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

multiple scales scheme for bifurcation in a delayed extended van der pol oscillator abstract the van der pol vdp oscillator is an essential nonlinear oscillator which has been extensively studied however the results of delayed generalized vdp oscillator are relatively less the issue of bifurcation control for a delayed extended vdp oscillator is fully considered in this paper firstly a nonlinear time delayed feedback controller is carefully designed to control the dynamics for the proposed oscillator and the results of stability of such oscillator are obtained by means of stability switches theory secondly a general explicit formula is derived to establish the properties of hopf bifurcation by utilizing the method of multiple scales moreover the impact of feedback gain on the bifurcation point for the controlled oscillator is demonstrated numerically finally the effectiveness of theoretical results is verified via a numerical example

a stage structured prey predator model with discrete time delay abstract a stage structured predator prey model stage structure on prey with gestation delay has been presented in this paper linear stability analysis reveals that certain thresholds on the rate at which juveniles becomes adults in terms of the predation rate and other system parameters a stability switch in the system due to variation of delay parameter has been observed so is the phenomena of hopf bifurcation and stable limit cycle the estimation of the length of delay to preserve stability has also been calculated numerical simulation with a hypothetical set of data has been done to support the analytical findings

on the cycle structure of mallows permutations we study the length of cycles of random permutations drawn from the mallows distribution under this distribution the probability of a permutation pi in mathbb s n is proportional to q operatorname inv pi where q 0 and operatorname inv pi is the number of inversions in pi we focus on the case that q 1 and show that the expected length of the cycle containing a given point is of order min 1 q 2 n this marks the existence of two asymptotic regimes with high probability when n tends to infinity with 1 q 2 ll n then all cycles have size o n whereas when n tends to infinity with 1 q 2 gg n then macroscopic cycles of size proportional to n emerge in the second regime we prove that the distribution of normalized cycle lengths follows the poisson dirichlet law as in a uniformly random permutation the results bear formal similarity with a conjectured localization transition for random band matrices further results are presented for the variance of the cycle lengths the expected diameter of cycles and the expected number of cycles the proofs rely on the exact sampling algorithm for the mallows distribution and make use of a special diagonal exposure process for the graph of the permutation

hopf bifurcation and stability for a differential algebraic biological economic system abstract in this paper we analyze the stability and hopf bifurcation of the biological economic system based on the new normal form and the hopf bifurcation theorem the basic model we consider is owed to a ratio dependent predator prey system with harvesting compared with other researches on dynamics of predator prey population this system is described by differential algebraic equations due to economic factor here as bifurcation parameter it is found that periodic solutions arise from stable stationary states when the parameter increases close to a certain limit finally numerical simulations illustrate the effectiveness of our results

complex dynamics in a singular leslie gower predator prey bioeconomic model with time delay and stochastic fluctuations in this paper a class of singular leslie gower predator prey bioeconomic models with environment fluctuations and time delays is investigated local stability analysis of the model reveals that there is a phenomenon of singularity induced bifurcation due to variation of economic interest of harvesting by choosing the delay as a bifurcation parameter it is shown that the hopf bifurcations can occur as the delay crosses some critical values then the effect of a fluctuating environment on the singular stochastic delayed predator prey bioeconomic model is discussed finally numerical simulations demonstrate that the amplitude of oscillation for population is enhanced when compared with the oscillation observed in the deterministic environment

probability laws related to the jacobi theta and riemann zeta functions and brownian excursions this paper reviews known results which connect riemann s integral representations of his zeta function involving jacobi s theta function and its derivatives to some particular probability laws governing sums of independent exponential variables these laws are related to one dimensional brownian motion and to higher dimensional bessel processes we present some characterizations of these probability laws and some approximations of riemann s zeta function which are related to these laws

q exchangeability via quasi invariance for positive q is not 1 the q exchangeability of an infinite random word is introduced as quasi invariance under permutations of letters with a special cocycle which accounts for inversions in the word this framework allows us to extend the q analog of de finetti s theorem for binary sequences see gnedin and olshanski electron j combin 16 2009 r78 to general real valued sequences in contrast to the classical case of exchangeability q 1 the order on plays a significant role for the q analogs an explicit construction of ergodic q exchangeable measures involves random shuffling of 1 2 by iteration of the geometric choice connections are established with transient markov chains on q pascal pyramids and invariant random flags over the galois fields

stochastic dynamics and optimal control in a hybrid bioeconomic system with telephone noise and levy jumps abstract in this paper a hybrid stochastic prey predator system with double time delays and commercial exploitation is established where combined dynamic effects of telephone noise and levy jumps on stochastic population dynamics are taken into accounts existence and uniqueness of globally positive solution to the proposed system are investigated by constructing appropriate stochastic lyapunov functions existence of an ergodic and unique stationary distribution of the positive solution is discussed sufficient conditions for permanence in mean and extinction of corresponding population are derived furthermore sufficient and necessary criteria for optimal exploitation strategy are studied numerical simulations are carried out to show consistency with theoretical analysis

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

diffusion in a symmetric bistable potential a variational approach an approximation procedure for the solution of stochastic nonlinear equations which was derived from a variational principle in a previous paper is applied to the problem of a particle that diffuses in a symmetric bistable potential starting from the point of unstable equilibrium the second moment left langle widetilde x 2 t right rangle and variance left langle widetilde x 4 t right rangle left langle widetilde x 2 t right rangle 2 for the particle s position widetilde x t are calculated as functions of the timet good agreement is found with results recently obtained by baibuzet al from an approximate evaluation of a path integral expression for the probability density

global stability for a class of predator prey systems this paper deals with the question of global stability of the positive locally asymptotically stable equilibrium in a class of predator prey systems the dulac s criterion is applied and liapunov functions are constructed to establish the global stability

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

dynamical analysis of a delayed ratio dependent prey predator model within fluctuating environment abstract in this paper we consider a two dimensional ratio dependent prey predator model involving discrete time delay within fluctuating environment firstly we discuss basic dynamical properties of non delayed and delayed model system in brief within deterministic environment next we construct the stochastic differential equation model and stochastic delay differential equation model to study the effect of environmental driving forces on the dynamical behaviour stochastic models are extension of deterministic models by perturbing two demographic parameters namely birth rate of prey population and death rate of predator population with white noise terms characterized by gaussian distribution having zero mean and unit spectral density we calculate population fluctuation intensity variance for prey and predator species by laplace transform methods for stochastic differential equation model and fourier transforms method for stochastic delay differential equation model numerical simulations are carried out to substantiate the analytical findings significant outcomes of our analytical findings and their interpretations from ecological point of view are provided in concluding section

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

global stability and hopf bifurcation of a plankton model with time delay abstract a differential delay equation model with a discrete time delay and a distributed time delay is introduced to simulate zooplankton nutrient interaction the differential inequalities methods and standard hopf bifurcation analysis are applied some sufficient conditions are obtained for persistence and for the global stability of the unique positive steady state respectively it was shown that there is a hopf bifurcation in the model by using the discrete time delay as a bifurcation parameter

spatial random permutations and infinite cycles we consider systems of spatial random permutations where permutations are weighed according to the point locations infinite cycles are present at high densities the critical density is given by an exact expression we discuss the relation between the model of spatial permutations and the ideal and interacting quantum bose gas

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

optimal gaussian solutions of nonlinear stochastic partial differential equations we present a linearization procedure of a stochastic partial differential equation for a vector field x i t x t 0 x r d i l n t x i t x b i x t x d x i t x i f i t x here is the laplace beltrami operator inr d and f i t x is a gaussian random field with f i t x f j t x ij t t x x the procedure is a natural extension of the equivalent linearization for stochastic ordinary differential equations the linearized solution is optimal in the sense that the distance between true and approximate solutions is minimal when it is measured by the kullback leibler entropy the procedure is applied to the scalar valued ginzburg landau model in r1 withb 1 z z vz 3 stationary values of mean variance and correlation length are calculated they almost agree with exact ones if 1 24 2 1 4 d 1 1 3 c when c there appear quasistationary states fluctuating around one of the bottoms of the potentialu z b 1 z dz the second moment at the quasistationary states almost agrees with the exact one transient phenomena are also discussed half width at half maximum of a structure function decays liket 1 2 for small t the diffusion term 2 x accelerates the relaxation from the neighborhood of an unstable initial statex 0 x 0

the distribution of the product of independent rayleigh random variables we derive the exact probability density functions pdf and distribution functions cdf of a product of n independent rayleigh distributed random variables the case n 1 is the classical rayleigh distribution while n spl ges 2 is the n rayleigh distribution that has recently attracted interest in wireless propagation research the distribution functions are derived by using an inverse mellin transform technique from statistics and are given in terms of a special function of mathematical physics the meijer g function series forms of the distribution function are also provided for n 3 4 5 we also derive a computationally simple moment based estimator for the parameter occurring in the distribution and evaluate its variance

extension of statistical replacement to systems with time correlated fluctuations nonlinear systems with correlated stochastic parameters are approximated by simpler systems this method is an extension of an earlier version of statistical replacement and statistical linearization the extended method is applicable to systems with correlated fluctuations we show how this general method reduces to the earlier methods in special cases

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

loop correlations in random wire models we introduce a family of loop soup models on the hypercubic lattice the models involve links on the edges and random pairings of the link endpoints on the sites we conjecture that loop correlations of distant points are given by poisson dirichlet correlations in dimensions three and higher we prove that in a specific random wire model that is related to the classical xy spin system the probability that distant sites form an even partition is given by the poisson dirichlet counterpart

optimal control of harvest and bifurcation of a prey predator model with stage structure abstract this paper describes a prey predator model with stage structure for prey the adult prey and predator populations are harvested in the proposed system the dynamic behavior of the model system is discussed it is observed that singularity induced bifurcation phenomenon is appeared when variation of the economic interest of harvesting is taken into account state feedback controller is incorporated to stabilize the model system in case of positive economic interest harvesting of prey and predator population are used as controls to develop a dynamic framework to investigate the optimal utilization of the resource sustainability properties of the stock and the resource rent earned from the resource the pontryagin s maximum principle is used to characterize the optimal controls the optimality system is derived and then solved numerically using an iterative method with runge kutta fourth order scheme simulation results show that the optimal control scheme can achieve sustainable ecosystem

sharp phase transition in the random stirring model on trees we establish that the phase transition for infinite cycles in the random stirring model on an infinite regular tree of high degree is sharp that is we prove that there exists d 0 such that for any d ge d 0 the set of parameter values at which the random stirring model on the rooted regular tree with offspring degree d almost surely contains an infinite cycle consists of a semi infinite interval the critical point at the left hand end of this interval is at least d 1 tfrac 1 2 d 2 and at most d 1 2d 2

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

spatio temporal delays in a nutrient plankton model on a finite domain linear stability and bifurcations the issue of how to incorporate time delays into a mathematical model in which individuals are moving around requires careful consideration any time delay term must also involve a weighted spatial averaging to account for movement of individuals during the time delay period most of the current literature on this subject is on reaction diffusion equations and concentrates on the simplest case when the spatial domain is infinite in this paper we consider what changes arise when the domain is finite spatial averaging kernels are computed explicitly for the case of a finite one dimensional domain to illustrate the ideas we concentrate on a diffusive nutrient plankton model the model is analysed in terms of the local stability of the steady states and bifurcations the results of some numerical simulations are also presented

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

dynamical behavior in a stage structured differential algebraic prey predator model with discrete time delay and harvesting a differential algebraic model system which considers a prey predator system with stage structure for prey and harvest effort on predator is proposed by using the differential algebraic system theory and bifurcation theory dynamic behavior of the proposed model system with and without discrete time delay is investigated local stability analysis of the model system without discrete time delay reveals that there is a phenomenon of singularity induced bifurcation due to variation of the economic interest of harvesting and a state feedback controller is designed to stabilize the proposed model system at the interior equilibrium furthermore local stability of the model system with discrete time delay is studied it reveals that the discrete time delay has a destabilizing effect in the population dynamics and a phenomenon of hopf bifurcation occurs as the discrete time delay increases through a certain threshold finally numerical simulations are carried out to show the consistency with theoretical analysis obtained in this paper

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

statistical replacement for systems with delta correlated fluctuations nonlinear systems with stochastic parameters are approximated by simpler systems using a method that we call statistical replacement this method is an extension of the previously developed agree which was restricted to systems with additive fluctuations statistical replacement incorporates the distinctions between globally stable thermodynamically closed systems and thermodynamically open systems that can be unstable

a variational approach to stochastic nonlinear problems a variational principle is formulated which enables the mean value and higher moments of the solution of a stochastic nonlinear differential equation to be expressed as stationary values of certain quantities approximations are generated by using suitable trial functions in this variational principle and some of these are investigated numerically for the case of a bernoulli oscillator driven by white noise comparison with exact data available for this system shows that the variational approach to such problems can be quite effective

on adding a list of numbers and other one dependent determinantal processes adding a column of numbers produces carries along the way we show that random digits produce a pattern of carries with a neat probabilistic description the carries form a one dependent determinantal point process this makes it easy to answer natural questions how many carries are typical where are they located we show that many further examples from combinatorics algebra and group theory have essentially the same neat formulae and that any one dependent point process on the integers is determinantal the examples give a gentle introduction to the emerging fields of one dependent and determinantal point processes

piecewise optimal linearization method for nonlinear stochastic differential equations a method for estimating the dynamical statistical properties of the solutions of nonlinear langevin type stochastic differential equations is presented the non linear equation is linearized within a small interval of the independent variable and statistical properties are expressed analytically within the interval the linearization procedure is optimal in the sense of the chebyshev inequality long term behavior of the solution process is obtained by appropriately matching the approximate solutions at the boundaries between intervals the method is applied to a model nonlinear equation for which the exact time dependent moments can be obtained by numerical methods the calculations demonstrate that the method represents a significant improvement over the method of statistical linearization in time regimes far from equilibrium

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

dynamical analysis of a delayed ratio dependent holling tanner predator prey model abstract in this paper a delayed holling tanner predator prey model with ratio dependent functional response is considered it is proved that the model system is permanent under certain conditions the local asymptotic stability and the hopf bifurcation results are discussed qualitative behaviour of the singularity 0 0 is explored by using a blow up transformation global asymptotic stability analysis of the positive equilibrium is carried out numerical simulations are presented for the support of our analytical findings

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

asymptotic statistics of cycles in surrogate spatial permutations we propose an extension of the ewens measure on permutations by choosing the cycle weights to be asymptotically proportional to the degree of the symmetric group this model is primarily motivated by a natural approximation to the so called spatial random permutations recently studied by betz and ueltschi hence the name surrogate spatial but it is of substantial interest in its own right we show that under the suitable thermodynamic limit both measures have the similar critical behaviour of the cycle statistics characterized by the emergence of infinitely long cycles moreover using a greater analytic tractability of the surrogate spatial model we obtain a number of new results about the asymptotic distribution of the cycle lengths both small and large in the full range of subcritical critical and supercritical domains in particular in the supercritical regime there is a parametric phase transition from the poisson dirichlet limiting distribution of ordered cycles to the occurrence of a single giant cycle our techniques are based on the asymptotic analysis of the corresponding generating functions using polya s enumeration theorem and complex variable methods

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

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

approximate gaussian representation of evolution equations i single degree of freedom nonlinear equations we have developed a generalization of the method of statistical linearization to enable us to describe transient and other nonstationary phenomena obeying stochastic nonlinear differential equations this approximation technique provides an optimal gaussian representation with time dependent parameters the algorithm specifies a set of ordinary differential equations for the gaussian parameters in terms of the time dependent average nonlinearities we apply the general formalism developed herein for single degree of freedom dissipative systems to a particular example

limit distributions for euclidean random permutations we study the length of cycles in the model of spatial random permutations in euclidean space in this model for given length l density rho dimension d and jump density varphi one samples rho l d particles in a d dimensional torus of side length l and a permutation pi of the particles with probability density proportional to the product of values of varphi at the differences between a particle and its image under pi the distribution may be further weighted by a factor of theta to the number of cycles in pi following matsubara and feynman the emergence of macroscopic cycles in pi at high density rho has been related to the phenomenon of bose einstein condensation for each dimension d ge 1 we identify sub critical critical and super critical regimes for rho and find the limiting distribution of cycle lengths in these regimes the results extend the work of betz and ueltschi our main technical tools are saddle point and singularity analysis of suitable generating functions following the analysis by bogachev and zeindler of a related surrogate spatial model

selective harvesting of two competing fish species in the presence of toxicity with time delay abstract in this paper we have considered a two competing fish species with the delay due to gestation each of which obeys the law of logistic growth and releases a substance toxic to the other we also consider the selective harvesting of fishes above a certain age or size by incorporating a time delay in the harvesting term the dynamical behavior of the exploited system is examined in the presence and absence of delay boundedness local and global stabilities are addressed the possibility of the existence of a dynamic equilibrium and the optimal harvesting policy is studied in the absence of delay it is shown that the time delay can cause a stable equilibrium to become unstable and even a switching of stabilities extensive numerical simulations are performed using analytical results for a hypothetical set of parameter values

qualitative analysis of a ratio dependent holling tanner model abstract in this paper we consider a holling tanner system with ratio dependence first we establish the sufficient conditions for the global stability of positive equilibrium by constructing lyapunov function second through a simple change of variables we transform the ratio dependent holling tanner model into a better studied lienard equation as a result the uniqueness of limit cycle can be solved

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

dynamical analysis and optimal control in a hybrid stochastic double delayed bioeconomic system with impulsive contaminants emission and levy jumps abstract in this paper a hybrid stochastic double delayed prey predator bioeconomic system with impulses and levy jumps is established where commercial harvesting on each population and impulsive contaminants emission from surrounding environment on each population growth are taken into account sufficient conditions for persistence in the mean and extinction of interacting population are investigated the asymptotical stability in distribution of the proposed system is studied furthermore optimal price control strategy and maximum of expectation of sustainable yield are discussed numerical simulations are carried out to illustrate theoretical analysis

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

local bifurcations and feasibility regions in differential algebraic systems the dynamics of a large class of physical systems such as the general power system can be represented by parameter dependent differential algebraic models of the form x spl dot f and 0 g typically such constrained models have singularities this paper analyzes the generic local bifurcations including those which are directly related to the singularity the notion of a feasibility region is introduced and analyzed it consists of all equilibrium states that can be reached quasistatically from the current operating point without loss of local stability it is shown that generically loss of stability at the feasibility boundary is caused by one of three different local bifurcations namely the saddle node and hopf bifurcations and a new bifurcation called the singularity induced bifurcation which is analyzed precisely here for the first time the latter results when an equilibrium point is at the singular surface under certain transversality conditions the change in the eigenstructure of the system jacobian at the equilibrium is established and the local dynamical structure of the trajectories near this bifurcation point is analyzed

diffusion in a bistable potential a comparative study of different methods of solution the problem of diffusion in a bistable potential is studied by considering the associated nonlinear langevin equation and its equivalent fokker planck equation two numerically exact methods of solution namely the monte carlo solution of the nonlinear langevin equation and the solution of the fokker planck equation via the finite difference technique are considered the latter method has the advantage that it directly gives the evolution of the probability distribution function approximate analyses of the fluctuations using the system size expansion the gaussian decoupling procedure and the scaling approach are also carried out these investigations are performed on a representative problem for two specific cases 1 evolution from intrinsically unstable states and 2 evolution from extensive regime the fluctuations obtained using these approximate methods are compared with those obtained via the numerically exact methods the study brings out the advantages and limitations of each of the methods considered

retracted stability and hopf bifurcations in a delayed leslie gower predator prey system in this paper we consider the following delayed leslie gower predator prey system x t r 1 x t 1 x t k mx t y t y t r 2 y t 1 y t x t by choosing the delay as a bifurcation parameter we show that hopf bifurcations can occur as the delay crosses some critical values by deriving the equation describing the flow on the center manifold we can determine the direction of the hopf bifurcations and the stability of the bifurcating periodic solutions in addition special attention is paid to the global continuation of local hopf bifurcations using a global hopf bifurcation result of wu j wu symmetric functional differential equations and neural networks with memory trans amer math soc 350 1998 4799 4838 for functional differential equations we may show the global existence of periodic solutions computer simulations illustrate the results

dynamical analysis of a differential algebraic bio economic model with stage structured and stochastic fluctuations abstract this study considers a class of differential algebraic stage structured bio economic models with stochastic fluctuations the stochastic bio economic model is simplified to an ito equation using the stochastic averaging method the stochastic stability hopf bifurcation and p bifurcation are discussed based on the singular boundary theory of the diffusion process for the system and the invariant measure theory of dynamic systems numerical simulations are presented to illustrate our main results

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

spatial random permutations with small cycle weights we consider the distribution of cycles in two models of random permutations that are related to one another in the first model cycles receive a weight that depends on their length the second model deals with permutations of points in the space and there is an additional weight that involves the length of permutation jumps we prove the occurrence of infinite macroscopic cycles above a certain critical density

unstable state dynamics treatment of colored noise the diffusion of a particle set near an unstable point in a bistable potential is considered the scaling theory of fluctuations proposed originally for onedimensional systems driven by gaussian white noise is extended to arbitrary dimensions the merits and drawbacks of the scaling theory are discussed by taking a model problem in one dimension it is shown in passing that the saddle point approximation enables one to get analytic expressions for various moments of the stochastic process the two different methods to include asymptotic fluctuations which are absent in the usual scaling solution are shown to be equivalent an alternate way of including asymptotic fluctuations is attempted by solving the associated fokker planck equation using the fer formula the reason for the failure of this method is traced after this it is argued that the unified scaling theory should be applicable for treatment of colored noise as well for the scaling assumption is independent of the statistical property of the driving noise explicit monte carlo simulation of a model onedimensional system driven by exponentially correlated gaussian noise is performed and compared with the scaling solution to bolster this point the agreement is very good

asymptotic behavior of a stochastic delayed seir epidemic model with nonlinear incidence abstract this paper is concerned with a stochastic delayed seir epidemic model with nonlinear incidence firstly we verify that there exists a unique global positive solution of the system then by constructing some suitable lyapunov functions we study the asymptotic behaviors of the disease free equilibrium and the endemic equilibrium respectively

reply to comments on on the distribution of the product of independent rayleigh random variables replies to the comment of nadarajah and kotz ieee trans antennas propag vol 54 no 11 p 3570 3571 2006 november on the original paper by salo et al ieee trans antennas propag vol 54 p 639 43 2006 february

the application of statistical linearization to the problem of decay from an unstable state abstract it is shown that the method of statistical linearization for the approximate treatment of stochastic nonlinear systems driven by gaussian white noise may be applied successfully to systems which evolve from a state of unstable equilibrium thereby developing non gaussian statistics the essential idea is the replacement of the full ensemble of realizations by subensembles according to the values taken by a small number of linear functionals of the noise the method is illustrated by applying it to two problems i strongly damped linear motion of a particle in a symmetric bistable potential ii the single mode laser in both cases it is found that low order moments can be calculated quite easily to an accuracy of a few per cent and that corrections with error estimates can be found by using the approximation to provide a control variate for numerical simulation

the duffing oscillator in the low friction limit theory and analog simulation by a joint use of theory and analog simulation the low friction regime of the duffing oscillator is explored in the weak temperature case it is shown that the low friction regime in turn must be divided in two well distinct subregimes in the former one characterized by the friction ranging from 2 0 0 is the harmonic frequency up to a lower bound t the method of statistical linearization applies and a continued fraction procedure cfp generated by the zwanzig mori projection techniques is shown to provide correct information for both the renormalized frequency of the oscillator and the corresponding line shape the latter subregime characterized by the friction ranging from 0 to t is fraught with the complete breakdown of the statistical linearization method the cfp is shown to provide an incorrect picture of the line shape while suggesting a novel mean field approximation which is then proven analytically via an alternative method of calculation this method consists of expressing the system in a form reminiscent of the model of kubo s stochastic oscillator by using this alternative approach we are in a position to account for the residual linewidth which is shown by the analog experiment to survive for 0

numerical estimation of the path integral and the diffusion in an anharmonic oscillator abstract the solution of the fokker planck equation given in the form of the path integral is estimated by the contribution from paths around the most probable path a numerical procedure for this estimation is given and applied to the regression of an anharmonic oscillator under a random force from unstable positions to a stable position

solution of fokker planck equation using trotter s formula solution of fokker planck equation using trotter s formula is discussed the method is illustrated on the linear fokker planck equation and the ornstein uhlenbeck solution is obtained for the case of a general nonlinear fokker planck equation the method yields an integral representation amenable to approximations in the lowest order approximation suzuki s scaling result emerges physical interpretation and limitations of the approximations are also discussed

hopf bifurcation for a differential algebraic biological economic system with time delay abstract in this paper we consider a differential algebraic biological economic system with time delay and harvesting where the dynamics is logistic with the carrying capacity proportional to prey population by considering the time delay as bifurcation parameter we analyze the stability and the hopf bifurcation of the differential algebraic biological economic system based on the normal form approach and the center manifold theory at last numerical simulations are performed to illustrate the analytical results

lengths of monotone subsequences in a mallows permutation we study the length of the longest increasing and longest decreasing subsequences of random permutations drawn from the mallows measure under this measure the probability of a permutation uppi in s n is proportional to q mathrm inv uppi where q is a real parameter and mathrm inv uppi is the number of inversions in uppi the case q 1 corresponds to uniformly random permutations the mallows measure was introduced by mallows in connection with ranking problems in statistics we determine the typical order of magnitude of the lengths of the longest increasing and decreasing subsequences as well as large deviation bounds for them we also provide a simple bound on the variance of these lengths and prove a law of large numbers for the length of the longest increasing subsequence assuming without loss of generality that q 1 our results apply when q is a function of n satisfying n 1 q rightarrow infty the case that n 1 q o 1 was considered previously by mueller and starr in our parameter range the typical length of the longest increasing subsequence is of order n sqrt 1 q whereas the typical length of the longest decreasing subsequence has four possible behaviors according to the precise dependence of n and q we show also that in the graphical representation of a mallows distributed permutation most points are found in a symmetric strip around the diagonal whose width is of order 1 1 q this suggests a connection between the longest increasing subsequence in the mallows model and the model of last passage percolation in a strip

on the linearization of nonlinear langevin type stochastic differential equations we show that a logical extension of the piecewise optimal linearization procedure leads to the gaussian decoupling scheme where no iteration is required the scheme is equivalent to solving a few coupled equations the method is applied to models which represent a a single steady state b passage from an initial unstable state to a final preferred stable state by virtue of a finite displacement from the unstable state and c a bivariate case of passage from an unstable state to a final stable state the results are shown to be in very good agreement with the monte carlo calculations carried out for these cases the method should be of much value in multidimensional cases

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

the stationary distribution and ergodicity of a stochastic phytoplankton zooplankton model with toxin producing phytoplankton under regime switching abstract this paper addresses a stochastic phytoplankton zooplankton model with toxin producing phytoplankton under regime switching the stochastic model in this paper includes white and colored noises for the model we first prove the existence of the global positive solution of the model and then by using khasminskii s method and lyapunov function we derive sufficient conditions for the existence of a unique ergodic stationary distribution finally numerical simulations are carried out to support our results

modeling and dynamical analysis of a triple delayed prey predator scavenger system with levy jumps abstract in this paper a hybrid triple delayed prey predator scavenger system with commercial harvesting and levy jumps is established where both maturation delay for prey population and gestation delays for predator and scavenger population are considered for deterministic system positivity and uniform permanence of solution are discussed local stability analysis of deterministic system around interior equilibrium is investigated due to variations of triple time delays for stochastic system without time delay sufficient conditions for stochastically ultimate boundedness and stochastic permanence are discussed for stochastic system with triple time delays existence and uniqueness of global positive solution are studied by constructing appropriate lyapunov functions asymptotic behavior of the hybrid stochastic system with triple time delays and levy jumps is discussed numerical simulations are supported to illustrate theoretical results

hopf bifurcation and harvesting control of a bioeconomic plankton model with delay and diffusion terms abstract in this paper we study the dynamics of a bioeconomic plankton model with delay and diffusion terms in which phytoplankton is assumed to undergo exploitation some sufficient conditions ensuring the stability and bifurcation for the model are provided by using stability and bifurcation theory our results show that harvest effort can control bifurcation and resume system s stability in the case of positive economic profit and over exploitation will result in the extinction of the population which is in line with reality finally some numerical simulations are given to verify the analytical results of nutrient phytoplankton zooplankton fish model

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

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

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

global stability in chemostat type competition models with nutrient recycling this note corrects some typos and errors in the paper s ruan and x z he siam j appl math 58 1998 pp 170 192

bounds for multihop relayed communications in nakagami m fading we present closed form lower bounds for the performance of multihop transmissions with nonregenerative relays over not necessarily identically distributed nakagami m fading channels the end to end signal to noise ratio is formulated and upper bounded by using an inequality between harmonic and geometric means of positive random variables rvs novel closed form expressions are derived for the moment generating function the probability density function and the cumulative distribution function of the product of rational powers of statistically independent gamma rvs these statistical results are then applied to studying the outage probability and the average bit error probability for phase and frequency modulated signaling numerical examples compare analytical and simulation results verifying the tightness of the proposed bounds

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

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

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