on a perturbed sparre andersen risk model with threshold dividend strategy and dependence in this paper we consider a sparre andersen risk model perturbed by a brownian motion where the individual claim sizes are dependent on the interclaim times we assume that dividends are paid off under a threshold strategy integral and integro differential equations satisfied by the gerber shiu functions are obtained and a solution procedure is also proposed

a perturbed risk process compounded by a geometric brownian motion with a dividend barrier strategy abstract in this paper we consider a perturbed risk process in which the inter occurrence times are generalized erlang n distributed compounded by a geometric brownian motion integro differential equations with certain boundary conditions for the moment generating function and the mth moment of the present value of all dividends until ruin are derived we also derive integro differential equations with boundary conditions for the gerber shiu function some special cases are considered in details

analysis of a predator prey model with modified leslie gower and holling type ii schemes with stochastic perturbation abstract in this paper we consider a predator prey model with modified leslie gower and holling type ii schemes with stochastic perturbation we show there is a unique positive solution to the system with positive initial value and mainly investigate the long time behavior of the system condition for the system to be extinct is given and persistent condition is established at last numerical simulations are carried out to support our results

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

an optimal dividend strategy in the discrete sparre andersen model with bounded dividend rates we consider the discrete sparre andersen risk model and its derivative models by anew setting up the initial times and assume that dividends are paid to the shareholders according to an admissible strategy with dividend rates bounded by a constant the company controls the amount of dividends in order to maximize the cumulative expected discounted dividends prior to ruin we show that the optimal value function is the unique bounded solution of a set of discrete hamilton jacobi bellman equations moreover we introduce bellman s recursive algorithm and offer a simpler algorithm to obtain the optimal strategy and the optimal value functions our method is mainly to transform the value functions numerical examples are presented to illustrate the transformation method

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

power associative nilalgebras of dimension 9 abstract in 19 authors described some properties about commutative power associative nilalgebras of nilindex 5 here we will get new results about the structure of this class of algebras those results will allow us to prove that every commutative power associative algebra of dimension 9 and nilindex 5 over a field of characteristic different from 2 3 and 5 is solvable consequently the famous albert s conjecture 1 problem 1 1 is setted for dimension 9 and characteristic 0 since the case of dimension 9 and nilindex 5 have already been examined in 27 11 14 and 20

data driven confidence intervals for diffusion process using double smoothing empirical likelihood abstract in this paper we propose an innovative estimation method for the volatility function in diffusion process and construct the empirical likelihood confidence interval for it compared with double smoothing local constant estimator double smoothing local linear estimator proposed in this paper is an inventive estimation method moreover we find that the empirical likelihood confidence interval constructed with the approximate estimating equation is much better than the one based on the estimating equation since the latter undermines the predictability of the estimator accordingly new algorithm for simulation is proposed through monte carlo simulation and empirical analysis both these approaches are superior to traditional asymptotic normality confidence interval in terms of coverage rate etc

nilpotent linear spaces and albert s problem abstract in 8 m a fasoli classified up to conjugation all the maximal vector subspaces of m 4 c in which all the elements are nilpotent matrices this result will allow us to solve albert s problem 5 for commutative power associative c nilalgebras of dimension n and nilindex n 3 in an affirmative way

on the solvability of the commutative power associative nilalgebras of dimension 6 abstract we prove that commutative power associative nilalgebras of dimension 6 over a field of characteristic 2 3 5 are solvable

synchronized hopf bifurcation analysis in a neural network model with delays we consider the synchronized periodic oscillation in a ring neural network model with two different delays in self connection and nearest neighbor coupling employing the center manifold theorem and normal form method introduced by hassard et al we give an algorithm for determining the hopf bifurcation properties using the global hopf bifurcation theorem for fde due to wu and bendixson s criterion for high dimensional ode due to li and muldowney we obtain several groups of conditions that guarantee the model have multiple synchronized periodic solutions when the transfer coefficient or time delay is sufficiently large

a renewal jump diffusion process with threshold dividend strategy in this paper we consider a jump diffusion risk process with the threshold dividend strategy both the distributions of the inter arrival times and the claims are assumed to be in the class of phase type distributions the expected discounted dividend function and the laplace transform of the ruin time are discussed motivated by asmussen s asmussen stationary distributions for fluid flow models with or without brownian noise stochastic models 11 1 1995 21 49 instead of studying the original process we study the constructed fluid flow process and their closed form formulas are obtained in terms of matrix expression finally numerical results are provided to illustrate the computation

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

s1 degree and global hopf bifurcation theory of functional differential equations abstract the recently developed s 1 degree and bifrucation theory are applied to provide a purely topological argument of a global hopf bifurcation theory for functional differential equations of mixed type in the special case where the equation is of retarded type the established result represents an analog of alexander and yorke s global hopf bifurcation theorem which has been obtained by chow fiedler mallet paret and nussbaum using different approaches

multistability and stable asynchronous periodic oscillations in a multiple delayed neural system abstract we consider a network of three identical neurons with multiple discrete signal transmission delays the model for such a network is a system of nonlinear delay differential equations after some consideration of the absolute synchronization of the system and the global attractivity of the zero solution we present a detailed discussion about the boundaries of the stability region of the trivial solution this allows us to determine the possible codimension one bifurcations which occur in the system in particular we show the existence of standard hopf bifurcations giving rise to synchronized periodic solutions and of d 3 equivariant hopf bifurcations giving rise to three types of periodic solutions phase locked mirror reflecting and standing waves hopf hopf and hopf steady state bifurcations interactions are shown to exist and give rise to coexistence of stable synchronized and desynchronized solutions perturbation techniques coupled with the floquet theory are used to determine the stability of the phase locked oscillations

on optimal dividends from reflection to refraction the problem goes back to a paper that bruno de finetti presented to the international congress of actuaries in new york 1957 in a stock company that is involved in risky business what is the optimal dividend strategy that is what is the strategy that maximizes the expectation of the discounted dividends until possible ruin to the shareholders jeanblanc picque and shiryaev russian math surveys 20 1995 257 277 and asmussen and taksar insurance math econom 20 1997 1 15 solved the problem by modeling the income process of the company by a wiener process and imposing the condition of a bounded dividend rate here we present some down to earth calculations in this context

stability and hopf bifurcation in a delayed competition system abstract in this paper hopf bifurcation for two species lotka volterra competition systems with delay dependence is investigated by choosing the delay as a bifurcation parameter we prove that the system is stable over a range of the delay and beyond that it is unstable in the limit cycle form i e there are periodic solutions bifurcating out from the positive equilibrium our results show that a stable competition system can be destabilized by the introduction of a maturation delay parameter further an explicit algorithm for determining the direction of the hopf bifurcation and the stability of the bifurcating periodic solutions is derived by using the theory of normal forms and center manifolds and numerical simulations supporting the theoretical analysis are also given

on a class of commutative power associative nilalgebras abstract we prove that commutative power associative nilalgebras of nilindex n and dimension n are nilpotent of index n we find a necessary and sufficient condition for such an algebra to be a jordan algebra and give all corresponding isomorphism classes

hopf bifurcation analysis in a delayed nicholson blowflies equation abstract the dynamics of a nicholson s blowflies equation with a finite delay are investigated we prove that a sequence of hopf bifurcations occur at the positive equilibrium as the delay increases explicit algorithm for determining the direction of the hopf bifurcations and the stability of the bifurcating periodic solutions are derived using the theory of normal form and center manifold global existence of periodic solutions are established using a global hopf bifurcation result of wu trans amer math soc 350 1998 4799 and a bendixson criterion for higher dimensional ordinary differential equations due to li and muldowney j differential equations 106 1994 27

periodicity and attractivity of a ratio dependent leslie system with impulses a ratio dependent leslie system with impulses is studied by using a comparison theorem continuation theorem base on coincidence degree and constructing a suitable lyapunov function we establish sufficient and necessary conditions for the existence and global attractivity of periodic solution examples show that the obtained criteria are easily verifiable

attractor minimal sets for non autonomous delay functional differential equations with applications for neural networks the dynamics of a class of non autonomous convex or concave and monotone delay functional differential systems is studied in particular we provide an attractivity result when two completely st

local hopf bifurcation and global periodic solutions in a delayed predator prey system abstract we consider a delayed predator prey system we first consider the existence of local hopf bifurcations and then derive explicit formulas which enable us to determine the stability and the direction of periodic solutions bifurcating from hopf bifurcations using the normal form theory and center manifold argument special attention is paid to the global existence of periodic solutions bifurcating from hopf bifurcations by using a global hopf bifurcation result due to wu trans amer math soc 350 1998 4799 we show that the local hopf bifurcation implies the global hopf bifurcation after the second critical value of delay finally several numerical simulations supporting the theoretical analysis are also given

numerical methods for optimal dividend payment and investment strategies of regime switching jump diffusion models with capital injections this work focuses on numerical methods for finding optimal investment dividend payment and capital injection policies to maximize the present value of the difference between the cumulative dividend payment and the possible capital injections the surplus is modeled by a regime switching jump diffusion process subject to both regular and singular controls using the dynamic programming principle the value function is a solution of the coupled system of nonlinear integro differential quasi variational inequalities in this paper the state constraint of the impulsive control gives rise to a capital injection region with free boundary which makes the problem even more difficult to analyze together with the regular control and regime switching the closed form solutions are virtually impossible to obtain we use markov chain approximation techniques to construct a discrete time controlled markov chain to approximate the value function and optimal controls convergence of the approximation algorithms is proved examples are presented to illustrate the applicability of the numerical methods

linear spaces of nilpotent matrices abstract we consider several questions on spaces of nilpotent matrices we present sufficient conditions for triangularizability and give examples of irreducible spaces we give a necessary and sufficient condition in terms of the trace for all linear combinations of a given set of operators to be nilpotent we also consider the question of the dimension of a space l of nilpotents on f n in particular we give a simple new proof of a theorem due to m gerstenhaber concerning the maximal dimension of such spaces

on solvability of noncommutative power associative nilalgebras abstract we show that noncommutative power associative nilalgebras of finite dimension n and nilindex k are solvable if k n 1 or k n for any given integer n 2 we present an example of a power associative nilalgebra of dimension n and nilindex n 1 which is not solvable this implies a power associative nilalgebra of dimension n and nilindex k need not be solvable if k n

convergence results in a well known delayed predator prey system abstract in this paper we provide a detailed and explicit procedure of obtaining some regions of attraction for the positive steady state assumed to exist of a well known lotka volterra type predator prey system with a single discrete delay our procedure requires the delay length to be small a detailed example is presented the method used here is to construct a proper liapunov functional in a restricted region

harmless delays in cohen grossberg neural networks without assuming monotonicity and differentiability of the activation functions and any symmetry of interconnections we establish some sufficient conditions for the globally asymptotic stability of a unique equilibrium for the cohen grossberg neural network with multiple delays lyapunov functionals and functions combined with the razumikhin technique are employed the criteria are all independent of the magnitudes of the delays and thus the delays under these conditions are harmless 2002 elsevier science b v all rights reserved msc 34d23 34k20 92b20

homotopy linearization and bifurcation on presente une prise en compte essentiellement auto contenue de la relation entre bifurcation locale et la determination a l aide de la linearisation de la non trivialite de certaines classes d homotopie d operateurs non lineaires

optimal dividends in the brownian motion risk model with interest in this paper we consider a brownian motion risk model and in addition the surplus earns investment income at a constant force of interest the objective is to find a dividend policy so as to maximize the expected discounted value of dividend payments it is well known that optimality is achieved by using a barrier strategy for unrestricted dividend rate however ultimate ruin of the company is certain if a barrier strategy is applied in many circumstances this is not desirable this consideration leads us to impose a restriction on the dividend stream we assume that dividends are paid to the shareholders according to admissible strategies whose dividend rate is bounded by a constant under this additional constraint we show that the optimal dividend strategy is formed by a threshold strategy

optimal harvesting strategies for stochastic competitive lotka volterra ecosystems this work develops optimal harvest strategies for lotka volterra systems so as to establish economically ecologically and environmentally reasonable strategies for populations subject to the risk of extinction to better reflect reality a continuous time markov chain is used to model the random environment the underlying systems are thus controlled regime switching diffusions that belong to the class of singular control problems starting with a model having multiple species we construct upper bounds for the value functions prove the finiteness of the harvesting value and derive properties of the value functions then we construct explicit chattering harvesting strategies and the corresponding lower bounds for the value functions by using the idea of harvesting only one species at a time we further show that this is a reasonable candidate for the best lower bound that one can expect moreover in some cases the lower bounds provide a good approximation of the value functions

convergent numerical scheme for singular stochastic control with state constraints in a portfolio selection problem we consider a singular stochastic control problem with state constraints that arises in problems of optimal consumption and investment under transaction costs numerical approximations for the value function using the markov chain approximation method of kushner and dupuis are studied the main result of the paper shows that the value function of the markov decision problem mdp corresponding to the approximating controlled markov chain converges to that of the original stochastic control problem as various parameters in the approximation approach suitable limits all our convergence arguments are probabilistic the main assumption that we make is that the value function be finite and continuous in particular uniqueness of the solutions of the associated hjb equations is neither needed nor available in the generality under which the problem is considered specific features of the problem that make the convergence analysis nontrivial include unboundedness of the state and control space and the cost function degeneracies in the dynamics mixed boundary dirichlet neumann conditions and presence of both singular and absolutely continuous controls in the dynamics finally schemes for computing the value function and optimal control policies for the mdp are presented and illustrated with a numerical study

spatiotemporal dynamics in a delayed diffusive predator model in this paper we investigate the spatiotemporal dynamics of a delayed reaction diffusion leslie gower model based on the stability analysis we demonstrate that delayed feedback may generate hopf and turing instability under some conditions resulting in spatial patterns one of the most interesting findings is that the model exhibits complex pattern replication pure turing instability gives birth to spots spots stripes mixture stripes stripes holes mixture and holes patterns pure hopf instability to spiral wave pattern and hopf turing instability to chaotic wave pattern our results well extend the findings of spatiotemporal dynamics in the delayed reaction diffusion predator prey model and indicate that time delay play an important roles in pattern formation

the perturbed compound poisson risk model with linear dividend barrier in this paper we consider a diffusion perturbed classical compound poisson risk model in the presence of a linear dividend barrier partial integro differential equations for the moment generating function and the nth moment of the present value of all dividends until ruin are derived moreover explicit solutions for the nth moment of the present value of dividend payments are obtained when the individual claim size distribution is exponential we also provided some numerical examples to illustrate the applications of the explicit solutions finally we derive partial integro differential equations with boundary conditions for the gerber shiu function

symmetric functional differential equations and neural networks with memory we establish an analytic local hopf bifurcation theorem and a topological global hopf bifurcation theorem to detect the existence and to describe the spatial temporal pattern the asymptotic form and the global continuation of bifurcations of periodic wave solutions for functional differential equations in the presence of symmetry we apply these general results to obtain the coexistence of multiple large amplitude wave solutions for the delayed hopfield cohen grossberg model of neural networks with a symmetric circulant connection matrix

on a perturbed by diffusion compound poisson risk model with delayed claims and multi layer dividend strategy in this paper we consider an extension to the compound poisson risk process perturbed by diffusion in which two types of dependent claims main claims and by claims are incorporated every by claim is induced by the main claim and may be delayed for one time period with a certain probability an integro differential equation system for the gerber shiu expected discounted penalty functions is derived and solved by proving that the gerber shiu function satisfies some defective renewal equation an exact representation for the solution of this equation is derived through an associated compound geometric distribution and an analytic expression for this quantity is given when both the claim and the by claim amounts belong to the rational family of distributions further the same risk model is considered in the presence of a multi layer dividend strategy a system of integro differential equations for the expected discounted penalty functions depending on the current surplus level with certain initial and boundary conditions is obtained to solve this we derive a general solution to a certain second order integro differential equation system this solution is obtained by transforming this system to a volterra type system of integral equations of second kind which is solved by using laplace transforms provided an explicit expression for the gerber shiu functions depending on the current surplus level finally numerical results for the ruin probability are given to illustrate the applicability of our results

optimal investment policies for a firm with a random risk process exponential utility and minimizing the probability of ruin we consider a firm that is faced with an uncontrollable stochastic cash flow or random risk process there is one investment opportunity a risky stock and we study the optimal investment decision for such firms there is a fundamental incompleteness in the market in that the risk to the investor of going bankrupt cannot be eliminated under any investment strategy since the random risk process ensures that there is always a positive probability of ruin bankruptcy we therefore focus on obtaining investment strategies which are optimal in the sense of minimizing the risk of ruin in particular we solve for the strategy that maximizes the probability of achieving a given upper wealth level before hitting a given lower level this policy also minimizes the probability of ruin we prove that when there is no risk free interest rate this policy is equivalent to the policy that maximizes utility from terminal wealth for a fixed terminal time when the firm has an exponential utility function this validates a longstanding conjecture about the relation between minimizing probability of ruin and exponential utility when there is a positive risk free interest rate the conjecture is shown to be false we also solve for the optimal policy for the related objective of minimizing the expected discounted penalty paid upon ruin

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

survival and growth with a liability optimal portfolio strategies in continuous time we study the optimal behavior of an investor who is forced to withdraw funds continuously at a fixed rate per unit time e g to pay for a liability to consume or to pay dividends the investor is allowed to invest in any or all of a given number of risky stocks whose prices follow geometric brownian motion as well as in a riskless asset which has a constant rate of return the fact that the withdrawal is continuously enforced regardless of the wealth level ensures that there is a region where there is a positive probability of ruin in the complementary region ruin can be avoided with certainty call the former region the danger zone and the latter region the safe region we first consider the problem of maximizing the probability that the safe region is reached before bankruptcy which we call the survival problem while we show among other results that an optimal policy does not exist for this problem we are able to construct explicit e optimal policies for any e 0 in the safe region where ultimate survival is assured we turn our attention to growth among other results we find the optimal growth policy for the investor i e the policy which reaches another higher valued goal as quickly as possible other variants of both the survival problem as well as the growth problem are also discussed our results for the latter are intimately related to the theory of constant proportions portfolio insurance

numerical solutions of optimal risk control and dividend optimization policies under a generalized singular control formulation this paper develops numerical methods for finding optimal dividend pay out and reinsurance policies a generalized singular control formulation of surplus and discounted payoff function is introduced where the surplus is modeled by a regime switching process subject to both regular and singular controls to approximate the value function and optimal controls markov chain approximation techniques are used to construct a discrete time controlled markov chain the proofs of the convergence of the approximation sequence to the surplus process and the value function are given examples of proportional and excess of loss reinsurance are presented to illustrate the applicability of numerical methods

an index for global hopf bifurcation in parabolic systems on considere le systeme non lineaire d t u a u f u 0 et on cherche des solutions periodiques en temps u t qui bifurquent a partir d une solution stationnaire

stochastic optimization algorithms for barrier dividend strategies this work focuses on finding optimal barrier policy for an insurance risk model when the dividends are paid to the share holders according to a barrier strategy a new approach based on stochastic optimization methods is developed compared with the existing results in the literature more general surplus processes are considered precise models of the surplus need not be known only noise corrupted observations of the dividends are used using barrier type strategies a class of stochastic optimization algorithms are developed convergence of the algorithm is analyzed rate of convergence is also provided numerical results are reported to demonstrate the performance of the algorithm

the perturbed sparre andersen model with a threshold dividend strategy in this paper we consider a sparre andersen model perturbed by diffusion with generalized erlang n distributed inter claim times and a threshold dividend strategy integro differential equations with certain boundary conditions for the moment generation function and the mth moment of the present value of all dividends until ruin are derived we also derive integro differential equations with boundary conditions for the gerber shiu functions the special case where the inter claim times are erlang 2 distributed and the claim size distribution is exponential is considered in some details

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

on a perturbed sparre andersen risk model with multi layer dividend strategy in this paper we consider a perturbed sparre andersen risk model in which the inter claim times are generalized erlang n distributed under the multi layer dividend strategy piece wise integro differential equations for the discounted penalty functions are derived and a recursive approach is applied to express the solutions a numerical example to calculate the ruin probabilities is given to illustrate the solution procedure

optimal consumption for general diffusions with absorbing and reflecting barriers two stochastic control problems of the storage or inventory type are considered for general diffusion processes in the absorption problem a diffusion process is controlled by subtracting a nondecreasing withdrawal process the controlled process is absorbed if it reaches zero the objective function to be maximized is the expected discounted value of the withdrawals plus a discounted penalty for absorption in the reflection problem the process can be controlled by subtracting a withdrawal process and adding a deposit process and the controlled process must be nonnegative one seeks to maximize an expected discounted weighted difference in withdrawals and deposits the value function is computed and a necessary and sufficient condition for the existence of an optimal policy is given when they exist optimal policies are found to be the minimal processes which keep the controlled process inside an interval

an artificial boundary method for american option pricing under the cev model the black scholes asset price dynamics is well known to be inadequate for capturing the volatility smile in the financial market therefore the constant elasticity of variance cev model has become a popular alternative to valuing options fitting to the smile american option pricing however is computationally intensive as there are no analytical formulas available this paper proposes an artificial boundary method for partial differential equations pdes to compute american option prices and greeks under the cev model the idea is to reduce the infinite computational domain to a finite one by introducing an artificial boundary on which an exact boundary condition is derived we then develop a crank nicolson scheme to solve the pde with the artificial boundary condition implemented with a numerical laplace inversion with a finite computational domain the optimal exercise boundary can be determined efficiently our numerical examples show that the proposed scheme is accurate robust with respect to

hopf bifurcation in a two competitor one prey system with time delay in this paper we consider a delayed two competitor one prey system in which both two competitors exhibit holling ii functional response by choosing the time delay as a bifurcation parameter it is found that the hopf bifurcation occurs when the delay passes through a certain critical value numerical simulations are performed to illustrate the analytical results

optimal dividends and bankruptcy procedures analysis of the ornstein uhlenbeck process abstract this paper investigates the impact of bankruptcy procedures on optimal dividend barrier policies we specifically focus on chapter 11 of the us bankruptcy code which allows a firm in default to continue its business for a certain period of time our model is based on the surplus of a firm that earns investment income at a constant rate of credit interest when it is in a creditworthy condition the firm pays a debit interest rate that depends on the deficit level when it is in financial distress thus the surplus follows an ornstein uhlenbeck ou process with a negative surplus dependent mean reverting rate default and liquidation are modeled as distinguishable events by using an excursion time or occupation time framework this paper demonstrates how the optimal dividend barrier can be obtained by deriving a closed form solution for the dividend value function it also characterizes the distributional property and expectation of bankruptcy time subject to the bankruptcy procedure our numerical examples show that under an optimal dividend barrier strategy the bankruptcy procedure may not prolong the expected bankruptcy time in some situations

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

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

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

nilpotence of a class of commutative power associative nilalgebras abstract let a be a commutative algebra over a field f of characteristic 2 3 in m gerstenhaber on nilalgebras and linear varieties of nilpotent matrices ii duke math j 27 1960 21 31 m gerstenhaber proved that if a is a nilalgebra of bounded index t and the characteristic of f is zero or greater than 2 t 3 then the right multiplication r x is nilpotent and r x 2 t 3 0 for all x a in this work we prove that this result is also valid for commutative power associative algebras of characteristic t in section 3 we prove that when a is a power associative nilalgebra of dimension 6 then a is nilpotent or a 2 2 0 in section 4 we prove that every power associative nilalgebra a of dimension n and nilindex t n 1 is either nilpotent of index t or isomorphic to the suttles example

the perturbed compound poisson risk model with constant interest and a threshold dividend strategy in this paper we consider the compound poisson risk model perturbed by diffusion with constant interest and a threshold dividend strategy integro differential equations with certain boundary conditions for the moment generation function and the nth moment of the present value of all dividends until ruin are derived we also derive integro differential equations with boundary conditions for the gerber shiu functions the special case that the claim size distribution is exponential is considered in some detail

numerical methods for stochastic singular control problems the paper develops a powerful class of numerical methods for stochastic singular control problems the basic models used are diffusion or reflected diffusions but the method is of general applicability the central idea is that of the markov chain approximation method where an approximation to the control problem is found for which an optimal solution is computable and which is an arbitrarily good approximation to the original problem and its optimal value function the methods are convenient to program and use and they have been used with success and they cover a wide variety of problems in fact for the singular problem they seem to be the only ones currently available owing to problems in proving tightness of certain processes that occur in the convergence proofs the methods of proof used for the nonsingular problems need modifications examples of useful approximations the algorithms and the convergence proofs are given to illustrate the power of the methods two classes of problems are d

stability and convergence in strongly monotone dynamical systems soit x un systeme dynamique x est un espace topologique et le flot t t r est une famille d applications continues de sous ensembles ouverts de x dans x on decrit qualitativement le comportement asymptotique quand t des trajectoires t t x pour les etats initiaux x dans le cas de systemes ayant un principe de comparaison fort

occupation times of the ornstein uhlenbeck process functional pca and evidence from electricity prices abstract we discuss the functional principal component analysis fpca of the occupation times of the ornstein uhlenbeck process for the eigenvalue problem of the covariance operator of the occupation times we derive the corresponding integral equation in the large time limit and we solve numerically for the principal components the formulation applies the path integral approach of feynman and kac the principal components are compared with those from empirical electricity price processes on energy markets the results indicate that fpca of the occupation times is a suitable tool in stochastic energy modeling to generate moderately sized scenario trees

numerical methods for optimal harvesting strategies in random environments under partial observations this work is concerned with optimal harvesting problems in random environments in contrast to the existing literature the markov chain is hidden and can only be observed in a gaussian white noise in our work we first use the wonham filter to estimate the markov chain from the observable evolution of the given process so as to convert the original problem to a completely observable one then we treat the resulting optimal control problem because the problem is virtually impossible to solve in closed form our main effort is devoted to developing numerical approximation algorithms to approximate the value function and optimal strategies markov chain approximation methods are used to construct a discrete time controlled markov chain convergence of the algorithm is proved by weak convergence method and suitable scaling a numerical example is provided to demonstrate the results

multiple hopf bifurcations of three coupled van der pol oscillators with delay abstract a system of three coupled van der pol oscillators with delay is considered hopf bifurcations at the zero equilibrium as the delay increases are exhibited the existence and stability of multiple periodic solutions are established using a symmetric hopf bifurcation result of wu trans amer math soc 350 1998 4799 4838

a predator prey system with stage structure for predator abstract this paper studies the asymptotoc behavior of a predator prey model with stage structure it is found that an orbitally asymptotically stable periodic orbit exists in that model when time delay due to gestation of predator and time delay from crowding effect of prey are incorporated we establish the condition for the permanence of populations and sufficient conditions under which positive equilibrium of the model is globally stable

the bifurcation structure of the holling tanner model for predator prey interactions using two timing the holling tanner model for predator prey systems has two hopf bifurcation points for certain parameters the dependence of the environmental parameters on the underlying bifurcation structure is uncovered using two timing emphasis is on how the bifurcation diagram changes as the hopf bifurcation points separate two degenerate cases require a modification of conventional two timing when the two hopf bifurcation points nearly coalesce the two stable periodic solution branches are shown to be connected as a ratio of linear growth rates varies the hopf bifurcation points separate further and one limit cycle becomes unstable this situation can correspond to an outbreak in populations the modified two timing analysis analytically captures the unstable and stable limit cycles of the new branch

circulant matrices and differential delay equations on etudie les solutions periodiques non triviales de familles parametrisees d equations differentielles a retard

complicated dynamics of a ring neural network with time delays this paper studies the dynamical behavior of a ring neural network with time delays on the basis of lyapunov s method the asymptotic stability of the equilibrium is first investigated and the delay dependent criteria ensuring global stability for the ring neural network are obtained moreover based on the global hopf bifurcation theorem for fde the conditions that guarantee the global existence of periodic solutions are determined it shows that periodic solutions bifurcating from the trivial equilibrium can continue when the time delay is far away from the critical value some examples are induced to illustrate our results in addition complicated dynamics of the model are investigated with the help of numerical simulation the study results show that the model exhibits period doubling bifurcations which lead eventually to chaos and the chaos can also directly occur via the bifurcations from the quasi periodic solutions

stability and hopf bifurcation analysis on a delayed leslie gower predator prey system incorporating a prey refuge in this paper a modified leslie gower predator prey system with time delays is investigated where the time delays are regarded as bifurcation parameters by analyzing the corresponding characteristic equation the local stability of a positive equilibrium is considered moreover we show that hopf bifurcations occur when time delay crosses some critical values by deriving the equation describing the flow on the center manifold we give the formula for determining the direction of the hopf bifurcation and the stability of bifurcating periodic solutions in addition we also try on the global existence of periodic solutions by using the 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 numerical simulations are carried out to illustrate the theoretical results and they show that the time delays in the system under consideration can destroy the stability of the system

hopf bifurcation and global periodic solutions in a delayed predator prey system this paper is concerned with a delayed predator prey system with same feedback delays of predator and prey species to their growth respectively we prove that a sequence of hopf bifurcations occur at the positive equilibrium as the delay increases monotonously from zero by using the theory of normal norm and center manifold reduction an explicit algorithm for determining the direction of hopf bifurcations and the stability of bifurcating periodic solutions is derived in addition the global existence results of periodic solutions bifurcating from hopf bifurcations are established by using a global hopf bifurcation result due to wu j wu symmetric functional differential equations and neural networks with memory trans amer math soc 350 1998 4799 4838 finally a numerical example supporting our theoretical prediction is also given our findings are contrasted with recent studies on a delayed predator prey system with the feedback time delay of prey species to its growth by song and wei y song j wei local hopf bifurcation and global periodic solutions in a delayed predator prey system j math anal appl 301 2005 1 21 as the feedback time delay increases monotonously from zero the positive equilibrium of the latter switches k times from stability to instability to stability in contrast the positive equilibrium of our system appears to lose the above property

nilpotent linear transformations and the solvability of power associative nilalgebras abstract we prove some results about nilpotent linear transformations as an application we solve some cases of albert s problem on the solvability of nilalgebras more precisely we prove the following results commutative power associative nilalgebras of dimension n and nilindex n 1 or n 2 are solvable commutative power associative nilalgebras of dimension 7 are solvable

monotone semiflows generated by functional differential equations abstract this obtains sufficient condition for an autonomous functional differential equation to generate a strongly monotone semiflow on a suitable state space this allows the application to functional differential equations of very powerful recent results on strongly monotone semiflows due to hirsch and matano in addition a very striking relationship is established between such functional differential equations and corresponding ordinary differential equations an example involving a biochemical feedback loop is considered keywords stability steady states

nilpotency of commutative finitely generated algebras satisfying lx3 γlx3 0 γ 1 0 abstract this paper deals with two varieties of commutative non associative algebras one variety satisfies l x 3 l x 3 0 the other variety satisfies l x 3 0 we prove that in either variety any finitely generated algebra is nilpotent our results require characteristic 2 3

on the renewal risk model under a threshold strategy in this paper we consider the renewal risk process under a threshold dividend payment strategy for this model the expected discounted dividend payments and the gerber shiu expected discounted penalty function are investigated integral equations integro differential equations and some closed form expressions for them are derived when the claims are exponentially distributed it is verified that the expected penalty of the deficit at ruin is proportional to the ruin probability

stability of nonlinear waves in a ring of neurons with delays abstract in this paper we consider a ring of identical neurons with self feedback and delays based on the normal form approach and the center manifold theory we derive some formula to determine the direction of hopf bifurcation and stability of the hopf bifurcated synchronous periodic orbits phase locked oscillatory waves standing waves mirror reflecting waves and so on in addition under general conditions such a network has a slowly oscillatory synchronous periodic solution which is completely characterized by a scalar delay differential equation despite the fact that the slowly oscillatory synchronous periodic solution of the scalar equation is stable we show that the corresponding synchronized periodic solution is unstable if the number of the neurons is large or arbitrary even