criteria for the existence of optimal harvesting policy are established and the optimal harvesting effort and the maximum of sustainable yield are also obtained we utilize the ergodic method to discuss the optimal harvesting problem the results show that white noises and levy noises significantly affect the optimal harvesting policy while time delays is harmless for the optimal harvesting strategy in some cases at last some numerical examples are introduced to show the validity of our results

travelling wave solutions for a nonlocal dispersal hiv infection dynamical model abstract this paper is devoted to developing a nonlocal dispersal hiv infection dynamical model the existence of travelling wave solutions is investigated by employing schauder s fixed point theorem that is we study the existence of travelling wave solutions for r 0 1 and each wave speed c c in addition the boundary asymptotic behaviour of travelling wave solutions at is obtained by constructing suitable lyapunov functions and employing lebesgue dominated convergence theorem by employing a limiting argument we investigate the existence of travelling wave solutions for r 0 1 and c c the main difficulties are that the semiflow generated by the model does not have the order preserving property and the solutions lack of regularity

global attractivity of nonautonomous stage structured population models with dispersal and harvest the nonautonomous stage structured single species dispersal model with harvesting of mature individuals in an n patch environment is considered in which the individual members of the population have a life history that takes them through two stages immature and mature by using the theory of monotone and concave operators to functional differential equations we establish conditions under which this population dynamical system admits a positive periodic solution which attracts all positive solutions

optimal harvesting policy for general stochastic logistic population model abstract we consider some optimal harvesting policies for a general stochastic logistic population model for two management objectives that are maximum sustainable yield and the maximum retained profits the optimal harvesting policies are obtained meanwhile the optimal harvest effort the maximum of expectation of sustainable yield or retained profits and the corresponding variance are given

the estimates of approximation by using a new type of weighted modulus of continuity in this paper we introduce a new type modulus of continuity for function f belonging to a particular weighted subspace of c 0 and show that it has some properties of ordinary modulus of continuity we obtain some estimates of approximation of functions with respect to a suitable weighted norm via the new type moduli of continuity finally we give some examples

global asymptotical stability of a n 1 dimensional leslie gower predator prey model abstract by constructing suitable lyapunov function we obtain the global asymptotical stability of n 1 dimensional leslie gower predator prey models it is shown that the prey refuge and the proportional harvesting have no influence on the global asymptotical stability of the system but they can change the position of the unique interior equilibrium finally mathematic analysis shows that if we choose and control the harvesting efforts e e i appropriately we can not only harvest the biological resources and achieve the economic interest but also protect the biological resources

traveling waves in a delayed sir epidemic model with nonlinear incidence we study the traveling waves of a diffusive sir epidemic model with a general nonlinear incidence we obtain the threshold dynamics for spatial spread of the disease we show that c is the minimum wave speed for the existence of traveling wave solutions we establish the existence and non existence of traveling wave solutions for a diffusive sir model with a general nonlinear incidence the existence proof is shown by introducing an auxiliary system applying schauder s fixed point theorem and then a limiting argument the nonexistence proof is obtained by two sided laplace transform when the speed is less than the critical velocity numerical simulations support the theoretical results we also point out the effects of the delay and the diffusion rate of the infective individuals on the spreading speed

optimal harvesting of a stochastic mutualism model with levy jumps in this letter a stochastic mutualism model with levy jumps and harvesting is considered under some simple assumptions sufficient and necessary criteria for the existence of optimal harvesting policy are established the optimal harvesting effort and the maximum of sustainable yield are also obtained the effects of random noises on the optimal harvesting of the model are discussed and some numerical simulations are introduced to illustrate the main results

asymptotic patterns of a structured population diffusing in a two dimensional strip abstract in this paper we derive a population model for the growth of a single species on a two dimensional strip with neumann and robin boundary conditions we show that the dynamics of the mature population is governed by a reaction diffusion equation with delayed global interaction using the theory of asymptotic speed of spread and monotone traveling waves for monotone semiflows we obtain the spreading speed c the non existence of traveling waves with wave speed 0 c c and the existence of monotone traveling waves connecting the two equilibria for c c

asymptotic behavior and traveling wave solutions for parabolic functional differential equations on presente une generalisation de la theorie des equations kpp et de diffusion bistables non lineaires on montre que des solutions onde de propagation existent pour des equations fonctionnelles paraboliques non lineaires

entire solutions for a multi type sis nonlocal epidemic model in r or z abstract in this paper we study entire solutions for a multi type sis nonlocal epidemic model in r or z the existence and asymptotic behavior of spatially independent solutions are first established some new entire solutions are then constructed by combining traveling wave fronts with different speeds and a spatially independent solution from the viewpoint of epidemiology the results provide some new spread ways of the epidemic

traveling wavefronts of a prey predator diffusion system with stage structure and harvesting from a biological point of view we consider a prey predator type free diffusion fishery model with stage structure and harvesting first we study the stability of the nonnegative constant equilibria in particular the effect of harvesting on the stability of equilibria is discussed and supported with numerical simulation then employing the upper and lower solution method we show that when the wave speed is large enough there exists a traveling wavefront connecting the zero solution to the positive equilibrium of the system numerical simulation is also carried out to illustrate the main result

delay induced traveling wave fronts in reaction diffusion equations of kpp fisher type this paper explores the impact of delay on the existence of traveling wave fronts in reaction diffusion equations of kpp fisher type for two such equations one being local and the other with nonlocal effect arising from the age structure of the population we show that delay can induce slow traveling wave fronts

modelling and analysis of a harvested prey predator system incorporating a prey refuge the present paper deals with a prey predator model incorporating a prey refuge and independent harvesting in either species our study shows that using the harvesting efforts as controls it is possible to break the cyclic behaviour of the system and drive it to a required state the possibility of existence of bionomic equilibria has been considered the problem of optimal harvest policy is then solved by using pontryagin s maximal principle

the landauer resistance of generalized fibonacci lattices the dynamical maps approach abstract we study the electronic properties of the generalized fibonacci lattices containing finite numbers of rectangular barriers distributed quasi periodically in the framework of the kronig penney model we derive the dynamical maps which allow to calculate the landauer resistance of the considered systems the maps obtained are an extension of the existing results to 1 the more general class of distributions of rectangular barriers and 2 the case of complex unimodular matrices

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

optimal harvesting of a stochastic delay competitive lotka volterra model with levy jumps abstract this paper systematically investigates the optimal harvesting of a stochastic delay competitive lotka volterra model with levy jumps under some simple assumptions the sufficient conditions for extinction and stable in the time average of each species are established the stability in distribution of this model is proved under our assumptions finally the sufficient and necessary criteria for the existence of optimal harvesting policy are established and the explicit expression of the optimal harvesting effort and the maximum of sustainable yield are also obtained and some numerical simulations are introduced to demonstrate the theoretical results

spreading speed and traveling waves for a multi type sis epidemic model abstract the theory of asymptotic speeds of spread and monotone traveling waves for monotone semiflows is applied to a multi type sis epidemic model to obtain the spreading speed c and the nonexistence of traveling waves with wave speed c c then the method of upper and lower solutions is used to establish the existence of monotone traveling waves connecting the disease free and endemic equilibria for c c this shows that the spreading speed coincides with the minimum wave speed for monotone traveling waves we also give an affirmative answer to an open problem presented by rass and radcliffe l rass j radcliffe spatial deterministic epidemics math surveys monogr 102 amer math soc providence ri 2003

bifurcations of a ratio dependent predator prey system with constant rate harvesting the ratio dependent predator prey model exhibits rich interesting dynamics due to the singularity of the origin the objective of this paper is to study the dynamical properties of the ratio depend

optimal harvesting policy for stochastic logistic population model abstract in this paper we consider some optimal harvesting policies for single population models in which the harvest effort and the intrinsic growth rate are disturbed by environment noises we choose the maximum sustainable yield and the maximum retained profits as two management objectives and obtain the optimal harvesting policies respectively for the two objectives we give the optimal harvest effort that maximizes the sustainable yield or retained profits the maximum of expectation of sustainable yield or retained profits and the corresponding variance their explicit expressions are determined by the coefficients of equation and the disturbance intensity

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

dynamic behaviour of a delayed predator prey model with harvesting abstract in this paper we analyze the dynamics of a delayed predator prey system in the presence of harvesting this is a modified version of the leslie gower and holling type ii scheme the main result is given in terms of local stability global stability influence of harvesting and bifurcation direction of hopf bifurcation and the stability of bifurcating periodic solutions are also studied by using the normal form method and center manifold theorem

optimal harvesting policy of a stochastic food chain population model this note studies the optimal harvesting policy of a stochastic three species food chain model the almost sufficient and necessary conditions for the existence of optimal harvesting policy are established meanwhile the optimal harvesting effort and the maximum of expectation of sustainable yield are obtained

complex dynamics of a diffusive predator prey model with strong allee effect and threshold harvesting abstract in this paper complex dynamics of a diffusive predator prey model is investigated where the prey is subject to strong allee effect and threshold harvesting the existence and stability of nonnegative constant steady state solutions are discussed the existence and nonexistence of nonconstant positive steady state solutions are analyzed to identify the ranges of parameters of pattern formation spatially homogeneous and nonhomogeneous hopf bifurcation and discontinuous hopf bifurcation are proved these results show that the introduction of strong allee effect and threshold harvesting increases the system spatiotemporal complexity finally numerical simulations are presented to validate the theoretical results

diffusion has no influence on the global asymptotical stability of the lotka volterra prey predator model incorporating a constant number of prey refuges by constructing a suitable lyapunov function we obtain the global asymptotical stability of the lotka volterra prey predator model incorporating a constant number of prey refuges and diffusion it is shown that diffusion has no influence on the global asymptotical stability of the system with homogeneous neumann boundary condition

spreading speeds and traveling wavefronts for second order integrodifference equations this paper is concerned with the spreading speeds and traveling wavefronts for second order integrodifference equations by introducing an auxiliary integrodifference system the spreading speed is established for the integrodifference equation it is shown that the spreading speed coincides with the minimal wave speed for monotonic traveling wavefronts furthermore we prove that the traveling wavefronts are stable by applying the squeezing technique finally we analyze the different effects of the delay term appearing in the integrodifference equation from the viewpoint of ecology

coexistence region and global dynamics of a harvested predator prey system the study of populational dynamics with harvesting is related to the optimal man agement of renewable resources in this paper we consider a predator prey model in which two ecologically interacting species are harvested independently with constant rates the main purpose of the present work is to offer a complete mathematical analysis for the model and to describe some of the significant qualitative results that may be expected to arise from the interplay of biological forces our study shows that the maximum safe harvest may be far less than what would be assumed from a local analysis for the equilibria it is also proved that the harvested predator prey system may exhibit very complicated dynamics such as a spontaneous appearance of a homoclinic orbit and multiple limit cycles

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

existence and stability of traveling wave fronts in reaction advection diffusion equations with nonlocal delay this paper is concerned with the existence uniqueness and globally asymptotic stability of traveling wave fronts in the quasi monotone reaction advection diffusion equations with nonlocal delay under bistable assumption we construct various pairs of super and subsolutions and employ the comparison principle and the squeezing technique to prove that the equation has a unique nondecreasing traveling wave front up to translation which is monotonically increasing and globally asymptotically stable with phase shift the influence of advection on the propagation speed is also considered comparing with the previous results our results recovers and or improves a number of existing ones in particular these results can be applied to a reaction advection diffusion equation with nonlocal delayed effect and a diffusion population model with distributed maturation delay some new results are obtained

dynamics in a ratio dependent predator prey model with predator harvesting abstract the objective of this paper is to study systematically the dynamical properties of a ratio dependent predator prey model with nonzero constant rate predator harvesting it is shown that the model has at most two equilibria in the first quadrant and can exhibit numerous kinds of bifurcation phenomena including the bifurcation of cusp type of codimension 2 i e bogdanov takens bifurcation the subcritical and supercritical hopf bifurcations these results reveal far richer dynamics compared to the model with no harvesting and different dynamics compared to the model with nonzero constant rate prey harvesting in d xiao l jennings bifurcations of a ratio dependent predator prey system with constant rate harvesting siam appl math 65 2005 737 753 biologically it is shown that nonzero constant rate predator harvesting can prevent mutual extinction as a possible outcome of the predator prey interaction and remove the singularity of the origin which was regarded as pathological behavior for a ratio dependent predator prey model in p yodzis predator prey theory and management of multispecies fisheries ecological applications 4 2004 51 58

critical traveling waves in a diffusive disease model abstract in this paper the existence of a non trivial positive and bounded critical traveling wave solution of a diffusive disease model whose reaction system has infinitely many equilibria is obtained for the first time this gives an affirmative answer to an open problem left in wang et al 2012 19 our result shows that the critical traveling wave in this model is a mix of front s component and pulse i component type

traveling waves for the diffusive nicholson s blowflies equation we consider traveling wave front solutions for the diffusive nicholson s blowflies equation on the real line the existence of such solutions is proved using the technique developed by j wu and x zou j dyn differ equations 13 3 2001 some numerical simulation using the iteration formula of wu and zou 7 is also provided

accelerating propagation in a recursive system arising from seasonal population models with nonlocal dispersal abstract the system of interest is defined by iterations of the poincare map of a time periodic population model with symmetric nonlocal dispersal and periodic time delay under the kpp type setting we show that the system admits the spreading speed c 0 that coincides with the minimal speed of traveling waves where c if the nonlocal dispersal kernel j is exponentially bounded and c if j is exponentially unbounded further the latter case gives rises to an accelerating propagation that the level set of solutions with compactly supported initial values locate in between two exponential functions in time

dynamics of prey threshold harvesting and refuge the dynamics of a predator prey model with continuous threshold prey harvesting and prey refuge is studied one central question is how harvesting and refuge could directly affect the dynamics of the ecosystem such as the stability properties of some coexistence equilibria and periodic solutions theoretical and numerical methods are used to investigate boundedness of solutions existence of bionomic equilibria as well as the existence and stability properties of equilibrium points and periodic solutions several bifurcations are also studied