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

polar factorization and monotone rearrangement of vector valued functions given a probability space x p and a bounded domain r in rd equipped with the lebesgue measure 1 i normalized so that 10 i i it is shown under additional technical assumptions on x and q that for every vector valued function u e lp x p rd there is a unique polar factorization u v s where is a convex function defined on r and s is a measure preserving mapping from x p into q i i provided that u is nondegenerate in the sense that p u e 0 for each lebesgue negligible subset e of rd through this result the concepts of polar factorization of real matrices helmholtz decomposition of vector fields and nondecreasing rearrangements of real valued functions are unified the monge amgre equation is involved in the polar factorization and the proof relies on the study of an appropriate monge kantorovich problem

hopf bifurcation and stability in predator prey model with a stage structure for prey a predator prey system with b d functional response and stage structure for prey is presented in the d t plane the regions of stability and hopf bifurcation are found by analyzing the associated characteristic transcendental equation further global stability of equilibria are studied by using comparison theorem some numerical simulations are also given to illustrate our results

a proof of sudakov theorem with strictly convex norms the paper establishes a solution to the monge problem in mathbb r n for a possibly asymmetric norm cost function and absolutely continuous initial measures under the assumption that the unit ball is strictly convex but not necessarily differentiable nor uniformly convex the proof follows the strategy initially proposed by sudakov in 1976 found to be incomplete in 2000 the missing step is fixed in the above case adapting a disintegration technique introduced for a variational problem by strict convexity mass moves along rays and we also investigate the divergence of the vector field of rays

harmless delays for uniform persistence abstract this paper studies a two dimensional predator prey system with a finite number of discrete delays our purpose is to demonstrate that the time delays are harmless for uniform persistence of the solutions of the system the results are obtained by constructing suitable persistence functionals

an elementary proof of the polar factorization of vector valued functions we present an elementary proof of an important result of y brenier br1 br2 namely that vector fields in d satisfying a nondegeneracy condition admit the polar factorization u x s x where is a convex function and s is a measure preserving mapping brenier solves a minimization problem using monge kantorovich theory whereas we turn our attention to a dual problem whose euler lagrange equation turns out to be

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

bifurcation analysis of modified leslie gower predator prey model with michaelis menten type prey harvesting abstract in the present paper we discuss bifurcation analysis of a modified leslie gower prey predator model in the presence of nonlinear harvesting in prey we give a detailed mathematical analysis of the model to describe some significant results that may arise from the interaction of biological resources the model displays a complex dynamics in the prey predator plane the permanence stability and bifurcation saddle node bifurcation transcritical hopf andronov and bogdanov takens of this model are discussed we have analyzed the effect of prey harvesting and growth rate of predator on the proposed model by considering them as bifurcation parameters as they are important from the ecological point of view the local existence and stability of the limit cycle emerging through hopf bifurcation is given the emergence of homoclinic loops has been shown through simulation when the limit cycle arising though hopf bifurcation collides with a saddle point this work reflects that the feasible upper bound of the rate of harvesting for the coexistence of the species can be guaranteed numerical simulations using matlab are carried out to demonstrate the results obtained

hopf bifurcation of a predator prey system with stage structure and harvesting abstract in this paper a two species predator prey system with stage structure and harvesting is investigated the existence of hopf bifurcations of the system is given and the stability and directions of hopf bifurcations are determined by applying the normal form theory and the center manifold theorem

chaotic dynamics of a three species prey predator competition model with noise in ecology in this paper we investigate a three species ecosystem consisting of a prey a predator and a top predator the predator survives on the prey and the top predator survives on both the prey and the predator the mathematical model consists of non linear simultaneous differential equations all the eight equilibrium points of the model are identified and by using routh hurwitz criteria as well as lyapunov function we derive the criteria for local and global stabilities also the population intensities of fluctuations variances around the positive equilibrium due to noise are computed their stability is also analyzed with computer simulation using matlab some numerical simulations for justifying the theoretical analysis are also provided the main conclusions are supplied in conclusion

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

bounded solutions and wavefronts for discrete dynamics this paper deals with the second order nonlinear difference equation dd r k dd u k q kg u k 1 0 where r k and q k are positive real sequences defined on n cup 0 and the nonlinearity g r to r is nonnegative and nontrivial sufficient and necessary conditions are given for the existence of bounded solutions starting from a fixed initial condition u 0 the same dynamic with f instead of g such that uf u 0 for u not 0 was recently extensively investigated on the contrary our nonlinearity g is of a small appearance in the discrete case its introduction is motivated by the analysis of wavefront profiles in biological and chemical models the paper emphasizes the many different dynamical behaviors caused by such a g with respect to the equation involving function f some applications in the study of wavefronts complete this work

on the stability of non autonomous perturbed lotka volterra models the paper is devoted to an extended lotka volterra system of differential equations of predator prey model the extension is proposed with perturbation terms which are null for the positive equilibrium state in the original lotka volterra system the equilibrium state is not asymptotically stable due to the fact that perturbations are periodic in time the aim of the paper is to characterize a form of perturbation terms guaranteeing the asymptotic stability or instability of equilibrium state the reason of the proposed model is that for large time scale the lotka volterra model is too simple to be realistic in the paper the non autonomous perturbations do not change the equilibrium state but introduce functions of time as well as for additional perturbed terms as for the main part of the equations modified from lotka volterra model theorems are proposed in a renormalized form of the differential equations for time and the two variables the key point of the paper comes from the use of a liapunov function introduced in section 2 which allows to obtain conditions for the asymptotic stability section 3 and instability section 4 by using a cetaiev instability theorem following conditions on the renormalized coefficients in time of system 6 an appendix recalls the main results of the liapunov direct method for non autonomous binary systems of ordinary differential equations

the monge problem for supercritical mane potentials on compact manifolds abstract we prove the existence of optimal transport maps for the monge problem when the cost is a finsler distance on a compact manifold our point of view consists in considering the distance as a mane potential and to rely on recent developments in the theory of viscosity solutions of the hamilton jacobi equation

least gradient problem with respect to a non strictly convex norm abstract we study the planar least gradient problem with respect to an anisotropic norm for continuous boundary data we prove existence of minimizers for strictly convex domains furthermore we inspect the issue of uniqueness and regularity of minimizers only in terms of the modes of convexity of the norm and the domain the results are independent from the regularity of the norm

constructing optimal maps for monge s transport problem as a limit of strictly convex costs the monge kantorovich problem is to move one distribution of mass onto another as efficiently as possible where monge s original criterion for efficiency 19 was to minimize the average distance transported subsequently studied by many authors it was not until 1976 that sudakov showed solutions to be realized in the original sense of monge i e as mappings from rn to rn 23 a second proof of this existence result formed the subject of a recent monograph by evans and gangbo 7 who avoided sudakov s measure decomposition results by using a partial differential equations approach in the present manuscript we give a third existence proof for optimal mappings which has some advantages and disadvantages relative to existing approaches it requires no continuity or separation of the mass distributions yet our explicit construction yields more geometrical control than the abstract method of sudakov indeed this control turns out to be essential for addressing a gap which has recently surfaced in sudakov s approach to the problem in dimensions n 3 see the remarks at the end of this section it is also shorter and more flexible than either and can be adapted to handle transportation on riemannian manifolds or around obstacles as we plan to show in a subsequent work 13 the problem considered here is the classical one problem 1 monge fix a norm d x y llx yll on rn and two densities non negative borel functions f fe ll rn satisfying the mass balance condition

free boundaries in optimal transport and monge ampere obstacle problems given compactly supported 0 f g 2 l 1 r n the problem of trans porting a fraction m min kfkl1 kgkl1 of the mass of f onto g as cheaply as possible is considered where cost per unit mass transported is given by a cost function c typically quadratic c x y x y 2 2 this question is shown to be equivalent to a double obstacle problem for the monge ampere equation for which sucient conditions are given to guarantee uniqueness of the solution such as f vanishing on sptg in the quadratic case the part of f to be transported increases monotonically with m and if sptf and sptg are separated by a hyperplane h then this part will separated from the balance of f by a semiconcave lipschitz graph over the hyperplane if f f and g g are bounded away from zero and infinity on separated strictly convex domains r n for the quadratic cost this graph is shown to be a c 1 loc hypersurface in whose normal coincides with the direction transported the optimal map between f and g is shown to be holder continuous up to this free bound ary and to those parts of the fixed boundary which map to locally convex parts of the path connected target region

algorithms for combining rooted triplets into a galled phylogenetic network this paper considers the problem of determining whether a given set t of rooted triplets can be merged without conflicts into a galled phylogenetic network and if so constructing such a network when the input t is dense we solve the problem in o t time which is optimal since the size of the input is theta t in comparison the previously fastest algorithm for this problem runs in o t 2 time we also develop an optimal o t time algorithm for enumerating all simple phylogenetic networks leaf labeled by l that are consistent with t where l is the set of leaf labels in t which is used by our main algorithm next we prove that the problem becomes np hard if extended to nondense inputs even for the special case of simple phylogenetic networks we also show that for every positive integer n there exists some set t of rooted triplets on n leaves such that any galled network can be consistent with at most 0 4883 cdot t of the rooted triplets in t on the other hand we provide a polynomial time approximation algorithm that always outputs a galled network consistent with at least a factor of frac 5 12 0 4166 of the rooted triplets in t

topological degree in the generalized gause prey predator model abstract we consider a generalized gause prey predator model with t periodic continuous coefficients in the case where the poincare map p over time t is well defined the result of the paper can be explained as follows we locate a subset u of r 2 such that the topological degree d i p u equals to 1 the novelty of the paper is that the later is done under only continuity and some monotonicity assumptions for the coefficients of the model a suitable integral operator is used in place of the poincare map to cope with possible nonuniqueness of solutions the paper therefore provides a new framework for studying the generalized gause model with functional differential perturbations and multi valued ingredients

competing subcommunities of mutualist and a generalized kamke theorem a model of a biological community of species is considered the community consists of two competing subcommunities each of which has the property that each pair of species of the subcommunity interact in a mutually beneficial or noninterfering manner sufficient conditions are given that the two subcommunities can coexist the coexistence state being a stable equilibrium the domains of attraction of stable equilibria are considered the sharpest results are for the special case of lotka volterra systems mathematically the fundamental tool is a generalized kamke theorem

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

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

faster computation of the robinson foulds distance between phylogenetic networks the robinson foulds distance a widely used metric for comparing phylogenetic trees has recently been generalized to phylogenetic networks given two phylogenetic networks n 1 n 2 with n leaf labels and at most m nodes and e edges each the robinson foulds distance measures the number of clusters of descendant leaves not shared by n 1 and n 2 the fastest known algorithm for computing the robinson foulds distance between n 1 and n 2 runs in o me time in this paper we improve the time complexity to o ne logn for general phylogenetic networks and o nm logn for general phylogenetic networks with bounded degree assuming the word ram model with a word length of logn bits and to optimal o m time for leaf outerplanar networks as well as optimal o n time for level 1 phylogenetic networks that is galled trees we also introduce the natural concept of the minimum spread of a phylogenetic network and show how the running time of our new algorithm depends on this parameter as an example we prove that the minimum spread of a level k network is at most k 1 which implies that for one level 1 and one level k phylogenetic network our algorithm runs in o k 1 e time

the monge problem for distance cost in geodesic spaces we address the monge problem in metric spaces with a geodesic distance x d is a polish space and dl is a geodesic borel distance which makes x dl a non branching geodesic space we show that under the assumption that geodesics are d continuous and locally compact we can reduce the transport problem to 1 dimensional transport problems along geodesics we introduce two assumptions on the transport problem which imply that the conditional probabilities of the first marginal on each geodesic are continuous or absolutely continuous w r t the 1 dimensional hausdorff distance induced by dl it is known that this regularity is sufficient for the construction of a transport map we study also the dynamics of transport along the geodesic the stability of our conditions and show that in this setting dl cyclical monotonicity is not sufficient for optimality

the concept of force in population dynamics abstract the area of population dynamics has a rich history of the development and analysis of models of biological and social phenomena using ordinary differential equations this paper describes a method for understanding the influence one variable exerts on another in such models as a force with the relative effects of these forces providing a narrative explanation of the curvature in variable behaviour using the stock flow form of a model a symbolic notation is developed that identifies the forces with the causal pathways of the model s feedback loops a force is measured by its impact defined as the ratio of acceleration to rate of change computed by differentiation along its associated pathway between variables different phases of force dominance are determined to enhance the standard stability analysis of the models providing an explanation of model behaviour in newtonian mechanical terms the concepts developed are applied to well known models from mathematical biology the spruce budworm model where force dominance identifies scenarios that give clarity to intervention points and the lotka volterra predator prey model where the analysis highlights the importance of dissipative forces in achieving stability conclusions are drawn on the explanatory power of this approach with suggestions made for future work

computing the maximum agreement of phylogenetic networks we introduce the maximum agreement phylogenetic subnetwork problem masn for finding branching structure shared by a set of phylogenetic networks we prove that the problem is np hard even if restricted to three phylogenetic networks and give an o n2 time algorithm for the special case of two level 1 phylogenetic networks where n is the number of leaves in the input networks and where n is called a level f phylogenetic network if every biconnected component in the underlying undirected graph induces a subgraph of n containing at most f nodes with indegree 2 we also show how to extend our technique to yield a polynomial time algorithm for any two level f phylogenetic networks n1 n2 satisfying f o log n more precisely its running time is o v n1 v n2 2f1 f2 where v ni and fi denote the set of nodes in ni and the level of ni respectively for i 1 2

spatio temporal complexity of a delayed diffusive model for plant invasion abstract in this paper we develop a diffusive plant invasion model with delay under the homogeneous neumann boundary condition first the existence and uniqueness of a non negative solution persistence property and local asymptotic stability of the constant steady states are established then by analyzing the associated characteristic equation the stability of steady states and the existence of hopf bifurcation are demonstrated under special circumstance the discontinuous hopf bifurcation is also investigated furthermore the existence and non existence of nonconstant positive steady states of this model are studied through considering the effect of large diffusivity finally in order to verify our theoretical results some numerical simulations are also included it shows that the numerically observed behaviors are in good agreement with the theoretically proposed results on the basis of numerical simulations we provide some useful comparisons for the readers between our results and the existing ones and discuss the effects of the delay and the diffusion term on dynamic behaviors numerical results indicate that diffusion can make the system unstable and increasing delay may cause the plant to go extinct

monge problem in metric measure spaces with riemannian curvature dimension condition abstract we prove the existence of solutions for the monge minimization problem addressed in a metric measure space x d m enjoying the riemannian curvature dimension condition rcd k n with n for the first marginal measure we assume that 0 m as a corollary we obtain that the monge problem and its relaxed version the monge kantorovich problem attain the same minimal value moreover we prove a structure theorem for d cyclically monotone sets neglecting a set of zero m measure they do not contain any branching structures that is they can be written as the disjoint union of the image of a disjoint family of geodesics

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

existence and uniqueness of optimal maps on alexandrov spaces the purpose of this paper is to show that in a finite dimensional metric space with alexandrov s curvature bounded below monge s transport problem for the quadratic cost admits a unique solution

existence of optimal transport maps for crystalline norms we show the existence of optimal transport maps in the case when the cost function is the distance induced by a crystalline norm in n assuming that the initial distribution of mass is absolutely continuous with respect to mathcal l n the proof is based on a careful decomposition of the space in transport rays induced by a secondary variational problem having the euclidean distance as cost function moreover improving a construction by larman we show the existence of a nikodym set in 3 having full measure in the unit cube intersecting each element of a family of pairwise disjoint open lines only in one point this example can be used to show that the regularity of the decomposition in transport rays plays an essential role in sudakov type arguments for proving the existence of optimal transport maps

persistence of periodic patterns for perturbed biological oscillators abstract we apply the perturbation method and the implicit function theorem to study the persistence of periodic patterns for two perturbed general biological oscillators one weakly coupled ordinary differential equation and one reaction diffusion system the proof relies also on the formal adjoint equation theory and the lyapunov schmidt method for the perturbed reaction diffusion model spatial temporal patterns such as rotating waves are shown to exist numerical simulations are presented to illustrate our analytical results

global attractivity in a periodic chemostat with general uptake functions a system of ode s is considered as a model of two populations competing for a nutrient where nutrient inputs and chemostat washouts are periodic as well general nutrient uptake functions which may also be time dependent and periodic are considered criteria are derived for there to exist a globally attracting positive periodic solution and a theorem on global monotonicity of attracting solutions between different systems is proved

dynamics of a general prey predator model with prey stage structure and diffusive effects in this paper we propose and study the dynamics of a diffusive prey predator model with general functional response and stage structure for the prey firstly we consider the asymptotical stability of equilibrium points and hopf bifurcation for the reduced ode system secondly the existence and uniform boundedness of global solutions and stability of equilibrium points for the corresponding reaction diffusion system are discussed finally we establish the existence and the nonexistence of nonconstant positive steady states of this reaction diffusion system which indicates the effect of large diffusivity our results shows the importance of the diffusion rate of the predator species i e d 3 the large diffusion rate of the predator alone will help the generation of patterns however a large diffusion rate of the immature prey species or a large diffusion rate of the mature prey species can lead to the nonexistence of spatial patterns

the disintegration of the lebesgue measure on the faces of a convex function we consider the disintegration of the lebesgue measure on the graph of a convex function f rn r w r t the partition into its faces which are convex sets and therefore have a well defined linear dimension and we prove that each conditional measure is equivalent to the k dimensional hausdorff measure on the k dimensional face on which it is concentrated the remarkable fact is that a priori the directions of the faces are just borel and no lipschitz regularity is known notwithstanding that we also prove that a green gauss formula for these directions holds on special sets

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

analysis of autonomous lotka volterra competition systems with random perturbation abstract this paper discusses a randomized n species lotka volterra competition system we show that this system is stable in time average under certain conditions furthermore there is a stationary distribution of this system if extra conditions are satisfied also we give the extinction condition of this system finally numerical simulations are carried out to support our results

dynamics of age structured predator prey population models a predator prey model is investigated in which the prey population is assumed to have age structure and is governed by the mckendrick von foerster partial differential equation and the predator population is described by the classical volterra lotka ordinary differential equation quite general hypotheses are assumed for the mortality function the fertility function and the functional responses of predation existence and stability of three biologically meaningful equilibria corresponding to extinction of both species persistence of one species prey and coexistence of two species are studied a particular example and some numerical results are given

neimark sacker bifurcations in a non standard numerical scheme for a class of positivity preserving odes we discuss the nature of neimark sacker bifurcations occurring in a non standard numerical scheme for a class of positivity preserving systems of ordinary differential equations odes which undergoes a corresponding hopf bifurcation extending previous work alexander moghadas 2005a electron j diff eqn conf 12 9 19 it is shown that the type of neimark sacker bifurcation supercritical or subcritical may be affected by the integration time step the general form of the scheme in the vicinity of a fixed point is given from which the expression for the first lyapunov coefficient for two dimensional systems valid for arbitrary time step is explicitly derived the analysis shows that this coefficient undergoes an o shift with respect to the corresponding coefficient of the original ode this could lead to a type of bifurcation which differs from the corresponding hopf bifurcation in the ode due to changes in the sign of the first lyapunov coefficient as varies this is especially problematic in the vicinity of certain types of degenerate hopf bifurcation at which this coefficient may vanish we also present a general method to eliminate the possible o shift in the bifurcation parameter of the scheme however the first lyapunov coefficient may still be subjected to an o shift leading to a possibly erroneous type of bifurcation examples are given to illustrate the theoretical results of the paper with applications to mathematical biology

stability and bifurcation in a delayed predator prey system with beddington deangelis functional response we consider a delayed predator prey system with beddington deangelis functional response the stability of the interior equilibrium will be studied by analyzing the associated characteristic transcendental equation by choosing the delay as a bifurcation parameter we show that hopf bifurcation can occur as the delay crosses some critical values the direction and stability of the hopf bifurcation are investigated by following the procedure of deriving normal form given by faria and magalhaes an example is given and numerical simulations are performed to illustrate the obtained 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

homoclinic bifurcation of prey predator model with impulsive state feedback control abstract in this paper homoclinic bifurcations of a prey predator system with state impulse are investigated firstly the existence of order 1 homoclinic cycle of system 1 2 with 0 is investigated secondly choosing q as a control parameter the sufficient conditions of existence and stability of order 1 periodic solution of system 1 2 with 0 are obtained by means of the geometry theory of semi continuous dynamic systems thirdly on the basis of the theory of rotated vector fields homoclinic bifurcation of system 1 2 about parameter are also studied finally some simulations are provided to prove the main results the methods used in this paper are intuitive to prove the existence of order 1 homoclinic cycle and homoclinic bifurcations

existence of a polycycle in non lipschitz gause type predator prey models abstract we study gause type predator prey models when the interaction between predator and prey is not locally lipschitz continuous in the absence of one of them we shall show that in this case there appears a polycycle which affects the existence of limit cycles for the system we apply the results to study the existence of limit cycles for a classical gause system

dynamical and numerical analyses of a generalized food chain model this paper focuses on the qualitative and quantitative analysis of a generalized three species food chain model the conditions for the existence and stability of the boundary and positive equilibria of the model are established by constructing an appropriate bifurcation function it is shown that the model undergoes a hopf bifurcation from the positive equilibrium for certain parameter values the root of this bifurcation function gives the bifurcation value a robust non standard numerical method is constructed and used to obtain the solution of the model numerical simulations using this method show that the hopf bifurcation is supercritical with a stable limit cycle in the positive octant

a characterization for solutions of the monge kantorovich mass transport problem a measure theoretical approach is presented to study the solutions of the monge kantorovich optimal mass transport problems this approach together with kantorovich duality provide an effective tool to answer a long standing question about the support of optimal plans for the mass transport problem involving general cost functions we also establish a criterion for the uniqueness

continuity for the monge mass transfer problem in two dimensions in this paper we prove the continuity of the monotone optimal mapping of the monge mass transfer problem in two dimensions under certain conditions on the domains and the mass distributions

on the sufficiency of c cyclical monotonicity for optimality of transport plans we consider a mass transport problem among polish spaces and we show that a transport plan concentrated in a c cyclical monotone set is optimal if the cost function is continuous and possibly valued the same result is proved for a generic l s c cost function in the case when the measures are purely atomic this generalizes the previously known results

dynamics of generalist predator in a stochastic environment modified ratio dependent holling tanner model with prey refuge is considered delays are taken in logistic growth of prey as feedback mechanism and gestation period of predator model system exhibits hopf bifurcation when the delay parameters cross their critical values stochastic analysis of the model system is carried out by incorporating gaussian white noise using fourier transform technique fluctuation and stability of the stochastic model is studied in this paper an attempt has been made to understand the dynamics of a prey predator system with multiple time delays where the predator population is regarded as a generalist type in this regard we consider a modified holling tanner prey predator system where a constant time delay is incorporated in the logistic growth of the prey to represent a delayed density dependent feedback mechanism and the second time delay is considered to account for the length of the gestation period of the predator predator s interference in prey predator relationship provides better descriptions of predator s feeding over a range of prey predator abundances so the predator s functional response is considered to be type ii ratio dependent and foraging efficiency of predator largely varies with the refuge strategy of prey population in accordance with previous studies it is observed that delay destabilizes the system in general and stability loss occurs via hopf bifurcation in particular we show that there exists critical values of the delay parameters below which the coexistence equilibrium is stable and above which it is unstable hopf bifurcation occurs when the delay parameters cross their critical values also environmental stochasticity in the form of gaussian white noise plays a significant role to describe the system and its values numerical computation is also performed to validate and visualize different theoretical results presented the analysis and results in this work are interesting both in mathematical and biological point of views

positive periodic solutions in a non selective harvesting predator prey model with multiple delays abstract this paper is concerned with a predator prey model with hassell varley type functional response non selective harvesting and multiple delays some new sufficient conditions are obtained for the existence of positive periodic solutions by applying the coincidence degree theorem in addition the results are delay dependent which is different from the previous work finally simulations illustrate the effectiveness of our results

singular perturbations of the holling i predator prey system with a focus abstract we study the occurrence of limit cyles in a model for two species predator prey interaction referred to as holling i this model is based on the phenomenological fitting of the so called functional response function to observed data in nature by a continuous piecewise differentiable function of the original models presented by holling it is the only model for which the possible asymptotic behaviour of the prey and predator densities has not been determined yet we extend the work of liu who showed that for certain values of parameters of the holling i system at least two nested limit cycles will occur surrounding a focus his case corresponds to a bifurcation problem where limit cycles are created from a system with a continuum of singularities i e a singular perturbation problem with slow fast solutions we prove that exactly two hyperbolic limit cycles occur after perturbation

stability and bifurcation analysis on a ratio dependent predator prey model with time delay a ratio dependent predator prey model with time delay due to the gestation of the predator is investigated by analyzing the corresponding characteristic equations the local stability of a positive equilibrium and a semi trivial boundary equilibrium is discussed respectively further it is proved that the system undergoes a hopf bifurcation at the positive equilibrium using the normal form theory and the center manifold reduction explicit formulae are derived to determine the direction of bifurcations and the stability and other properties of bifurcating periodic solutions by means of an iteration technique sufficient conditions are obtained for the global attractiveness of the positive equilibrium by comparison arguments the global stability of the semi trivial equilibrium is also addressed numerical simulations are carried out to illustrate the main results

permanence and stability in non autonomous predator prey lotka volterra systems with feedback controls the main purpose of this article is considering whether or not the feedback controls have an influence on a non autonomous predator prey lotka volterra type system general criteria on permanence are established which is described by an integral form and independent of some feedback controls by constructing suitable lyapunov functionals a set of easily verifiable sufficient conditions are derived for the global stability of any positive solution to the model

the basins of attraction in a modified may holling tanner predator prey model with allee affect abstract i analyse a modified may holling tanner predator prey model considering an allee effect in the prey and alternative food sources for predator additionally the predation functional response or predation consumption rate is linear the extended model exhibits rich dynamics and we prove the existence of separatrices in the phase plane separating basins of attraction related to oscillation co existence and extinction of the predator prey population we also show the existence of a homoclinic curve that degenerates to form a limit cycle and discuss numerous potential bifurcations such as saddle node hopf and bogdanov takens bifurcations we use simulations to illustrate the behaviour of the model

dynamic analysis of fractional order singular holling type ii predator prey system abstract in this paper a fractional order singular fos predator prey model with holling type ii functional response has been introduced and the mathematical behavior of the model from the aspect of local stability is investigated through the fractional calculus and economic theory a new and more realistic predator prey model has been extended and the solvability condition is presented besides numerical simulations are considered to illustrate the effectiveness of the numerical method and confirm the theoretical results to explore the impacts of fractional order and economic interest on the presented system in biological context it is found that the presence of fractional order in the differential model can improve the stability of the solutions and enrich the dynamics of system in addition singular models exhibit more complicated dynamics rather than standard models especially the bifurcation phenomena which can reveal the instability mechanism of systems

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

finite element approximation of spatially extended predator prey interactions with the holling type ii functional response we study the numerical approximation of the solutions of a class of nonlinear reaction diffusion systems modelling predator prey interactions where the local growth of prey is logistic and the predator displays the holling type ii functional response the fully discrete scheme results from a finite element discretisation in space with lumped mass and a semi implicit discretisation in time we establish a priori estimates and error bounds for the semi discrete and fully discrete finite element approximations numerical results illustrating the theoretical results and spatiotemporal phenomena are presented in one and two space dimensions the class of problems studied in this paper are real experimental systems where the parameters are associated with real kinetics expressed in nondimensional form the theoretical techniques were adapted from a previous study of an idealised reaction diffusion system garvie and blowey in eur j appl math 16 5 621 646 2005

persistence in dynamical systems soit un espace metrique localement compact de metrique d et soit e un sous ensemble clos de a frontiere e et interieur e on suppose que l on a un flot continu 7b f defini sur e tel que e est invariant par 7b f on considere la notion de persistance et on donne un critere de persistance

the geometry of optimal transportation introduction 113 1 summary of main results 120 2 background on optimal measures 126 part i strictly convex costs 133 3 existence and uniqueness of optimal maps 133 4 characterization of the optimal map 137 part ii costs which are strictly concave as a function of d i s t a n c e 141 5 the role of optimal maps 141 6 uniqueness of optimal solutions 144 part iii appendices 148 a legendre transforms and conjugate costs 148 b examples of c concave potentials 152 c regularity of c concave potentials 154 references 159