complete lagrange family for the cube in finite element interpolations abstract noting a vagueness in the serendipity definition the complete lagrange family for the cube and the mixed complete lagrange family are introduced the unisolvent lagrange interpolations over rectangular finite elements are then presented definitively in hierarchy ranking expressions so that the polynominal completeness is realized with appropriately necessary minimum nodes the corresponding interpolation bases in the conventional form can easily be derived through the basis transformation without matrix inversion

on an n person noncooperative markov game with a metric state space abstract we consider a noncooperative n person discounted markov game with a metric state space and define the total expected discounted gain under some conditions imposed on the objects in the game system we prove that our game system has an equilibrium point and each player has his equilibrium strategy moreover in the case of a nondiscounted game the total expected gain up to a finite time can be obtained and we define the long run expected average gain thus if we impose a further assumption for the objects besides the conditions in the case of the discounted game then it is proved that the equilibrium point exists in the nondiscounted markov game the technique for proving the nondiscounted case is essentially to modify the objects of the game so that they become objects of a modified markov game with a discounted factor which has an equilibrium point in addition to the equilibrium point of the discounted game

scale free animal movement patterns levy walks outperform fractional brownian motions and fractional levy motions in random search scenarios the movement patterns of a diverse range of animals have scale free characteristics these characteristics provide necessary but not sufficient conditions for the presence of movement patterns that can be approximated by levy walks nevertheless it has been widely assumed that the occurrence of scale free animal movements can indeed be attributed to the presence of levy walks this is in part because it is known that the super diffusive properties of levy walks can be advantageous in random search scenarios when searchers have little or no prior knowledge of target locations however fractional brownian motions fbms and fractional levy motions flms are both scale free and super diffusive and so it is possible that these motions rather than levy walks underlie some or all occurrences of scale free animal movement patterns here this possibility is examined in numerical simulations through a determination of the searching efficiencies of fbm and flm searches it is shown that these searches are less efficient than levy walk searches this finding does not rule out the possibility that some animals with scale free movement patterns are executing fbm and flm searches but it does make levy walk searches the more likely possibility

fractional fokker planck equation for nonlinear stochastic differential equations driven by non gaussian levy stable noises the fokker planck equation has been very useful for studying dynamic behavior of stochastic differential equations driven by gaussian noises however there are both theoretical and empirical reasons to consider similar equations driven by strongly non gaussian noises in particular they yield strongly non gaussian anomalous diffusion which seems to be relevant in different domains of physics in this paper we therefore derive a fractional fokker planck equation for the probability distribution of particles whose motion is governed by a nonlinear langevin type equation which is driven by a levy stable noise rather than a gaussian we obtain in fact a general result for a markovian forcing we also discuss the existence and uniqueness of the solution of the fractional fokker planck equation

stationary states in langevin dynamics under asymmetric levy noises properties of systems driven by white non gaussian noises can be very different from these of systems driven by the white gaussian noise we investigate stationary probability densities for systems driven by ensuremath alpha stable l evy type noises which provide natural extension to the gaussian noise having however a new property namely a possibility of being asymmetric stationary probability densities are examined for a particle moving in parabolic quartic and in generic double well potential models subjected to the action of ensuremath alpha stable noises relevant solutions are constructed by methods of stochastic dynamics in situations where analytical results are known they are compared with numerical results furthermore the problem of estimation of the parameters of stationary densities is investigated

levy flights in inhomogeneous environments and 1 f noise abstract complex dynamical systems which are governed by anomalous diffusion often can be described by langevin equations driven by levy stable noise in this article we generalize nonlinear stochastic differential equations driven by gaussian noise and generating signals with 1 f power spectral density by replacing the gaussian noise with a more general levy stable noise the equations with the gaussian noise arise as a special case when the index of stability 2 we expect that this generalization may be useful for describing 1 f fluctuations in the systems subjected to levy stable noise

on a d solution of a cooperative m person discounted markov game in the game theory the dynamic multiperson model on infinte horizon have been studied by many authors the literature in this area is mostly concerned with the noncooperative equilibrium point although such an equilibrium point enables individual stability for each player it does not guarantee the collective stability actually there are many cases in which the players can find a multistrategy that will yield a smaller total expected discounted loss if we consider game processes which require some cooperation between the players if the cooperation is provided it is natural to set aside the multistrategies which can be improved on the strategies of one player and keep the others cf lai and tanaka 6 7 81 to this end we propose to consider the d solution see definition 3 1 which is analogous to the domination structure for a multiobjective decision problem of yu 12 one can consult lai and ho 9 for the pareto minimum of multiobjective programming see also lai and liu 10 111 for the conditions of pareto and weak pareto optimalities of mul tiobjective functions in this paper we use a convex cone instead of the nonnegative orthant r we will see that the d solution is a more general concept than usual pareto minimum solution in a game process the purpose of this paper is to find a d solution from a feasible set of the total expected dis counted losses for all players here all multistrategies used by the players 578

rising relative fluctuation as a warning indicator of discontinuous transitions in symbiotic metapopulations abstract the long time limit behavior of the stochastic lotka volterra model of a symbiotic metapopulation subjected to generalized verhulst self regulation is considered the influence of a time variable environment on the carrying capacities of subpopulations is modeled as a periodic deterministic part and a symmetric dichotomous noise relying on the mean field approach it is established that at certain parameter regimes the mean field average subpopulations size exhibits hysteresis in respect to the noise correlation time manifested in the appearance of colored noise induced discontinuous transitions especially it is shown that the relative fluctuation of the subpopulation sizes exhibits accelerated increase prior to abrupt transitions of the metapopulation state moreover in certain cases the autocorrelation function of the population sizes demonstrates anticorrelation at some values of the lag time

econophysics scaling and its breakdown in finance we discuss recent empirical results obtained by analyzing high frequency data of a stock market index the standard and poor s 500 we focus on the scaling properties and on its breakdown of the index dynamics a simple stochastic model the truncated levy flight is illustrated successes and limitations of this model are presented a discussion about similarities and differences between the scaling properties observed in financial markets and in fully developed turbulence is also provided

double stochastic resonance in an insect ecosystem with time delays abstract considering additive and multiplicative periodic signals we have investigated the stochastic resonance sr phenomenon in an insect ecosystem with two different types of time delays at which the insect dynamics is assumed to be disturbed by both additive and multiplicative noises the signal to noise ratio snr is calculated when two different weak periodic signals are added to the insect system it is shown from the snr that the additive and multiplicative periodic signals can cause the sr and double sr in the case of time delays in the stochastic and deterministic force respectively a detailed study of the snr depending on various noise characteristics is performed and the main results about sr are compared for two different cases of time delays

transport in a levy ratchet group velocity and distribution spread we consider the motion of an overdamped particle in a periodic potential lacking spatial symmetry under the influence of symmetric white levy noise being a minimal setup for a levy ratchet due to the nonthermal character of the levy noise the particle exhibits a motion with a preferred direction even in the absence of whatever additional time dependent forces the examination of the levy ratchet has to be based on the characteristics of directionality which are different from typically used measures such as mean current and the dispersion of particle positions since these become inappropriate when the moments of the noise diverge to overcome this problem we discuss robust measures of directionality of transport such as the position of the median of the particle displacement distribution characterizing the group velocity and the interquantile distance giving the measure of the distribution width moreover we analyze the behavior of splitting probabilities for leaving an interval of a given length unveiling qualitative differences between the noises with levy indices below and above unity

escape driven by α stable white noises we explore the archetype problem of an escape dynamics occurring in a symmetric double well potential when the brownian particle is driven by white levy noise in a dynamical regime where inertial effects can safely be neglected the behavior of escaping trajectories from one well to another is investigated by pointing to the special character that underpins the noise induced discontinuity which is caused by the generalized brownian paths that jump beyond the barrier location without actually hitting it this fact implies that the boundary conditions for the mean first passage time mfpt are no longer determined by the well known local boundary conditions that characterize the case with normal diffusion by numerically implementing properly the set up boundary conditions we investigate the survival probability and the average escape time as a function of the corresponding levy white noise parameters depending on the value of the skewness beta of the levy noise the escape can either become enhanced or suppressed a negative asymmetry parameter beta typically yields a decrease for the escape rate while the rate itself depicts a non monotonic behavior as a function of the stability index alpha that characterizes the jump length distribution of levy noise exhibiting a marked discontinuity at alpha 1 we find that the typical factor of 2 that characterizes for normal diffusion the ratio between the mfpt for well bottom to well bottom and well bottom to barrier top no longer holds true for sufficiently high barriers the survival probabilities assume an exponential behavior versus time distinct non exponential deviations occur however for low barrier heights

effects of time delay on symmetric two species competition subject to noise noise and time delay act simultaneously on real ecological systems the lotka volterra model of symmetric two species competition with noise and time delay was investigated in this paper by means of stochastic simulation we find that i the time delay induces the densities of the two species to periodically oscillate synchronously ii the stationary probability distribution function of the two species densities exhibits a transition from multiple to single stability as the delay time increases iii the characteristic correlation time for the sum of the two species densities squared exhibits a nonmonotonic behavior as a function of delay time our results have the implication that the combination of noise and time delay could provide an efficient tool for understanding real ecological systems

fluctuations in multiplicative systems with jumps fluctuation properties of the langevin equation including a multiplicative power law noise and a quadratic potential are discussed the noise has the l evy stable distribution if this distribution is truncated the covariance can be derived in the limit of large time it falls exponentially covariance in the stable case studied for the cauchy distribution exhibits a weakly stretched exponential shape and can be approximated by the simple exponential the dependence of that function on system parameters is determined then we consider a dynamics which involves the above process and obeys the generalized langevin equation the same as for the gaussian case the resulting distributions possess power law tails which fall similarly to those for the driving noise whereas central parts can assume the gaussian shape moreover a process with the covariance 1 t at large time is constructed and the corresponding dynamical equation is solved diffusion properties of systems for both covariances are discussed

stock market dynamics and turbulence parallel analysis of fluctuation phenomena abstract we report analogies and differences between the fluctuations in an economic index and the fluctuations in velocity of a fluid in a fully turbulent state specifically we systematically compare i the statistical properties of the s p 500 cash index recorded during the period january 84 december 89 with ii the statistical properties of the velocity of turbulent air measured in the atmospheric surface layer about 6 m above a wheat canopy in the connecticut agricultural research station we find non gaussian statistics and intermittency for both processes i and ii but the deviation from a gaussian probability density function are different for stock market dynamics and turbulence

general complete lagrange interpolations with applications to three dimensional finite element analysis abstract in this paper we have first derived the interpolation polynomials for the general serendipity solid elements of rectangular shape which allow arbitrarily placed nodes along the edges we have then presented a method to determine the interpolation functions for the general complete lagrange elements which allow arbitrarily placed nodes explicit expressions for interpolation functions of the serendipity and complete lagrange families with uniform spacing of nodes over the element domain are derived for elements of orders 4 10 we have also modified the shape functions of complete lagrange family to correctly interpolate the complete polynomials in the global space for angular distortions of quadrilaterals over the six planar facets of linear solid hexahedron elements

optimal harvesting policy of a stochastic two species competitive model with levy noise in a polluted environment abstract as well known that the sudden environmental shocks and toxicant can affect the population dynamics of fish species a mechanistic understanding of how sudden environmental change and toxicant influence the optimal harvesting policy requires development this paper presents the optimal harvesting of a stochastic two species competitive model with levy noise in a polluted environment where the levy noise is used to describe the sudden climate change due to the discontinuity of the levy noise the classical optimal harvesting methods based on the explicit solution of the corresponding fokker planck equation are invalid the object of this paper is to fill up this gap and establish the optimal harvesting policy by using of aggregation and ergodic methods the approximation of the optimal harvesting effort and maximum expectation of sustainable yields are obtained numerical simulations are carried out to support these theoretical results our analysis shows that the levy noise and the mean stress measure of toxicant in organism may affect the optimal harvesting policy significantly

a two person zero sum markov game with a stopped set abstract we consider a two person zero sum markov game with continuous time up to the time that the game process goes into a fixed subset of a countable state space this subset is called a stopped set of the game we show that such a game with a discount factor has optimal value function and both players will have their optimal stationary strategies the same result is proved for the case of a nondiscounted markov game under some additional conditions that is a reward rate function is nonnegative and the first time entrance time of the game process going to the stopped set is finite with probability one i e p

bistable kinetic model driven by correlated noises steady state analysis a simple rule to obtain the fokker planck equation for a general one dimensional system driven by correlated gaussian white noises is proved by the functional method the fokker planck equation obtained in this paper is applied to the bistable kinetic model we find the following for the steady state 1 in the ensuremath alpha d parameter plane ensuremath alpha is the strength of the additive noise and d is the multiplicative noise strength the critical curve separating the unimodal and bimodal regions of the stationary probability distribution spd of the model is shown to be affected by ensuremath lambda the degree of correlation of the noises as ensuremath lambda is increased the area of the bimodal region in the ensuremath alpha d plane is contracted 2 when we take a point fixed in the ensuremath alpha d plane and increase ensuremath lambda the form of the spd changes from a bimodal to a unimodal structure 3 the positions of the extreme value of the spd of the model sensitively depend on the strength of the multiplicative noise and weakly depend on the additive noise strength 4 for ensuremath lambda 1 the case of perfectly correlated noises when the parameters ensuremath alpha and d take values in the neighborhood of the line ensuremath alpha d in the ensuremath alpha d plane the spd s corresponding to the points ensuremath alpha dg1 and ensuremath alpha d1 exhibit a very different shape of divergence therefore the ratio ensuremath alpha d 1 plays the role of a critical ratio

deterministic walks with inverse square power law scaling are an emergent property of predators that use chemotaxis to locate randomly distributed prey the results of numerical simulations indicate that deterministic walks with inverse square power law scaling are a robust emergent property of predators that use chemotaxis to locate randomly and sparsely distributed stationary prey items it is suggested that chemotactic destructive foraging accounts for the apparent levy flight movement patterns of oxyrrhis marina microzooplankton in still water containing prey items this challenges the view that these organisms are executing an innate optimal levy flight searching strategy crucial for the emergence of inverse square power law scaling is the tendency of chemotaxis to occasionally cause predators to miss the nearest prey item an occurrence which would not arise if prey were located through the employment of a reliable cognitive map or if prey location were visually cued and perfect

levy flights in a steep potential well levy flights in steeper than harmonic potentials have been shown to exhibit finite variance and a critical time at which a bifurcation from an initial monomodal to a terminal bimodal distribution occurs chechkin et al phys rev e 67 010102 r 2003 in this paper we present a detailed study of levy flights in potentials of the type u x x c with c 2 apart from the bifurcation into bimodality we find the interesting result that for c 4 a trimodal transient exists due to the temporal overlap between the decay of the central peak around the initial condition and the building up of the two emerging side peaks which are characteristic for the stationary state thus for certain system parameters there exists a transient trimodal distribution of the levy flight these properties of levy flights in external potentials of the power law type can be represented by certain phase diagrams we also present details about the proof of multimodality and the numerical procedures to establish the probability distribution of the process

on a dynamic fractional game consider a two person zero sum game constructed by a dynamic fractional form we establish the upper value as well as the lower value of a dynamic fractional game and prove that the dual gap is equal to zero under certain conditions it is also established that the saddle point function exists in the fractional game system under certain conditions so that the equilibrium point exists in this game system

anomalous diffusion in systems driven by the stable levy noise with a finite noise relaxation time and inertia dynamical systems driven by a general levy stable noise are considered the inertia is included and the noise represented by a generalized ornstein uhlenbeck process has a finite relaxation time a general linear problem the additive noise is solved the resulting distribution converges with time to the distribution for the white noise massless case moreover a multiplicative noise is discussed it can make the distribution steeper and the variance which is finite depends sublinearly on time subdiffusion for a small mass a white noise limit corresponds to the stratonovich interpretation on the other hand the distribution tails agree with the ito interpretation if the inertia is very large an escape time from the potential well is calculated

mean field limit of systems with multiplicative noise a detailed study of the mean field solution of langevin equations with multiplicative noise is presented three different regimes depending on noise intensity weak intermediate and strong noise are identified by performing a self consistent calculation on a fully connected lattice the most interesting strong noise regime is shown to be intrinsically unstable with respect to the inclusion of fluctuations as a ginzburg criterion shows on the other hand the self consistent approach is shown to be valid only in the thermodynamic limit while for finite systems the critical behavior is found to be different in this last case the self consistent field itself is broadly distributed rather than taking a well defined mean value its fluctuations described by an effective zero dimensional multiplicative noise equation govern the critical properties these findings are obtained analytically for a fully connected graph and verified numerically both on fully connected graphs and on random regular networks the results presented here shed some doubt on what is the validity and meaning of a standard mean field approach in systems with multiplicative noise in finite dimensions where each site does not see an infinite number of neighbors but a finite one the implications of all this on the existence of a finite upper critical dimension for multiplicative noise and kardar parisi zhang problems are briefly discussed

diffusion equations for a markovian jumping process we consider a markovian jumping process which is defined in terms of the jump size distribution and the waiting time distribution with a position dependent frequency in the diffusion limit we assume the power law form for the frequency for small steps we derive the fokker planck equation and show the presence of the normal diffusion subdiffusion and superdiffusion for the l evy distribution of the step size we construct a fractional equation which possesses a variable coefficient and solve it in the diffusion limit then we calculate fractional moments and define the fractional diffusion coefficient as a natural extension to the cases with the divergent variance we also solve the master equation numerically and demonstrate that there are deviations from the l evy stable distribution for large wave numbers

non gaussian noise weakened stability in a foraging colony system with time delay abstract in this paper the dynamical properties in a foraging colony system with time delay and non gaussian noise were investigated using delay fokker planck approach the stationary probability distribution spd the associated relaxation time art and normalization correlation function ncf are obtained respectively the results show that i the time delay and non gaussian noise can induce transition from a single peak to double peaks in the spd i e a type of bistability occurring in a foraging colony system where time delay and non gaussian noise not only cause transitions between stable states but also construct the states themselves numerical simulations are presented and are in good agreement with the approximate theoretical results ii there exists a maximum in the art as a function of the noise intensity this maximum for art is identified as the characteristic of the non gaussian noise weakened stability of the foraging colonies in the steady state iii the art as a function of the noise correlation time exhibits a maximum and a minimum where the minimum for art is identified as the signature of the non gaussian noise enhanced stability of the foraging colonies and iv the time delay can enhance the stability of the foraging colonies in the steady state while the departure from gaussian noise can weaken it namely the time delay and departure from gaussian noise play opposite roles in art or ncf

stretched gaussian asymptotics of the truncated levy flights for the diffusion in nonhomogeneous media abstract the levy jumping process defined in terms of the jumping size distribution and the waiting time distribution is considered the jumping rate depends on the process value the fractional diffusion equation which contains the variable diffusion coefficient is solved in the diffusion limit that solution resolves itself to the stretched gaussian when the order parameter 2 the truncation of the levy flights in the exponential and power law form is introduced and the corresponding random walk process is simulated by the monte carlo method the stretched gaussian tails are found in both cases the time which is needed to reach the limiting distribution strongly depends on the jumping rate parameter when the cutoff function falls slowly the tail of the distribution appears to be algebraic

general complete lagrange family for the cube in finite element interpolations abstract in this paper we have first derived the interpolation polynomials for the general serendipity elements which allow arbitrarily placed nodes along the edges we have then presented a method to determine the interpolation functions for the general complete lagrange elements which allow arbitrarily placed nodes explicit expressions for interpolation functions of the serendipity and complete lagrange family elements which allow uniform spacing of nodes over the element domain are derived for elements of orders 4 10 we have also modified the shape functions of complete lagrange family so that they can correctly interpolate the complete polynomial in the global space for angular distortions

ito versus stratonovich a survey is given of the facts and fancies concerning the nonlinear langevin or ito equation actually it is merely a pre equation which becomes an equation when an interpretation rule is added the rules of ito and stratonovich differ but both are mathematically consistent and therefore equally admissible conventions the reason why they seem to lead to physical differences is that the langevin approach used to arrive at the equation involves a tacit assumption for systems with external noise this assumption can be justified and it is then clear that the stratonovich rule applies systems with internal noise however can only be properly described by a master equation and the ito stratonovich controversy never enters afterward one is free to model the resulting fluctuations either with an ito or a stratonovich scheme but that does not lead to any new information

stability in a system subject to noise with regulated periodicity the stability of a simple dynamical system subject to multiplicative one side pulse noise with hidden periodicity is investigated both analytically and numerically the stability analysis is based on the exact result for the characteristic functional of the renewal pulse process the influence of the memory effects on the stability condition is analyzed for two cases i the dead time distorted poissonian process and ii the renewal process with pareto distribution we show that for fixed noise intensity the system can be stable when the noise is characterized by high periodicity and unstable at low periodicity

effects of small time delay on a bistable system subject to levy stable noise l vy stable noise is often used to describe impulsive noise bursting in communication systems this paper investigates the effects of small time delay on a bistable system driven by an aperiodic bipolar pulse signal and l vy stable noise we obtain the dynamical probability density of the system response by solving the approximated time delayed fractional fokker planck equation ffpe via an implicit finite difference method a new approach to evaluate the system response time is presented the bit error rate ber is employed to measure the performance of the bistable system in detecting binary signals the theoretical ber is validated by the monte carlo simulation we find that the existence of time delay can change both the drift term and the diffusion coefficient in time delayed ffpe for small noise intensity the time delay extends the system response time and thus reduces the detection performance however effects of this kind will fade away with the increase of noise intensity

the closest solution to the shadow minimum of a cooperative dynamic game abstract a cooperative m person discounted markov game with a continuous time and a metric state space is investigated an optimization problem in the m person game is to find a pareto solution determined by the positive orthant in the m dimentional euclid space but in general the set of pareto solutions may be rather large this is quite a drawback for a solution concept in this paper introducing the norm from the multiloss to the shadow minimum as a collective loss function we consider the minimization norm problem in general it seems difficult to find directly a pareto solution for the norm problem so we transfer the primal problem to a dual problem and would find an optimal solution in the dual problem which is called a weak optical solution moreover when a pareto solution in the primal problem exists we give a relation between the pareto solution and a weak optimal solution

effects of element distortions on the performance of isoparametric elements we discuss the effects of element distortions on the performance of displacement based isoparametric quadrilateral finite elements suitable example problems for both the lagrangian and the serendipity types of elements are used to show numerically the effects of element distortions the effects of angular and curved edge distortions are evaluated analytically in terms of the abilities of the elements to represent exactly various polynomial displacement fields we then solve a plane stress problem adaptively to demonstrate the effect of element distortions on the accuracy of the stress distribution the conclusion is that the lagrangian elements are not affected by angular distortions and are therefore the more reliable elements for general use

fractional diffusion and levy stable processes anomalous diffusion in which the mean square distance between diffusing quantities increases faster than linearly in time has been observed in all manner of physical and biological systems from macroscopic surface growth to dna sequences herein we relate the cause of this nondiffusive behavior to the statistical properties of an underlying process using an exact statistical model this model is a simple two state process with long time correlations and is shown to produce a random walk described by an exact fractional diffusion equation fractional diffusion equations describe anomalous transport and are shown to have exact solutions in terms of fox functions including l evy ensuremath alpha stable processes in the superdiffusive domain 1 21

dynamical behaviors determined by the lyapunov function in competitive lotka volterra systems dynamical behaviors of the competitive lotka volterra system even for 3 species are not fully understood in this paper we study this problem from the perspective of the lyapunov function we construct explicitly the lyapunov function using three examples of the competitive lotka volterra system for the whole state space 1 the general 2 species case 2 a 3 species model and 3 the model of may leonard the basins of attraction for these examples are demonstrated including cases with bistability and cyclical behavior the first two examples are the generalized gradient system where the energy dissipation may not follow the gradient of the lyapunov function in addition under a new type of stochastic interpretation the lyapunov function also leads to the boltzmann gibbs distribution on the final steady state when multiplicative noise is added

phase transition and alternation in a model of perceptual bistability in the presence of levy noise abstract the stochastic dynamics of the energy based model of perceptual bistability are numerically studied under the influence of levy noise we obtain the stationary probability distribution for the system driven by gaussian and non gaussian noise by comparing the results we demonstrate that the interplay of levy noise and the input strength of each percept can generate a variety of different effects we next show the influences of levy noise on the mean dominance duration of each percept the alternation rate is also considered as functions of the different parameters of levy noise it shows that changing the value of one or more of the parameters of levy noise can change the mean dominance duration of the percepts and their alternation rate

stochastic resonance and noise delayed extinction in a model of two competing species abstract we study the role of the noise in the dynamics of two competing species we consider generalized lotka volterra equations in the presence of a multiplicative noise which models the interaction between the species and the environment the interaction parameter between the species is a random process which obeys a stochastic differential equation with a generalized bistable potential in the presence of a periodic driving term which accounts for the environment temperature variation we find noise induced periodic oscillations of the species concentrations and stochastic resonance phenomenon we find also a nonmonotonic behavior of the mean extinction time of one of the two competing species as a function of the additive noise intensity

fractional diffusion equation for a power law truncated levy process abstract truncated levy flights are stochastic processes which display a crossover from a heavy tailed levy behavior to a faster decaying probability distribution function pdf putting less weight on long flights overcomes the divergence of the levy distribution second moment we introduce a fractional generalization of the diffusion equation whose solution defines a process in which a levy flight of exponent is truncated by a power law of exponent 5 a closed form for the characteristic function of the process is derived the pdf of the displacement slowly converges to a gaussian in its central part showing however a power law far tail possible applications are discussed

dynamics of two competing species in the presence of levy noise sources we consider a lotka volterra system of two competing species subject to multiplicative stable levy noise the interaction parameter between the species is a random process which obeys a stochastic differential equation with a generalized bistable potential in the presence both of a periodic driving term and an additive stable levy noise we study the species dynamics which is characterized by two different regimes exclusion of one species and coexistence of both we find quasiperiodic oscillations and stochastic resonance phenomenon in the dynamics of the competing species analyzing the role of the levy noise sources

multiplicative levy processes ito versus stratonovich interpretation langevin equation with a multiplicative stochastic force is considered that force is uncorrelated it has the levy distribution and the power law intensity the fokker planck equations which correspond both to the ito and stratonovich interpretation are presented they are solved for the case without drift and for the harmonic oscillator potential the variance is evaluated it is always infinite for the ito case whereas for the stratonovich one it can be finite and rise with time slower that linearly which indicates subdiffusion analytical results are compared with numerical simulations

optimal harvesting strategy for a stochastic mutualism system in a polluted environment with regime switching abstract in this paper we stochastically perturb the harvesting mutualism system into stochastic system in a polluted environment by white noise telegraph noise and levy jump we first prove the existence and uniqueness of the global positive solution of the stochastic system and establish the sufficient condition for persistence in mean of the two cooperative species then using aggregation and ergodic methods the explicit forms of optimal harvesting strategy and the maximum of sustainable yield are obtained we also give some examples and numerical simulations to illustrate the theoretical results the impacts of toxicant in organism telegraph noise and levy jump on the persistence in mean and optimal harvesting strategy are revealed

fractional fokker planck equation for levy flights in nonhomogeneous environments the fractional fokker planck equation which contains a variable diffusion coefficient is discussed and solved it corresponds to the l evy flights in a nonhomogeneous medium for the case with the linear drift the solution is stationary in the long time limit and it represents the l evy process with a simple scaling the solution for the drift term in the form ensuremath lambda text text sgn x possesses two different scales which correspond to the l evy indexes ensuremath mu and ensuremath mu 1 ensuremath mu l1 the former component of the solution prevails at large distances but it diminishes with time for a given x the fractional moments as a function of time are calculated they rise with time and the rate of this growth increases with ensuremath lambda

intrinsic noise induced phase transitions beyond the noise interpretation we discuss intrinsic noise effects in stochastic multiplicative noise partial differential equations which are qualitatively independent of the noise interpretation ito vs stratonovich in particular in the context of noise induced ordering phase transitions we study a model which contrary to all cases known so far exhibits such ordering transitions when the noise is interpreted not only according to stratonovich but also to ito the main feature of this model is the absence of a linear instability at the transition point the dynamical properties of the resulting noise induced growth processes are studied and compared in the two interpretations and with a reference ginzburg landau type model a detailed discussion of a different numerical algorithm valid for both interpretations is also presented

an n person noncooperative discounted vector valued dynamic game with a stopped set abstract the optimization problem of an n person noncooperative discounted vector valued dynamic game with a stopped set is investigated a d convex equilibrium point as the optimization criterion in the game is defined under a domination structure of a convex cone d we show that there exists such a d convex equilibrium point in the game system a modified game system of the original game is formulated which is weighted by a vector factor so that an equilibrium point of the modified game system is still a d convex equilibrium point of the original game system conversely under some additional conditions a d convex equilibrium point will become an equilibrium point of the modified game system further a relation of d convex equilibrium point and the super gradient is discussed

an improved isoparametric transformation for finite element analysis the standard isoparametric transformation for finite element analysis is shown to be only a special case of a more general transformation which allows for flexibility in locating side and interior element nodes side nodes positioned at the same relative distance from corner nodes in both local and global space and interior nodes positioned such that they do not affect the jacobian of the co ordinate transformation provide improved accuracy over nodes positioned locally without regard for the global configuration this concept is demonstrated in the context of two dimensional quadratic quadrilateral isoparametrics but is also applicable to higher orders and dimensions in the test cases examined the new formulation provides a reduction in error of up to three orders of magnitude and also provides accurate solutions for nodal placements which are not allowed using the standard transformations

non cooperative n person game with a stopped set a continuous time non cooperative n person markov game with a stopped set is studied in this paper we prove that in the game process with or without discount factor there exists an optimal stationary point of strategies called the equilibrium point and each player has his equilibrium stationary strategy such that the total expected discounted or non discounted gain are maximums

levy flights from a continuous time process l evy flight dynamics can stem from simple random walks in a system whose operational time number of steps n typically grows superlinearly with physical time t thus this process is a kind of continuous time random walk ctrw dual to the typical scher montroll model in which n grows sublinearly with t models in which l evy flights emerge due to a temporal subordination allow one easily to discuss the response of a random walker to a weak outer force which is shown to be nonlinear on the other hand the relaxation of an ensemble of such walkers in a harmonic potential follows a simple exponential pattern and leads to a normal boltzmann distribution mixed models describing normal ctrw s in superlinear operational time and l evy flights under the operational time of subdiffusive ctrw s lead to a paradoxical diffusive behavior similar to the one found in transport on polymer chains the relaxation to the boltzmann distribution in such models is slow and asymptotically follows a power law

levy flights in nonhomogeneous media distributed order fractional equation approach a jumping process defined in terms of the l evi distributed jumping size and the poissonian position dependent waiting time with the algebraic jumping rate is discussed on the assumption that parameters of both distributions are themselves random variables which are determined from given probability distributions the fractional equation for the distributed l evy order parameter ensuremath mu is derived and solved the solution is of the form of a combination of the fox functions and simple scaling is lacking the problem of accelerated diffusion is also discussed the case of the distributed waiting time parameter ensuremath theta is similarly solved and the solution offers a possibility to manage processes which are characterized by more general forms of the jumping rate not only algebraic moreover we mention a possibility that the parameters ensuremath mu and ensuremath theta are mutually dependent

different delays induced regime shifts in a stochastic insect outbreak dynamics abstract considering time delays in the deterministic and stochastic forces we construct stochastic delayed differential equations to investigate the regime shifts in an insect ecosystem the stationary probability distribution spd and mean first passage time mfpt are obtained respectively our main results show i the multiplicative noise positive cross correlation noise between two noises and time delays can induce the regime shifts from the boom outbreak state to the bust one but the additive noise and negative cross correlation can induce the regime shifts from the bust outbreak state to the boom one ii for the negative cross correlation the mfpt as a function of noise strengths exhibits one maximum which shows the characteristic of the noise delayed switching for the boom outbreak state but for the no cross correlation or positive cross correlation the mfpt decreases with the noise strengths iii two different types of time delays play same roles on the maximal mfpt with additive noise and play opposite roles on the maximal mfpt with multiplicative noise the mechanisms for noises and delays induced regime shifts between two states can be explained physically through the effective potential of ecological model