bifurcation analysis of a predator prey system involving group defence a class of odes of generalized gause type modeling predator prey interaction is considered the prey are assumed to exhibit a phenomenon called group defence that is predation is decreased or even eliminated due to the ability of the prey to defend or disguise themselves as their numbers increase using the carrying capacity of the environment as the bifurcation parameter it is shown that the model undergoes a sequence of bifurcations that includes a homoclinic bifurcation as well as a hopf bifurcation conditions that hold even in the case of no group defence that ensure a subcritical hopf bifurcation and also the spontaneous appearance of a semistable periodic orbit that splits into a pair one stable and one unstable of periodic orbits are given ecological ramifications are considered unlike the classical model sufficient enrichment of the environment combined with group defence leads to extinction of the predator deterministically for almost all initial conditions providing strong support fo

non constant positive steady states of a predator prey system with non monotonic functional response and diffusion this paper deals with non constant positive steady state solutions of a predator prey system with non monotonic functional response also called holling type iv interaction terms and diffusion under the homogeneous neumann boundary condition we first establish positive upper and lower bounds for such solutions and then study their non existence global existence and bifurcation

relative positions of limit cycles in a kolmogorov type system to estimate the relative position of limit cycles for a system is always useful in the qualitative analysis of the system if the system has only one limit cycle determining the position of the limit cycle is more important the author constructs an annular region containing all the limit cycles for a kolmogorov type system since the system contains the lotka volterra gausse kuang and freedman and huang models as special cases the results obtained are also valid for those models furthermore the approach to the location of limit cycles is very applicable because the region is easy to compute

on the location and period of limit cycles in gause type predator prey systems in this paper an attempt is made to estimate the location and period of the limit cycles of gause type predator prey systems in the case when there is a unique unstable positive equilibrium an annular region which contains all the limit cycles is determined and an upper bound for the period of the limit cycles is given both the annular region and the upper bound of the period are explicitly computable

the perturbed korteweg de vries equation considered anew the perturbed korteweg de vries equation is studied in a new way by a green s function formalism without use of inverse scattering methods the green s function is determined by employing the backlund transformation and green s theorem after a thorough analysis of the exact first order solution with regard to secular terms a two time scale expansion leads to the adiabatic approximation and the first order correction in accordance with the results of karpman and maslov contrary to statements in the literature the term tanh2 z in the expression for the modified phase of the perturbed soliton arises as a consequence of the systematically conducted first order perturbation theory

priority assignment a conditioned sets approach abstract the author suggests how conditioned sets of fuzzy variables may be used to provide priority weights a case is presented where the conditioned sets approach is contrasted with the prioritization information generated by the eigenvalue priority assignment model

hopf bifurcation for a predator prey model with age structure abstract this paper deals with a prey predator model with age structure where the prey population is infected with pathogenic bacteria we formulate the model as an abstract non densely defined cauchy problem and derive the conditions for the existence of all the feasible equilibrium points of the system the criteria for global stability of two boundary equilibria are obtained the criteria for local stability and instability of positive equilibrium is also discussed bifurcation analysis indicates that the predator prey system with age structure exhibits bifurcation which is the main result of this paper finally some numerical examples are provided to illustrate our obtained results

conservation laws and the perturbed kdv equation examines the integral for the correction to the soliton position in the adiabatic approximation using the modified conservation laws for the mass and the energy the general correction to the soliton position is obtained it is easily seen that this correction is due to the formation of the shelf

global analysis of a system of predator prey equations we study a class of ode s modelling the interaction of one predator and one prey the prey is assumed to be asocial in the sense that there is a threshold below which it will die even in the absence of predators knowledge of the separatrices of the flow and the local nature of the equilibrium points yields an analogue of the kolmogorov theorem a more detailed study of the direction of hopf bifurcation and uniqueness of limit cycles together with recent work on their continuation allows us to exhibit a very rich dynamics for both this system as well as for the more classical case of a prey without threshold we briefly discuss the implications of this work for ecology

non constant positive steady state of one resource and two consumers model with diffusion abstract in this paper a predator prey reaction diffusion system with one resource and two consumers is considered assume that one consumer species exhibits holling ii functional response while the other consumer species exhibits beddington deangelis functional response and they compete for the common resource first it is proved that the unique positive constant steady state is stable for the ode system and the reaction diffusion system second a prior estimates of positive steady state is given finally the non existence of non constant positive steady state the existence and bifurcation of non constant positive steady state are studied

systematic perturbation theory for sine gordon solitons without use of inverse scattering methods the perturbed sine gordon soliton solutions kinks breathers in laboratory coordinates are derived by a green function formalism in a novel way dispensing with any inverse scattering methods besides the backlund transformation a simple approach based on green s theorem is employed for determining the green functions a systematic treatment allows the adiabatic approximation to be derived in a new manner the results are compared to those of the relevant papers in this field and thereby further insight is provided in a simple example a kink scattered by an impurity the calculation of energy radiation is demonstrated

a direct approach to studying soliton perturbations starting with an integrable nonlinear evolution equation the author investigates perturbations about a one soliton solution through the inversion of a linear equation for the first order correction to the soliton solution this inversion differs from past methods as the proposed method takes place in coordinate space not spectral space while it employs some of the tools of inverse scattering theory the method is applied to the korteweg de vries nonlinear schrodinger and sine gordon equations the first order corrections are then obtained

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

snakes oriented families of periodic orbits their sources sinks and continuation abstract poincare observed that for a differential equation x x depending on a parameter each periodic orbit generally lies in a connected family of orbits in x space in order to investigate certain large connected sets denoted q of orbits containing a given orbit we introduce two indices an orbit index and a center index defined at certain stationary points we show that genetically there are two types of hopf bifurcation those we call sources 1 and sinks 1 generically if the set q is bounded in x space and if there is an upper bound for periods of the orbits in q then q must have as many source hopf bifurcations as sink hopf bifurcations and each source is connected to a sink by an oriented one parameter snake of orbits a snake is a maximal path of orbits that contains no orbits whose orbit index is 0 see fig 1 1

the relationships between equilibria and positive solutions of certain nonlinear elliptic systems abstract letm u v 0 n u v 0 define two distinct phase curves 1 2in the u v phase plane this paper presents results on the relationships among the positive equilibria the phase curves and the existence of positive solutions to the pde system u um u v 0 v vn u v 0 in r n under dirichlet boundary conditions where is a bounded domain andm nare monotone functions

consequences of double allee effect on the number of limit cycles in a predator prey model the main goal of this work is to show a comparative analysis of simple continuous time predator prey models considering the allee effect affecting the prey population also known as depensation in fisheries sciences this phenomenon may be expressed by different mathematical forms yielding a distinct number of limit cycles surrounding a positive equilibrium point when two of these different formalizations are considered in the same system it is known that the volterra predation model using the most usual form to express the allee effect has a unique limit cycle in this work considering a more complex mathematical expression the existence of two limit cycles is proved by means of the lyapunov quantities we argue that the second equation explains the existence of two allee effects affecting the same population which could justify the difference observed between the models these results imply that the election of mathematical formulation can have consequences on the fit of the observed data thus leading to mistakes for ecologists we conclude that the oscillatory behaviors and overall dynamics depend strongly on the algebraic expression of the allee effect making difficult the proposition of general results nevertheless the techniques reviewed in this paper emerge as key tools to analyze the existence of limit cycles in the presence of multiple allee effects

a michaelis menten type food chain model with strong allee effect on the prey dynamical behaviours of a tritrophic food chain model with strong allee effect in the prey are studied in this paper positivity and boundedness of the system are discussed some global results on extinction of the species are derived stability analysis of the equilibrium points is presented the effect of discrete time delay is studied where the delay may be regarded as the gestation period of the superpredator numerical simulations are carried out to validate our analytical findings implications of our analytical and numerical findings are discussed critically

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

investigating the interactions between allee effect and harvesting behaviour of a single species model an evolutionary dynamics approach abstract in this study we propose an ecological model which is based on the smith growth model and subject to multiplicative allee effect we then investigate the equilibrium bifurcation induced by the harvesting behaviour and the allee effect and pitch fork bifurcation and saddle node bifurcation may occur assuming that the carrying capacity and harvesting rate obey a gaussian distribution we then consider the evolutionary dynamics by using continuous strategy evolutionary game theory our study shows that strong allee effect and low harvesting rate can induce bistability it also suggests that evolution prevents extinction even if population has strong allee effect numerical analysis shows that the evolutionary model can admit up to nine equilibrium points including up to four evolutionary stable strategy equilibria

on the continuability of periodic orbits of parametrized three dimensional differential equations on considere un systeme autonome a n dimensions d equations differentielles ordinaires a 1 parametre x f x on suppose que f est definie et continue sur un sous ensemble ouvert o de r r n et que f x 0 sur o on etudie les orbites periodiques du systeme contenues dans o

evolutionary dynamics of single species model with allee effect abstract by considering a continuous strategy evolutionary game theory egt a single species population subject to additive allee effect is investigated we assume that the carrying capacity and predator evasion ability following a gaussian distribution this assumption shows that evolution prevents extinction even if population has strong allee effect the ratio of competition and anti predation phenotypes has an important effect on determining global dynamics of the egt model the numerical simulations present the model can have nine equilibria and the model has multiple evolutionarily stable strategy equilibria ess