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

the unbounded parallel batch machine scheduling with release dates and rejection to minimize makespan in this paper we consider the unbounded parallel batch machine scheduling with release dates and rejection a job is either rejected with a certain penalty having to be paid or accepted and processed in batches on the parallel batch machine the processing time of a batch is defined as the longest processing time of the jobs contained in it the objective is to minimize the sum of the makespan of the accepted jobs and the total rejection penalty of the rejected jobs we show that this problem is binary np hard and provide a pseudo polynomial time algorithm when the jobs have the same rejection penalty the problem can be solved in polynomial time finally a 2 approximation algorithm and a fully polynomial time approximation scheme are given for the problem

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

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

preemptive scheduling with rejection we consider the problem of preemptively scheduling a set of n jobs on m identical uniformly related or unrelated parallel machines the scheduler may reject a subset of the jobs and thereby incur job dependent penalties for each rejected job and he must construct a schedule for the remaining jobs so as to optimize the preemptive makespan on the m machines plus the sum of the penalties of the jobs rejected we provide a complete classification of these scheduling problems with respect to complexity and approximability our main results are on the variant with an arbitrary number of unrelated machines this variant is apx hard and we design a 1 58 approximation algorithm for it all other considered variants are weakly np hard and we provide fully polynomial time approximation schemes for them finally we argue that our results for unrelated machines can be carried over to the corresponding preemptive open shop scheduling problem with rejection

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

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

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

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

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

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

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 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

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

bin packing problems with rejection penalties and their dual problems in this paper we consider the following problems we are given a set of n items u1 un and a number of unit capacity bins each item ui has a size wi 0 1 and a penalty pi 0 an item can be either rejected in which case we pay its penalty or put into one bin under the constraint that the total size of the items in the bin is no greater than 1 no item can be spread into more than one bin the objective is to minimize the total number of used bins plus the total penalty paid for the rejected items we call the problem bin packing with rejection penalties and denote it as bpr for the on line bpr problem we present an algorithm with an absolute competitive ratio of 2 618 while the lower bound is 2 343 and an algorithm with an asymptotic competitive ratio arbitrarily close to 1 75 while the lower bound is 1 540 for the off line bpr problem we present an algorithm with an absolute worst case ratio of 2 while the lower bound is 1 5 and an algorithm with an asymptotic worst case ratio of 1 5 we also study a closely related bin covering version of the problem in this case pi means some amount of profit if an item is rejected we get its profit or it can be put into a bin in such a way that the total size of the items in the bin is no smaller than 1 the objective is to maximize the number of covered bins plus the total profit of all rejected items we call this problem bin covering with rejection bcr for the on line bcr problem we show that no algorithm can have absolute competitive ratio greater than 0 and present an algorithm with asymptotic competitive ratio 1 2 which is the best possible for the off line bcr problem we also present an algorithm with an absolute worst case ratio of 1 2 which matches the lower bound

single machine scheduling with release dates and rejection abstract in this paper we consider the single machine scheduling problem with release dates and rejection a job is either rejected in which case a rejection penalty has to be paid or accepted and processed on the machine the objective is to minimize the sum of the makespan of the accepted jobs and the total rejection penalty of the rejected jobs we show that the problem is np hard in the ordinary sense then we provide two pseudo polynomial time algorithms consequently two special cases can be solved in polynomial time finally a 2 approximation algorithm and a fully polynomial time approximation scheme are given for the problem

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

penalty cost constrained identical parallel machine scheduling problem we consider a version of parallel machine scheduling with rejection an instance of the problem is given by m identical parallel machines and a set of n independent jobs with each job having a processing time and a penalty a job may be accepted to be processed or be rejected at its penalty the objective of the problem is to partition the set of jobs into two subsets the subset of accepted and the subset of rejected jobs and to schedule the set of accepted jobs such that the makespan is minimized under the constraint that the total penalty of the rejected jobs is no more than a given bound in this paper we present a 2 approximation algorithm within strongly polynomial time for the problem we also present a polynomial time approximation scheme whose running time is o n m o 1 2 mn 2 for the problem moreover for the case where the number of machines is a fixed constant m our results lead to a fully polynomial time approximation scheme for the problem our result is fairly good in the sense that in a reasonable size of jobs our fptas improves previous best running time from o n m 2 m to o 1 2 m 3 mn 2

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

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

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

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

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

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

minimizing the makespan on a single parallel batching machine in this paper we consider the problem of scheduling with release dates and rejection on a single parallel batching machine where the jobs have non identical sizes our objective is to minimize the makespan of the accepted jobs plus the total penalty of the rejected jobs first we give a polynomial time approximation scheme ptas for the case where jobs can be split then we propose a 2 approximation algorithm for the special case with identical release dates finally we present an approximation algorithm for the general problem with worst case ratio email protected where e 0 is an arbitrarily small constant

on the disjunctive set problem abstract a monoid m is called syntactic if it has a disjunctive subset the latter being defined as a part p m which is not a union of classes of a non equality congruence on m the syntactic monoid problem asks to decide for an arbitrary finite monoid m whether or not m is syntactic our contribution to this problem is twofold 1 we give an algorithm solving syntactic monoid for a large class of finite monoids in o m 3 time in o m 2 od oh 2 we show that a slight generalization of syntactic monoid is np complete this leaves us with the syntactic monoid problem still open but with its hard core better circumscribed

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

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

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

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

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

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

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

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 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

extremal minimality conditions on automata in this paper we investigate the minimality problem of dfas by varying the set of final states in other words we are interested on how the choice of the final states can affect the minimality of the automata the state pair graph is a useful tool to investigate such a problem the choice of a set of final states for the automaton a defines a coloring of the closed components of the state pair graph and the minimality of a corresponds to a property of these colored components a particular attention is devoted to the analysis of some extremal cases such as for example the automata that are minimal for any choice of the subset of final states f from the state set q of the automaton uniformly minimal automata the automata that are minimal for any proper subset f of q almost uniformly minimal automata and the automata that are never minimal under any assignment of final states never minimal automata more generally we seek to characterize those families of automata and show that some of them are related to well known objects in a different context e g multiple entry automata and fischer covers of irreducible sofic shifts in symbolic dynamics next we study the complexity of the related decision problems and show in some cases how to derive a polynomial algorithm finally we pay particular attention to the relationship between the problem to decide if an automaton is never minimal and the syntactic monoid problem

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

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

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

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

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

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

scheduling linear deteriorating jobs with rejection on a single machine we consider several single machine scheduling problems in which the processing time of a job is a linear function of its starting time and jobs can be rejected by paying penalties the objectives are to minimize the makespan the total weighted completion time and the maximum lateness tardiness plus the total penalty of the rejected jobs we show that these problems are np hard and design algorithms based on dynamic programming including pseudo polynomial time optimal algorithms and fully polynomial time approximation schemes to solve them

fast algorithms constructing minimal subalgebras congruences and ideals in a finite algebra abstract fast algorithms are presented which find the minimal nontrivial congruences subalgebras and ideals of a finite algebra given by tables of its operations our method involves finding objects which are minimal among all nontrivial objects i e objects distinct from the least one the running times of the presented algorithms are o n r 1 in case of congreunces and o n r in case of subalgebras and ideals where n is the number of elements of the algebra and r is the maximal arity of its operations for the minimal nontrivial congruences in groups and rings better algorithms are presented working in o n 2 time the algorithm for minimal nontrivial congruences is used for a test whether a given algebra is simple or subdirectly irreducible this algorithm is both a generalization and an improvement of that for sequential automata published by the present authors 1981

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