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

a stochastic model for internal hiv dynamics in this paper we analyse a stochastic model representing hiv internal virus dynamics the stochasticity in the model is introduced by parameter perturbation which is a standard technique in stochastic population modelling we show that the model established in this paper possesses non negative solutions as this is essential in any population dynamics model we also carry out analysis on the asymptotic behaviour of the model we approximate one of the variables by a mean reverting process and find out the mean and variance of this process numerical simulations conclude the paper

c cosine functions and the abstract cauchy problem ii for a bounded linear injectioncon a banach spacexand a closed linear operatora d a x xwhich commutes withcwe prove that 1 the abstract cauchy problem u t au t t r u 0 cx u 0 cy has a unique strong solution for everyx y d a if and only if 2 a1 a d a2 generates ac1 cosine function onx1 d a with the graph norm if and only if in caseahas nonempty resolvent set 3 agenerates ac cosine function onx herec1 c x1 under the assumption thatais densely defined andc 1ac a statement 3 is also equivalent to each of the following statements 4 the problemv t av t c x ty t0 cg r dr t r v 0 v 0 0 has a unique strong solution for everyg l1locandx y x 5 the problemw t aw t cg t t r w 0 cx w 0 cy has a unique weak solution for everyg l1locandx y x finally as an application it is shown that for any bounded operatorbwhich commutes withcand has range contained in the range ofc a bis also a generator

dynamics of a predator prey model we describe the bifurcation diagram of limit cycles that appear in the first realistic quadrant of the predator prey model proposed by r m may stability and complexity in model ecosystems princeton university press princeton nj 1974 in particular we give a qualitative description of the bifurcation curve when two limit cycles collapse on a semistable limit cycle and disappear moreover we show that locally asymptotic stability of a positive equilibrium point does not imply global stability for this class of predator prey models

powering by a table look up and a multiplication with operand modification an efficient method for generating a power of an operand i e x sup p for an operand x and a given p is proposed it is applicable to ps in the form of spl plusmn 2 sup k where k is any integer and of spl plusmn 2 k sub 1 spl plusmn 2 k sub 2 where k sub 1 is any integer and k sub 2 is any nonnegative integer the reciprocal the square root the reciprocal square root the reciprocal square the reciprocal cube and so forth are included the method is a modification of the piecewise linear approximation a power of an operand is generated through a table look up and a multiplication with operand modification the same accuracy is achieved as the piecewise linear approximation the multiplication and an addition required for the piecewise linear approximation are replaced by only one double sized multiplication with a slight modification of the operand and hence one clock cycle may be reduced the required table size is reduced because only one coefficient instead of two has to be stored

matrices of operators and regularized cosine functions this paper is concerned with matrices of abstract differential operators which are parabolic in the sense of shilov or correct in the sense of petrovskij we show that they generate regularized cosine functions with suitable regularizing operators under sharper conditions the results then are applied to matrices of partial differential operators on many function spaces finally the wellposedness of the associated second order systems is discussed

power and area efficient unified computation of vector and elementary functions for handheld 3d graphics systems a unified computation method of vector and elementary functions is proposed for handheld 3d graphics systems it unifies vector operations like vector multiply multiply and add divide divide by square root and dot product and elementary functions like trigonometric inverse trigonometric hyperbolic inverse hyperbolic power xy with two variables and logarithm to an arbitrary base into a single four way arithmetic platform a number system called the fixed point hybrid number system fxp hns which combines the fixed point number system fxp and the logarithmic number system lns is proposed for the power and area efficient unification power and area efficient logarithmic and antilogarithmic conversion schemes are also proposed for the data conversions between fixed point and logarithmic numbers in the fxp hns and achieve 0 41 percent and 0 08 percent maximum conversion errors respectively the unified arithmetic unit based on the proposed schemes is presented with less than 6 3 percent operation error its fully pipelined architecture achieves single cycle throughput with maximum four cycle latency for all of the supported operations comparison results show that the proposed arithmetic unit achieves 30 percent power and 10 9 percent area reductions and runs two times faster than the previous approach

high speed double precision computation of reciprocal division square root and inverse square root a new method for the high speed computation of double precision floating point reciprocal division square root and inverse square root operations is presented in this paper this method employs a second degree minimax polynomial approximation to obtain an accurate initial estimate of the reciprocal and the inverse square root values and then performs a modified goldschmidt iteration the high accuracy of the initial approximation allows us to obtain double precision results by computing a single goldschmidt iteration significantly reducing the latency of the algorithm two unfolded architectures are proposed the first one computing only reciprocal and division operations and the second one also including the computation of square root and inverse square root the execution times and area costs for both architectures are estimated and a comparison with other multiplicative based methods is presented the results of this comparison show the achievement of a lower latency than these methods with similar hardware requirements

complex function approximation using two dimensional interpolation this paper presents a new scheme for evaluating complex reciprocal and exponential functions in hardware the proposed method utilizes a two dimensional convolution algorithm to interpolate bivariate functions from tabulated function values in the complex domain to reduce the memory requirements for lookup tables the interpolation is decomposed into independent row and column computations such that the same coefficient table can be shared three different interpolation kernels from degree 1 linear to degree 2 quadratic lagrange and degree 3 cubic lagrange are explored to find the optimal design parameters and the most acceptable trade offs between performance and hardware resources moreover a generic hardware architecture is designed to provide scalable implementation capabilities for computation precision and interpolation degree to verify the proposed architecture eight complex reciprocal and eight complex exponential design instances are implemented the asic and fpga based experimental results show that the proposed scheme can efficiently approximate the complex reciprocal and exponential functions with up to 16 bit precision as well as achieve a considerable reduction of memory requirements compared with traditional bipartite and multipartite schemes the proposed method is also applicable to other complex functions

stochastic persistence and stationary distribution in a holling tanner type prey predator model abstract in this paper we study a stochastic predator prey model with beddington deangelis type functional response and logistic growth for predators the deterministic model is already well studied and we recall some important results here we construct the stochastic model from the deterministic model by introducing multiplicative noise terms into the growth equations of prey and predator populations for the stochastic model we show that the system admits unique positive global solution starting from the positive initial value then we prove that the system is strongly persistent in mean when the intensity of environmental forcing is less than some threshold magnitudes finally we show that the system has a stationary distribution under certain parametric restrictions numerical simulations are carried out to substantiate the analytical results

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

an algorithmic introduction to numerical simulation of stochastic differential equations a practical and accessible introduction to numerical methods for stochastic differential equations is given the reader is assumed to be familiar with euler s method for deterministic differential equations and to have at least an intuitive feel for the concept of a random variable however no knowledge of advanced probability theory or stochastic processes is assumed the article is built around 10 matlab programs and the topics covered include stochastic integration the euler maruyama method milstein s method strong and weak convergence linear stability and the stochastic chain rule

threshold behavior of a stochastic sis model with levy jumps in this paper the dynamics of a stochastic sis model with levy jumps are investigated we first prove that this model has a unique global positive solution starting from the positive initial value then taking the accumulated jump size into account we find a threshold of the model denoted by r 0 which completely determines the extinction and prevalence of the disease if r 0 1 the disease dies out exponentially with probability one if r 0 1 the solution of the model tends to a point in time average which leads to the stochastical persistence of the disease from the view of epidemiology the existence of threshold is useful in determining treatment strategies and forecasting epidemic dynamics moreover we find that levy noise can suppress disease outbreak finally we introduce some numerical simulations to support the main results obtained

global analysis in a predator prey system with nonmonotonic functional response a predator prey system with nonmonotonic functional response is considered global qualitative and bifurcation analyses are combined to determine the global dynamics of the model the bifurcation a

trichotomous noise induced catastrophic shifts in symbiotic ecosystems an n species lotka volterra stochastic model of a symbiotic ecological system with the verhulst self regulation mechanism is considered the effect of fluctuating environment on the carrying capacity of a population is modeled as the colored three level markovian trichotomous noise in the framework of the mean field theory an explicit self consistency equation for stationary states is presented stability and instability conditions and colored noise induced discontinuous transitions catastrophic shifts in the model are investigated in some cases the mean field exhibits hysteresis as a function of the noise parameters it is shown that the occurrence of catastrophic shifts can be controlled by noise parameters such as correlation time amplitude and flatness the dependence of the critical coupling strengths on the noise parameters is found and illustrated by phase diagrams implications of the results on some modifications of the model are discussed

role of the noise on the transient dynamics of an ecosystem of interacting species abstract we analyze the transient dynamics of an ecosystem described by generalized lotka volterra equations in the presence of a multiplicative noise and a random interaction parameter between the species we consider specifically three cases i two competing species ii three interacting species one predator two preys iii n interacting species the interaction parameter in case i is a stochastic process which obeys a stochastic differential equation we find noise delayed extinction of one of two species which is akin to the noise enhanced stability phenomenon other two noise induced effects found are temporal oscillations and spatial patterns of the two competing species in case ii the noise induces correlated spatial patterns of the predator and of the two preys concentrations finally in case iii we find the asymptotic behavior of the time average of the ith population when the ecosystem is composed of a great number of interacting species

on the dynamics of predator prey models with the beddington deangelis functional response abstract the dynamics of predator prey models with the beddington deangelis functional response are analyzed primarily from the viewpoint of permanence uniform persistence the beddington deangelis functional response is similar to the holling type 2 functional response but contains an extra term describing mutual interference by predators both spatially homogeneous models based on ordinary differential equations and reaction diffusion models are considered criteria for permanence and for predator extinction are derived for systems without diffusion or with no flux boundary conditions criteria are derived for the existence of a globally stable coexistence equilibrium or alternatively for the existence of periodic orbits

hardware implementation trade offs of polynomial approximations and interpolations this paper examines the hardware implementation trade offs when evaluating functions via piecewise polynomial approximations and interpolations for precisions of up to 24 bits in polynomial approximations polynomials are evaluated using stored coefficients polynomial interpolations however require the coefficients to be computed on the fly by using stored function values although it is known that interpolations require less memory than approximations but at the expense of additional computations the trade offs in memory area delay and power consumption between the two approaches have not been examined in detail this work quantitatively analyzes these trade offs for optimized approximations and interpolations across different functions and target precisions hardware architectures for degree 1 and degree 2 approximations and interpolations are described the results show that the extent of memory savings realized by using interpolation is significantly lower than what is commonly believed furthermore experimental results on a field programmable gate array fpga show that for high output precision degree 1 interpolations offer considerable area and power savings over degree 1 approximations but similar savings are not realized when degree 2 interpolations and approximations are compared the availability of both interpolation based and approximation based designs offers a richer set of design trade offs than what is available using either interpolation or approximation alone

high speed function approximation using a minimax quadratic interpolator a table based method for high speed function approximation in single precision floating point format is presented in this paper our focus is the approximation of reciprocal square root square root reciprocal exponentials logarithms trigonometric functions powering with a fixed exponent p or special functions the algorithm presented here combines table look up an enhanced minimax quadratic approximation and an efficient evaluation of the second degree polynomial using a specialized squaring unit redundant arithmetic and multioperand addition the execution times and area costs of an architecture implementing our method are estimated showing the achievement of the fast execution times of linear approximation methods and the reduced area requirements of other second degree interpolation algorithms moreover the use of an enhanced minimax approximation which through an iterative process takes into account the effect of rounding the polynomial coefficients to a finite size allows for a further reduction in the size of the look up tables to be used making our method very suitable for the implementation of an elementary function generator in state of the art dsps or graphics processing units gpus

a unified architecture for the accurate and high throughput implementation of six key elementary functions this paper presents a unified architecture for the compact implementation of several key elementary functions including reciprocal square root and logarithm in single precision floating point arithmetic the proposed high throughput design is based on uniform domain segmentation and curve fitting techniques numerically accurate least squares regression is utilized to calculate the polynomial coefficients the architecture is optimized by analyzing the trade off between the size of the required memory and the precision of intermediate variables to achieve the minimum 23 bit accuracy required for single precision floating point representation the efficiency of the proposed unified data path is demonstrated on a common field programmable gate array

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

algorithm architecture and floating point unit codesign of a matrix factorization accelerator this paper examines the mapping of algorithms encountered when solving dense linear systems and linear least squares problems to a custom linear algebra processor specifically the focus is on cholesky lu with partial pivoting and qr factorizations and their blocked algorithms as part of the study we expose the benefits of redesigning floating point units and their surrounding data paths to support these complicated operations we show how adding moderate complexity to the architecture greatly alleviates complexities in the algorithm we study design tradeoffs and the effectiveness of architectural modifications to demonstrate that we can improve power and performance efficiency to a level that can otherwise only be expected of full custom asic designs a feasibility study of inner kernels is extended to blocked level and shows that at block level the linear algebra core lac can achieve high efficiencies with up to 45 gflops w for both cholesky and lu factorization and over 35 gflops w for qr factorization while maintaining such efficiencies our extensions to the mac units can achieve up to 10 12 and 20 percent speedup for the blocked algorithms of cholesky lu and qr factorization respectively

asymptotic behaviour of the stochastic lotka volterra model this paper examines the asymptotic behaviour of the stochastic extension of a fundamentally important population process namely the lotka volterra model the stochastic version of this process appears to have far more intriguing properties than its deterministic counterpart indeed the fact that a potential deterministic population explosion can be prevented by the presence of even a tiny amount of environmental noise shows the high level of difference which exists between these two representations

hardware designs for exactly rounded elementary functions this paper presents hardware designs that produce exactly rounded results for the functions of reciprocal square root 2 sup x and log sub 2 x these designs use polynomial approximation in which the terms in the approximation are generated in parallel and then summed by using a multi operand adder to reduce the number of terms in the approximation the input interval is partitioned into subintervals of equal size and different coefficients are used for each subinterval the coefficients used in the approximation are initially determined based on the chebyshev series approximation they are then adjusted to obtain exactly rounded results for all inputs hardware designs are presented and delay and area comparisons are made based on the degree of the approximating polynomial and the accuracy of the final result for single precision floating point numbers a design that produces exactly rounded results for all four functions has an estimated delay of 80 ns and a total chip area of 98 mm sup 2 in a 1 0 micron cmos technology allowing the results to have a maximum error of one unit in the last place reduces the computational delay by 5 to 30 and the area requirements by 33 to 77

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

bounded noise induced transitions in a tumor immune system interplay by studying a recent biophysical model of tumor growth in the presence of the immune system here we propose that the phenomenon of evasion of tumors from immune control at a temporal mesoscale might in some cases be due to random fluctuations in the levels of the immune system bounded noises are considered but the gaussian approach is also used for analytical reference after showing that in the case of bounded noises there may be multiple attractors in the space of probability densities we numerically show that the velocity of convergence toward asymptotic density is very slow and that a transitory analysis is needed then by simulations using the sine wiener and the tsallis noises we show that if the level of the noise is sufficiently large then there may be the onset of noise induced transitions in the transitory density evaluated at realistic times namely the transitions are from unimodal density centered at low values of tumor burden to bimodal densities that have a second maximum centered at higher values however those transitions depend on the distribution of the noise

colored noise induced hopf bifurcations in predator prey communities a broad class of n 1 species ratio dependent predator prey stochastic models which consist of one predator population and n prey populations is considered the effect of a fluctuating environment on the carrying capacities of prey populations is taken into account as colored noise in the framework of the mean field theory approximate self consistency equations for prey populations mean density and for predator population density are derived to the first order in the noise variance in some cases the mean field exhibits hopf bifurcations as a function of noise correlation time the corresponding transitions are found to be reentrant e g the periodic orbit appears above a critical value of the noise correlation time but disappears again at a higher value of the noise correlation time the nonmonotonous dependence of the critical control parameter on the noise correlation time is found and the conditions for the occurrence of hopf bifurcations are presented our results provide a possible scenario for environmental fluctuations induced transitions between the oscillatory regime and equilibrium state of population sizes observed in nature

qualitative analysis of a stochastic ratio dependent predator prey system a stochastic ratio dependent predator prey model is investigated in this paper by the comparison theorem of stochastic equations and ito s formula we obtain the global existence of a positive unique solution of the ratio dependent model besides a condition for species to be extinct is given and a persistent condition is established we also conclude that both the prey population and the ratio dependent function are stable in time average in the end numerical simulations are carried out to confirm our findings

periodic solution of a stochastic hbv infection model with logistic hepatocyte growth a stochastic hbv model within logistic hepatocyte growth is developed existence of at least one periodic solution induced by white noise is shown existence of a unique stationary distribution is displayed results are supported numerically in this paper we present a stochastic hepatitis b virus hbv infection model with logistic hepatocyte growth we show that the stochastic differential equation sde hbv model has at least one periodic solution induced by the white noise and a unique stationary distribution which is stable one of the most interesting findings is that random perturbations may be beneficial to format the periodic solution to the sde hbv model

stochastic dynamics of michaelis menten kinetics based tumor immune interactions abstract in this paper we investigate deterministic and stochastic dynamics of michaelis menten kinetics based tumor immune interactions for the deterministic case stability analysis is performed by routh hurwitz criteria chaos is observed in bifurcation analysis and examined by the method of 0 1 test the stochastic system is constructed by incorporating multiplicative white noise terms into the deterministic system we establish a unique positive solution ensuring the positiveness and boundedness of solution from the positive initial condition the sufficient condition is obtained for weak persistence in mean we also derive the parametric restrictions for stochastic permanence and global attractivity in mean finally we validate the extinction of tumor cells with the transition from co existence domain by crossing the estimated threshold values of intensity of environmental noise

stationary distribution and periodic solutions for stochastic holling leslie predator prey systems abstract the stochastic autonomous and periodic predator prey systems with holling and leslie type functional response are investigated for the autonomous system we prove that there exists a unique stationary distribution which is ergodic by constructing a suitable lyapunov function under relatively small white noise the result shows that stationary distribution doesn t rely on the existence and the stability of the positive equilibrium in the undisturbed system furthermore for the corresponding non autonomous system we show that there exists a positive periodic markov process under relatively weaker condition finally numerical simulations illustrate our theoretical results

elementary functions hardware implementation using constrained piecewise polynomial approximations a novel technique for designing piecewise polynomial interpolators for hardware implementation of elementary functions is investigated in this paper in the proposed approach the interval where the function is approximated is subdivided in equal length segments and two adjacent segments are grouped in a segment pair suitable constraints are then imposed between the coefficients of the two interpolating polynomials in each segment pair this allows reducing the total number of stored coefficients it is found that the increase in the approximation error due to constraints between polynomial coefficients can easily be overcome by increasing the fractional bits of the coefficients overall compared with standard unconstrained piecewise polynomial approximation having the same accuracy the proposed method results in a considerable advantage in terms of the size of the lookup table needed to store polynomial coefficients the calculus of the coefficients of constrained polynomials and the optimization of coefficients bit width is also investigated in this paper results for several elementary functions and target precision ranging from 12 to 42 bits are presented the paper also presents vlsi implementation results targeting a 90 nm cmos technology and using both direct and horner architectures for constrained degree 1 degree 2 and degree 3 approximations

stochastic delay lotka volterra model we reveal in this paper that the environmental noise will not only suppress a potential population explosion in the stochastic delay lotka volterra model but will also make the solutions to be stochastically ultimately bounded to reveal these interesting facts we stochastically perturb the delay lotka volterra model x t diag x1 t xn t b ax t into the ito form dx t diag x1 t xn t b ax t dt x t dw t and show that although the solution to the original delay equation may explode to infinity in a finite time with probability one that of the associated stochastic delay equation does not we also show that the solution of the stochastic equation will be stochastically ultimately bounded without any additional condition on the matrix a

iterative algorithm and architecture for exponential logarithm powering and root extraction an algorithm and architecture for powering computation and root extraction with fixed point and floating point exponents is presented in this paper the algorithm is based on an optimized iterative sequence of parallel and or overlapped operations 1 reciprocal 2 high radix digit recurrence logarithm 3 left to right carry free multiplication and 4 high radix online exponential a redundant number system is used to allow for the overlapping of the different operations of the algorithm as the logarithm and exponential are part of the sequence of operations some minor changes are made to allow for the independent computation of the logarithm and exponential functions a sequential implementation of the algorithm is proposed and the execution times and hardware requirements are estimated for single and double precision floating point computations these estimates are obtained for several radices according to an approximate model for the delay and area of the main logic blocks and help to determine the radix values which lead to the most efficient implementations

asymptotic properties of hybrid diffusion systems in response to the increasing needs for control and optimization of hybrid systems this work is concerned with such asymptotic properties as recurrence also known as weak stochastic stability in the literature and ergodicity of regime switching diffusions using liapunov functions necessary and sufficient conditions for positive recurrence are developed then ergodicity of positive recurrent regime switching diffusions is obtained by constructing cycles using the associated discrete time markov chains

permanence and asymptotical behavior of stochastic prey predator system with markovian switching in this paper we investigate the stochastic permanence and extinction of a stochastic ratio dependent prey predator model controlled by a markov chain in the permanent case we estimate the superior limit and the inferior limit of the average in time of the sample path of the solution the boundaries are related to the stationary probability distribution of the markov chain and the parameters of the subsystems finally we illustrate our main results by two examples and some numerical experiments

persistence and global stability in a delayed predator prey system with michaelis menten type functional response a delayed three species predator prey food chain model with michaelis menten type functional response is investigated it is proved that the system is uniformly persistent under some appropriate conditions by means of constructing suitable lyapunov functional sufficient conditions are derived for the global asymptotic stability of the positive equilibrium of the system

approximating elementary functions with symmetric bipartite tables this paper presents a high speed method for function approximation that employs symmetric bipartite tables this method performs two parallel table lookups to obtain a carry save borrow save function approximation which is either converted to a two s complement number or is booth encoded compared to previous methods for bipartite table approximations this method uses less memory by taking advantage of symmetry and leading zeros in one of the two tables it also has a closed form solution for the table entries provides tight bounds on the maximum absolute error and can be applied to a wide range of functions a variation of this method provides accurate initial approximations that are useful in multiplicative divide and square root algorithms

a remark on a stochastic logistic model with levy jumps this note is concerned with a famous stochastic logistic equation with levy noises sufficient and necessary conditions for extinction and permanence are established the results reveal that the levy noise may change the properties of population dynamics significantly the results also reveal an important property of the levy noise it is unfavorable for the permanence of the population some numerical simulations are introduced to validate the analytical results

a comparative study of deterministic and stochastic dynamics for a non autonomous allelopathic phytoplankton model abstract in this paper we investigate a non autonomous competitive phytoplankton model with periodic coefficients in deterministic and stochastic environment respectively we prove the existence of at least one positive periodic solution together with it s global asymptotic stability the existence of periodic solution has been obtained by using the continuation theorem of coincidence degree theory proposed by gaines and mawhin we formulate the corresponding stochastic model by perturbing the growth rate parameters by white noise terms we prove that all the higher order moments of the solution to the stochastic system is uniformly bounded which ensure that the solution of the stochastic system is stochastically bounded we provide easily verifiable sufficient conditions for non persistence in mean extinction and stochastic permanence of the stochastic system sufficient condition for permanence shows that if the noise intensity is very low then the solution of the stochastic system persists in the periodic coexistence domain of the deterministic system we perform exhaustive numerical simulations to validate our analytical findings

stochastic extinction and persistence of a parasite host epidemiological model abstract in this paper we investigate the stochastic extinction and persistence of a parasite host epidemiological model we show that the global dynamics of the stochastic model can be governed by the basic reproduction number r 0 s if r 0 s 1 under mild extra conditions the disease goes to extinction with probability one and the disease free dynamics occurs while r 0 s 1 under mild extra conditions the disease persists and endemic dynamics occurs almost surely the solutions of the stochastic model fluctuate around the steady state of the deterministic model and a unique stationary distribution can be found based on realistic parameters of daphnia microparasite system numerical simulations have been performed to verify extend our analytical results epidemiologically we find that 1 large environment fluctuations can suppress the outbreak of disease 2 the distributions are governed by r 0 s 3 the noise perturbations can be beneficial to control the spread of disease on average

colored noise induced discontinuous transitions in symbiotic ecosystems a symbiotic ecosystem is studied by means of the lotka volterra stochastic model using the generalized verhulst self regulation the effect of fluctuating environment on the carrying capacity of a population is taken into account as dichotomous noise the study is a follow up of our investigation of symbiotic ecosystems subjected to three level trichotomous noise r mankin a ainsaar a haljas and e reiter phys rev e 65 051108 2002 relying on the mean field theory an exact self consistency equation for stationary states is derived in some cases the mean field exhibits hysteresis as a function of noise parameters it is established that random interactions with the environment can cause discontinuous transitions the dependence of the critical coupling strengths on the noise parameters is found and illustrated by phase diagrams predictions from the mean field theory are compared with the results of numerical simulations our results provide a possible scenario for catastrophic shifts of population sizes observed in nature