共查询到20条相似文献,搜索用时 0 毫秒
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Haojie GuoSining Zheng 《Applied mathematics and computation》2011,217(16):6934-6949
This paper studies a un-stirred chemostat with two species competing for two growth-limiting, non-reproducing resources. We determine the conditions for positive steady states of the two species, and then consider the global attractors of the model. In addition, we obtain the conditions under which the two populations uniformly strongly persist or go to extinction. Since the diffusion mechanism with homogeneous boundary conditions inhibits the growth of the organism species, it can be understood that the coexistence will be ensured by proportionally smaller diffusions for the two species. In particular, it is found that both instability and bi-stability subcases of the two semitrivial steady states are included in the coexistence region. The two populations will go to extinction when both possess large diffusion rates. If just one of them spreads faster with the other one diffusing slower, then the related semitrivial steady state will be globally attracting. The techniques used for the above results consist of the degree theory, the semigroup theory, and the maximum principle. 相似文献
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Shaohong Cai 《Applied mathematics and computation》2010,217(6):2320-2326
In this paper, a Monod type chemostat model with delayed response in growth and impulsive input the polluted nutrient is considered. Using the discrete dynamical system determined by the stroboscopic map, we obtain a microorganism-extinction periodic solution. Further, it is globally attractive. The permanent condition of the investigated system is also obtained by the theory of impulsive delay differential equation. Our results reveal that the delayed response in growth plays an important role on the outcome of the chemostat. 相似文献
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Patrick De Leenheer David Angeli 《Journal of Mathematical Analysis and Applications》2006,319(1):48-60
This paper deals with an almost-global stability result for a particular chemostat model. It deviates from the classical chemostat because crowding effects are taken into consideration. This model can be rewritten as a negative feedback interconnection of two systems which are monotone (as input/output systems). Moreover, these subsystems behave nicely when subject to constant inputs. This allows the use of a particular small-gain theorem which has recently been developed for feedback interconnections of monotone systems. Application of this theorem requires—at least approximate—knowledge of two gain functions associated to the subsystems. It turns out that for the chemostat model proposed here, these approximations can be obtained explicitly and this leads to a sufficient condition for almost-global stability. In addition, we show that coexistence occurs in this model if the crowding effects are large enough. 相似文献
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Hua Nie 《Journal of Mathematical Analysis and Applications》2009,355(1):231-242
This paper deals with a competition model between two species for two growth-limiting and perfectly complementary resources in the unstirred chemostat. The main purpose is to determine the exact range of the parameters of two species so that the system possesses positive solutions, and to investigate multiple positive steady states of the system. The main tools used here include the monotone methods and the topological fixed point theory developed by Amann. 相似文献
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Dynamics of a stochastic chemostat competition model with plasmid-bearing and plasmid-free organisms 下载免费PDF全文
Miaomiao Gao Daqing Jiang Tasawar Hayat Ahmed Alsaedi Bashir Ahmad 《Journal of Applied Analysis & Computation》2020,10(4):1464-1481
In this paper, we consider a chemostat model of competition between plasmid-bearing and plasmid-free organisms, perturbed by white noise. Firstly, we prove the existence and uniqueness of the global positive solution. Then by constructing suitable Lyapunov functions, we establish sufficient conditions for the existence of a unique ergodic stationary distribution. Furthermore, conditions for extinction of plasmid-bearing organisms are obtained. Theoretical analysis indicates that large noise intensity $\sigma_{2}^{2}$ is detrimental to the survival of plasmid-bearing organisms and is not conducive to the commercial production of genetically altered organisms. Finally, numerical simulations are presented to illustrate the results. 相似文献
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Xiao-yu Xing Xue-qiang Wang 《应用数学学报(英文版)》2008,24(1):75-84
Consider a storage model fed by a Markov modulated Brownian motion. We prove that the stationary distribution of the model exits and that the running maximum of the storage process over the interval [0, t] grows asymptotically like log t as t→∞. 相似文献
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We investigate how the stationary distribution of a Markov chain changes when transitions from a single state are modified. In particular, adding a single directed edge to nearest neighbor random walk on a finite discrete torus in dimensions one, two, or three changes the stationary distribution linearly, logarithmically, or only locally. Related results are derived for birth and death chains approximating Bessel diffusions and for random walk on the Sierpinski gasket. 相似文献
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Miaomiao Gao Daqing Jiang Tasawar Hayat Ahmed Alsaedi 《Mathematical Methods in the Applied Sciences》2021,44(1):1013-1028
In this paper, we study the dynamical behavior of a stochastic food chain chemostat model, in which the white noise is proportional to the variables. Firstly, we prove the existence and uniqueness of the global positive solution. Then by constructing suitable Lyapunov functions, we show the system has a unique ergodic stationary distribution. Furthermore, the extinction of microorganisms is discussed in two cases. In one case, both the prey and the predator species are extinct, and in the other case, the prey species is surviving and the predator species is extinct. Finally, numerical experiments are performed for supporting the theoretical results. 相似文献
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We propose a model of competition of n species in a chemostat, with constant input of some species. We mainly emphasize the case that can lead to coexistence in the chemostat in a non-trivial way, i.e., where the n−1 less competitive species are in the input. We prove that if the inputs satisfy a constraint, the coexistence between the species is obtained in the form of a globally asymptotically stable (GAS) positive equilibrium, while a GAS equilibrium without the dominant species is achieved if the constraint is not satisfied. This work is round up with a thorough study of all the situations that can arise when having an arbitrary number of species in the chemostat inputs; this always results in a GAS equilibrium that either does or does not encompass one of the species that is not present in the input. 相似文献
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V.V. Anisimov 《Annals of Operations Research》2002,112(1-4):63-82
An approximation of Markov type queueing models with fast Markov switches by Markov models with averaged transition rates is studied. First, an averaging principle for two-component Markov process (x
n
(t),
n
(t)) is proved in the following form: if a component x
n
() has fast switches, then under some asymptotic mixing conditions the component
n
() weakly converges in Skorokhod space to a Markov process with transition rates averaged by some stationary measures constructed by x
n
(). The convergence of a stationary distribution of (x
n
(),
n
()) is studied as well. The approximation of state-dependent queueing systems of the type M
M,Q
/M
M,Q
/m/N with fast Markov switches is considered. 相似文献
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Dynamical behavior of a stochastic food chain chemostat model with Monod response functions 下载免费PDF全文
Miaomao Gao Daqing Jiang Kai Qi Tasawar Hayat Ahmed Alsaedi Bashir Ahmad 《Journal of Applied Analysis & Computation》2019,9(6):2278-2294
This paper studies a food chain chemostat model with Monod response functions, which is perturbed by white noise. Firstly, we prove the existence and uniqueness of the global positive solution. Then sufficient conditions for the existence of a unique ergodic stationary distribution are established by constructing suitable Lyapunov functions. Moreover, we consider the extinction of microbes in two cases. In the first case, both the predator and prey species are extinct. In the second case, only the predator species is extinct, and the prey species survives. Finally, numerical simulations are carried out to illustrate the theoretical results. 相似文献
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In this paper, the competitor-competitor-mutualist three-species Lotka-Volterra model is discussed. Firstly, by Schauder fixed point theory, the coexistence state of the strongly coupled system is given. Applying the method of upper and lower solutions and its associated monotone iterations, the true solutions are constructed. Our results show that this system possesses at least one coexistence state if cross-diffusions and cross-reactions are weak. Secondly, the existence and asymptotic behavior of T-periodic solutions for the periodic reaction-diffusion system under homogeneous Dirichlet boundary conditions are investigated. Sufficient conditions which guarantee the existence of T-periodic solution are also obtained. 相似文献
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Moshe Haviv 《Stochastic Processes and their Applications》1985,19(1):151-160
In this paper we suggest a new successive approximation method to compute the optimal discounted reward for finite state and action, discrete time, discounted Markov decision chains. The method is based on a block partitioning of the (stochastic) matrices corresponding to the stationary policies. The method is particularly attractive when the transition matrices are jointly nearly decomposable or nearly completely decomposable. 相似文献
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Joseph A Yahav 《Stochastic Processes and their Applications》1976,4(1):41-54
A discrete-time Markov process on [0, ∞) is considered. The process is generated by selecting at each time, in an independent and stationary way, a concave non-decreasing function. Sufficient conditions for the existence of a unique stationary limiting distribution are given. 相似文献
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《Mathematical and Computer Modelling》2007,45(3-4):371-377
In this paper, the cooperative two-species Lotka–Volterra model is discussed. We study the existence of solutions to a elliptic system with homogeneous Dirichlet boundary conditions. Our results show that this problem possesses at least one coexistence state if the birth rates are big and self-diffusions and the intra-specific competitions are strong. 相似文献
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Hua Nie 《Journal of Mathematical Analysis and Applications》2007,334(2):889-908
This paper deals with a chemostat model with an internal inhibitor. First, the elementary stability and asymptotic behavior of solutions of the system are determined. Second, the effects of the inhibitor are considered. It turns out that the parameter μ, which measures the effect of the inhibitor, plays a very important role in deciding the stability and longtime behavior of solutions of the system. The results show that if μ is sufficiently large, this model has no coexistence solution and one of the semitrivial equilibria is a global attractor when the maximal growth rate a of the species u lies in certain range; but when a belongs to another range, all positive solutions of this model are governed by a limit problem, and two semitrivial equilibria are bistable. The main tools used here include monotone system theory, degree theory, bifurcation theory and perturbation technique. 相似文献
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This paper presents two main results: first, a Liapunov type criterion for the existence of a stationary probability distribution for a jump Markov process; second, a Liapunov type criterion for existence and tightness of stationary probability distributions for a sequence of jump Markov processes. If the corresponding semigroups TN(t) converge, under suitable hypotheses on the limit semigroup, this last result yields the weak convergence of the sequence of stationary processes (TN(t), πN) to the stationary limit one. 相似文献