hopf transcritical bifurcation in toxic phytoplankton zooplankton model with delay abstract in this paper a phytoplankton zooplankton model with toxic liberation delay is considered firstly the critical values of hopf bifurcation transcritical bifurcation and hopf transcritical bifurcation are given and to give more detailed information about the periodic oscillations the direction and stability of hopf bifurcation is studied by using the normal form theory and center manifold theorem then we give the detailed bifurcation set by calculating the universal unfoldings near the hopf transcritical bifurcation point finally we show that the plankton system may exhibit quasi periodic oscillations which are verified both theoretically and numerically and explain the experimental observed fluctuation phenomenon of plankton population

bifurcation analysis in van der pol s oscillator with delayed feedback in this paper a classical van der pol s equation with generally delayed feedback is considered it is shown that there are bogdanov takens bifurcation triple zero and hopf zero singularities by analyzing the distribution of the roots of the associated characteristic equation in the situation that the zero is as a simple eigenvalue the normal forms of the reduced equations are obtained by the center manifold theory and normal form method for functional differential equation and hence the stability of the fixed point is determined and transcritical and pitchfork bifurcations are found

multiple bifurcations in a delayed predator prey system with nonmonotonic functional response abstract a delayed predator prey system with nonmonotonic functional response is studied by using the normal form theory of retarded functional differential equations developed by faria and magalhaes the bifurcation analysis of the model indicates that there is a bogdanov takens singularity for any time delay value a versal unfolding of the model at the bogdanov takens singularity is obtained on the other hand it is shown that small delay changes the stability of the equilibrium of the model for some parameters and the system can exhibit hopf bifurcation as the time delay passes through some critical values

bifurcations stability and monotonicity properties of a delayed neural network model abstract a delay differential equation modelling an artificial neural network with two neurons is investigated a linear stability analysis provides parameter values yielding asymptotic stability of the stationary solutions these can lose stability through either a pitchfork or a hopf bifurcation which is shown to be supercritical at appropriate parameter values an interaction takes place between the pitchfork and hopf bifurcations conditions are also given for the set of initial conditions that converge to a stable stationary solution to be open and dense in the functional phase space analytic results are illustrated with numerical simulations

using least squares and tobit in second stage dea efficiency analyses the paper examines second stage dea efficiency analyses within the context of a censoring data generating process dgp and a fractional data dgp when efficiency scores are treated as descriptive measures of the relative performance of units in the sample it is argued that the efficiency scores are not generated by a censoring process but are fractional data tobit estimation in this situation is inappropriate in contrast ordinary least squares is a consistent estimator and if white s white h 1980 a heteroskedastic consistent covariance matrix and a direct test for heteroskedasticity econometrica 48 817 838 heteroskedastic consistent standard errors are calculated large sample tests can be performed which are robust to heteroskedasticity and the distribution of the disturbances for a more refined analysis papke and wooldridge s papke l e wooldridge j m 1996 econometric methods for fractional response variables with an application to 401 k plan participation rates journal of applied econometrics 11 6 619 632 method has some advantages but is more complex and requires special programming

dynamical analysis in a bioeconomic phytoplankton zooplankton system with double time delays and environmental stochasticity abstract this paper presents a double delayed bioeconomic phytoplankton zooplankton system with commercial harvesting on zooplankton and environmental stochasticity maturation delay for toxin producing phytoplankton and gestation delay for zooplankton are considered environmental stochasticity is incorporated into the proposed system in form of gaussian white noises some sufficient conditions are derived to show that the proposed system has a unique global positive solution in absence of double time delays stochastic stability and existence of stochastic hopf bifurcation are studied based on invariant measure theory and singular boundary theory of diffusion process for the proposed system in presence of double time delays asymptotic behaviors of the interior equilibrium are discussed by constructing some appropriate lyapunov functions

dynamic analysis of a hybrid bioeconomic plankton system with double time delays and stochastic fluctuations abstract in this paper we establish a double delayed hybrid bioeconomic plankton system with stochastic fluctuations and commercial harvesting on zooplankton where maturation delay for toxin producing phytoplankton and gestation delay for zooplankton are considered stochastic fluctuations are incorporated into the proposed system in form of gaussian white noises to depict stochastic environmental factors in plankton system for deterministic system without double time delays existence of singularity induced bifurcation is studied due to variation of economic interest of commercial harvesting and state feedback controllers are designed to eliminate singularity induced bifurcation for deterministic system with double time delays positivity and uniform persistence of solutions are studied and some sufficient conditions associated with asymptotic stability of interior equilibrium are investigated for stochastic system without double time delays stochastic stability and existence of stochastic hopf bifurcation are discussed based on singular boundary theory of diffusion process and invariant measure theory for stochastic system with double time delays existence and uniqueness of global positive solution are investigated and asymptotic behaviors of the interior equilibrium are studied by constructing appropriate lyapunov functions numerical simulations are carried out to validate theoretical analysis

the effects of harvesting and time delay on predator prey systems with holling type ii functional response in this paper the effects of harvesting and time delay on two different types of predator prey systems with delayed predator specific growth and holling type ii functional response are studied by applying the normal form theory of retarded functional differential equations developed by faria and magalhaes j differential equations 122 1995 pp 181 200 j differential equations 122 1995 pp 201 224 hopf bifurcations are demonstrated in models with harvesting of the prey at a constant rate by taking the delay as a bifurcation parameter and numerical examples supporting our theoretical prediction are also given furthermore bifurcation analysis indicates that delayed predator prey systems with predator harvesting exhibit bogdanov takens bifurcation the versal unfoldings of the models at the bogdanov takens singularity are obtained and numerical simulations and bifurcation diagrams are given to illustrate the obtained results

van der pol s oscillator under delayed feedback the effect of delayed feedback on oscillatory behaviour is investigated for the classical van der pol oscillator it is shown how the presence of delay can change the amplitude of limit cycle oscillations or suppress them altogether the result is compared to the conventional proportional and derivative feedback the derivative like effect of delay is also demonstrated in a modified equation where a delayed term provides the damping

stability and bifurcation analysis in hematopoietic stem cell dynamics with multiple delays abstract this paper is devoted to the analysis of a maturity structured system of hematopoietic stem cell hsc populations in the bone marrow the model is a system of differential equations with several time delays we discuss the stability of equilibria and perform the analysis of hopf bifurcation more precisely we first obtain a set of improved sufficient conditions ensuring the global asymptotical stability of the zero solution using the lyapunov method and the embedding technique of asymptotically autonomous semiflows then we prove that there exists at least one positive periodic solution for the n dimensional system as a time delay varies in some region this result is established by combining hopf bifurcation theory the global hopf bifurcation theorem due to wu j wu symmetric functional differential equations and neural networks with memory trans amer math soc 350 1998 4799 4838 and a continuation theorem of coincidence degree theory some numerical simulations are also presented to illustrate the analytic results

evaluating contextual variables affecting productivity using data envelopment analysis a dea based stochastic frontier estimation framework is presented to evaluate contextual variables affecting productivity that allows for both one sided inefficiency deviations as well as two sided random noise conditions are identified under which a two stage procedure consisting of dea followed by ordinary least squares ols regression analysis yields consistent estimators of the impact of contextual variables conditions are also identified under which dea in the first stage followed by maximum likelihood estimation mle in the second stage yields consistent estimators of the impact of contextual variables this requires the contextual variables to be independent of the input variables but the contextual variables may be correlated with each other monte carlo simulations are carried out to compare the performance of our two stage approach with one stage and two stage parametric approaches simulation results indicate that dea based procedures with ols maximum likelihood or even tobit estimation in the second stage perform as well as the best of the parametric methods in the estimation of the impact of contextual variables on productivity simulation results also indicate that dea based procedures perform better than parametric methods in the estimation of individual decision making unit dmu productivity overall the results establish dea as a nonparametric stochastic frontier estimation sfe methodology

oscillations in a van der pol equation with delayed argument we consider the van der pol equation d2dt2u t eddtu t eu2 t r ddtu t r u t 0 with the delayed time r where r and e are real parameters with e 0 small and 0 r 2 and prove the existence and stability of a periodic solution with period near 2 and amplitude near 2 cosr with these properties this solution is unique up to translations in time

one stage and two stage dea estimation of the effects of contextual variables abstract two stage data envelopment analysis 2 dea is commonly used in productive efficiency analysis to estimate the effects of operational conditions and practices on performance in this method the dea efficiency estimates are regressed on contextual variables representing the operational conditions we re examine the statistical properties of the 2 dea estimator and find that it is statistically consistent under more general conditions than earlier studies assume we further show that the finite sample bias of dea in the first stage carries over to the second stage regression causing bias in the estimated coefficients of the contextual variables this bias is particularly severe when the contextual variables are correlated with inputs to address this shortcoming we apply the result that dea can be formulated as a constrained special case of the convex nonparametric least squares cnls regression applying the cnls formulation we develop a new semi nonparametric one stage estimator for the coefficients of the contextual variables that directly incorporates contextual variables to the standard dea problem the proposed method is hence referred to as one stage dea 1 dea evidence from monte carlo simulations suggests that the new 1 dea estimator performs systematically better than the conventional 2 dea estimator both in deterministic and noisy scenarios

stability and bifurcation analysis in van der pol s oscillator with delayed feedback abstract the classical van der pol equation with delayed feedback and a modified equation where a delayed term provides the damping are considered linear stability of the equations is investigated by analyzing the associated characteristic equations it is found that there exist the stability switches when delay varies and the hopf bifurcation occurs when the delay passes through a sequence of critical values the bifurcation diagram is drawn in e k plane and the stability and direction of the hopf bifurcation are determined by applying the normal form theory and the center manifold theorem

hopf bifurcations in a reaction diffusion population model with delay effect abstract a reaction diffusion population model with a general time delayed growth rate per capita is considered the growth rate per capita can be logistic or weak allee effect type from a careful analysis of the characteristic equation the stability of the positive steady state solution and the existence of forward hopf bifurcation from the positive steady state solution are obtained via the implicit function theorem where the time delay is used as the bifurcation parameter the general results are applied to a food limited population model with diffusion and delay effects as well as a weak allee effect population model

estimation and inference in two stage semi parametric models of production processes many papers have regressed non parametric estimates of productive efficiency on environmental variables in two stage procedures to account for exogenous factors that might affect firms performance none of these have described a coherent data generating process dgp moreover conventional approaches to inference employed in these papers are invalid due to complicated unknown serial correlation among the estimated efficiencies we first describe a sensible dgp for such models we propose single and double bootstrap procedures both permit valid inference and the double bootstrap procedure improves statistical efficiency in the second stage regression we examine the statistical performance of our estimators using monte carlo experiments

limit cycle oscillators subject to a delayed feedback the coexistence of two stable limit cycles exhibiting different periods is examined for a nonlinear oscillator subject to a delayed feedback for the case of a weakly nonlinear oscillator we discuss the validity of a previously determined phase equation for the case of a strongly nonlinear oscillator we derive a phase equation and analyze its bifurcation diagram our analysis is motivated by previous experimental studies of chemical oscillators controlled by a delayed feedback

hopf pitchfork bifurcation in van der pol s oscillator with nonlinear delayed feedback abstract first we identify the critical values for hopf pitchfork bifurcation second we derive the normal forms up to third order and their unfolding with original parameters in the system near the bifurcation point by the normal form method and center manifold theory then we give a complete bifurcation diagram for original parameters of the system and obtain complete classifications of dynamics for the system furthermore we find some interesting phenomena such as the coexistence of two asymptotically stable states two stable periodic orbits and two attractive quasi periodic motions which are verified both theoretically and numerically

hopf transcritical bifurcation in retarded functional differential equations abstract firstly we analyze a codimension two unfolding for the hopf transcritical bifurcation and give complete bifurcation diagrams and phase portraits in particular we express explicitly the heteroclinic bifurcation curve and obtain conditions under which the secondary bifurcation periodic solutions and the heteroclinic orbit are stable secondly we show how to reduce general retarded functional differential equation with perturbation parameters near the critical point of the hopf transcritical bifurcation to a 3 dimensional ordinary differential equation which is restricted on the center manifold up to the third order with unfolding parameters and further reduce it to a 2 dimensional amplitude system where these unfolding parameters can be expressed by those original perturbation parameters finally we apply the general results to the van der pol s equation with delayed feedback and obtain the existence of stable or unstable equilibria periodic solutions and quasi periodic solutions

persistence and global stability in a delayed leslie gower type three species food chain abstract our investigation concerns the three dimensional delayed continuous time dynamical system which models a predator prey food chain this model is based on the holling type ii and a leslie gower modified functional response this model can be considered as a first step towards a tritrophic model of leslie gower and holling tanner type with inverse trophic relation and time delay that is when a certain species that is usually eaten can consume immature predators it is proved that the system is uniformly persistent under some appropriate conditions by constructing a proper lyapunov function we obtain a sufficient condition for global stability of the positive equilibrium

normal forms for retarded functional differential equations with parameters and applications to hopf bifurcation abstract the paper addresses for retarded functional differential equations fdes with parameters the computation of normal forms associated with the flow on a finite dimensional invariant manifold tangent to an invariant space for the infinitesimal generator of the linearized equation at a singularity the analysis is based on the theory previously developed for fdes without parameters by considering an extension of a phase space appropriate to the computation of these normal forms as an application the generic hopf bifurcation for scalar retarded fdes is considered

on the inertia and range of transformations of positive definite matrices abstract results are established which relate the range and inertia of general transformations on positive definite matrices included are a bound theorem for certain eigenvalues of these transformations a characterization of positive definite preserving completely positive transformations and generalizations of the theorems of stein 8 and of stein and pfeffer 9

saddle node hopf bifurcation in a modified leslie gower predator prey model with time delay and prey harvesting abstract from the saddle node hopf bifurcation point of view this paper considers a modified leslie gower predator prey model with time delay and the michaelis menten type prey harvesting firstly we discuss the stability of the equilibria obtain the critical conditions for the saddle node hopf bifurcation and give the completion bifurcation set by calculating the universal unfoldings near the saddle node hopf bifurcation point by using the normal form theory and center manifold theorem then we derive the parameter conditions for the existence of monostable coexistence equilibrium and the parameter regions in which both the prey extinction and the coexistence equilibrium or coexistence periodic or quasi periodic solutions are simultaneously stabilized we also investigate the heteroclinic bifurcation and describe the phenomenon that the periodic behavior disappears as through the heteroclinic bifurcation finally some numerical simulations are performed to support our analytic results

normal forms for retarded functional differential equations and applications to bogdanov takens singularity abstract the paper addresses for retarded functional differential equations fdes the computation of normal forms associated with the flow on a finite dimensional invariant manifold tangent to invariant spaces for the infinitesimal generator of the linearized equation at a singularity a phase space appropriate to the computation of these normal forms is introduced and adequate nonresonance conditions for the computation of the normal forms are derived as an application the general situation of bogdanov takens singularity and its versal unfolding for scalar retarded fdes with nondegeneracy at second order is considered both in the general case and in the case of differential delay equations of the form t x t x t 1

double hopf bifurcation and quasi periodic attractors in delay coupled limit cycle oscillators abstract we investigate the double hopf bifurcation at zero equilibrium point firstly we give the critical values of hopf and double hopf bifurcations secondly we implement the normal form method and the center manifold theory for delay coupled limit cycle oscillators and derive the universal unfolding and a complete bifurcation diagram of the system thirdly many interesting phenomena such as attractive periodic motion and three dimensional invariant torus are observed using numerical simulation finally the normal forms of several strong resonant cases are listed

maximum likelihood consistency and data envelopment analysis a statistical foundation this paper provides a formal statistical basis for the efficiency evaluation techniques of data envelopment analysis dea dea estimators of the best practice monotone increasing and concave production function are shown to be also maximum likelihood estimators if the deviation of actual output from the efficient output is regarded as a stochastic variable with a monotone decreasing probability density function while the best practice frontier estimator is biased below the theoretical frontier for a finite sample size the bias approaches zero for large samples the dea estimators exhibit the desirable asymptotic property of consistency and the asymptotic distribution of the dea estimators of inefficiency deviations is identical to the true distribution of these deviations this result is then employed to suggest possible statistical tests of hypotheses based on asymptotic distributions

on a planar system modelling a neuron network with memory abstract we consider a delay differential equation modelling a network of two neurons with memory the situations without self connections and two delays and with self connections and two equal delays are addressed in terms of local stability and bifurcation analysis in the first case the dynamical behavior is studied by taking one of the delays as the bifurcating parameter namely the hopf bifurcation whose existence was proven in former works occurs as the delay crosses some critical values and is completely described conditions ensuring the stability of the periodic cycles are given when self connections are present hopf and pitchfork bifurcations co exist and the equation describing the flow on the center manifold is derived

two stage estimation of the impact of contextual variables in stochastic frontier production function models using data envelopment analysis second stage ols versus bootstrap approaches abstract banker and natarajan 2008 identified sufficient conditions in a stochastic framework to justify the popular two stage approach of data envelopment analysis followed by ordinary least squares dea ols to estimate the impact of contextual variables on productivity simar and wilson 2007 suggested an alternative approach involving a second stage truncated regression model and bootstrap method to estimate confidence intervals we show that the effectiveness of the simar wilson approach critically depends on the assumption that the actual data generating process dgp exactly matches their assumed dgp and their approach does not yield correct inferences in environments characterized by stochastic noise extensive simulations from a stochastic frontier data generating process document that the simple two stage dea ols model significantly outperforms the more complex simar wilson model with lower mean absolute deviation mad lower median absolute deviation mead as well as higher coverage rates when the contextual variables significantly impact productivity subject classifications data envelopment analysis productivity two stage contextual variables performance nonparametric simulation area of review optimization

stability and hopf bifurcation in a diffusive logistic population model with nonlocal delay effect abstract a reaction diffusion model with logistic type growth nonlocal delay effect and dirichlet boundary condition is considered and combined effect of the time delay and nonlocal spatial dispersal provides a more realistic way of modeling the complex spatiotemporal behavior the stability of the positive spatially nonhomogeneous positive equilibrium and associated hopf bifurcation are investigated for the case of near equilibrium bifurcation point and the case of spatially homogeneous dispersal kernel

novel algorithms to estimate nonlinear fdes applied to fractional order nutrient phytoplankton zooplankton system abstract in this paper dynamical behavior of a mathematical model for the interaction of nutrient phytoplankton and its predator zooplankton is investigated numerically stability analysis of the phytoplankton zooplankton model is studied by using the fractional routh hurwitz stability conditions we have studied the local stability of the equilibrium points then a new numerical algorithm as well as its modification for solving fractional differential equations fdes based on the polynomial interpolation is proposed the algorithms are designed to estimate linear and nonlinear fdes and they have the capability to apply for solving fractional order systems the convergence order and stability of the fractional higher order algorithms are proved and stability regions of the algorithms are achieved extensive numerical simulation results are provided and compared with the literature for illustrating the effectiveness and applicability of the presented algorithms to solve fractional differential equations the obtained analytical results are validated by numerical simulations and the global dynamics of the model system is studied

bogdanov takens singularity in van der pol s oscillator with delayed feedback abstract in this paper we study the classical van der pol s equation with delayed feedback we investigate the bogdanov takens singularity and bifurcation occurring in the system with the variation of the original parameters by using the normal form method and predict the suitable choice in the feedback control in order to obtain the asymptotic stable state

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

second stage dea comparison of approaches for modelling the dea score tobit regression is often encountered in second stage data envelopment analysis dea i e when the relationship between exogenous factors non physical inputs and dea efficiency scores is assessed it is however not obvious that tobit is the only or optimal approach to modelling dea scores this paper presents two alternative approaches to second stage dea the results of which are compared with the tobit approach through a case study for the danish fishery furthermore the three models are compared to ols regression representing a linear approximation to the models it is firstly concluded that the tobit approach will in most cases be sufficient in representing second stage dea models secondly it is shown that ols may actually in many cases replace tobit as a sufficient second stage dea model

an inertial decomposition and related range results abstract with quasicommutative n square complex matrices a1 as and s square hermitian g gij relationships are given between the image s i j 1 g ij a i ha j of a linear transformation on h n being positive definite and the action of h on generalized inertial decompositions of c n

normal forms of non resonance and weak resonance double hopf bifurcation in the retarded functional differential equations and applications the norm forms of the double hopf bifurcation for a general dde is established the van der pol duffing oscillator with delayed position and velocity feedback is investigated the dynamical classification near the double hopf bifurcation point is studied the stable periodic doubling solutions and unstable three dimensional torus are found in this paper we firstly present the general framework of calculation of normal forms of non resonance and weak resonance double hopf bifurcation for the general retarded functional differential equations by using the normal form theory of delay differential equations due to faria and magalh a es then the dynamical behavior of van der pol duffing oscillator with delayed position and velocity feedback is considered specifically the dynamical classification near the double hopf bifurcation point is investigated by analyzing the obtained normal form finally the numerical simulations support the theoretical results and present some interesting phenomena

a complete analysis of the global dynamics of a diffusive predator and toxic prey model considering many species can release toxic substances to protect themselves against predators a diffusive predator and toxic prey system with spatial heterogeneity in predator and prey populations has been investigated for this system we give a complete and rigorous analysis of the global dynamics with the boundedness globally asymptotical stability transcritical bifurcation hopf bifurcation and its direction and the stability of the bifurcating periodic solutions meanwhile we consider the effects of toxins produced by the prey on the dynamic behavior the consequence of the global stability of the coexistence equilibrium is that the toxin s intrinsic characteristic will not change the stability of the system irreversibly our results show that the toxin produced by the prey phytoplankton may be used as a bio control agent for the harmful algal bloom problems