The effects of delayed growth response on the dynamic behaviors of the Monod type chemostat model with impulsive input nutrient concentration

Meng, Xinzhu; Gao, Qian; Li, Zhenqing

doi:10.1016/j.nonrwa.2010.05.030

Cited by 24 publications

(13 citation statements)

References 25 publications

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“…Considering the inevitability of time delay in many practical projects [50][51][52][53][54][55][56][57] and motivated by the above discussions, the state estimation problem for complex-valued memristive neural networks with time-varying delays is investigated in this paper. The contribution of this paper is mainly embodied in the following respects: (1) The state estimation of complex-valued memristive neural networks with time-varying delays is studied for the first time.…”

Section: Introductionmentioning

confidence: 99%

State estimation for complex-valued memristive neural networks with time-varying delays

2018

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This paper focuses on the state estimation problem for complex-valued memristive neural networks with time-varying delays. By utilizing Lyapunov stability theory and some matrix inequality techniques, based on a novel Lyapunov functional, a sufficient delay-dependent condition which guarantees that the error-state system is global asymptotically stable is firstly derived for the addressed system, and a suitable state estimator is also designed. Finally, an example is given to illustrate the present method.

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Section: Introductionmentioning

confidence: 99%

State estimation for complex-valued memristive neural networks with time-varying delays

2018

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“…d) Other approaches: as crowding effects [7], flocculation [12], multi-substrate feeding [11], [23], impulsive input of substrate concentration [28], [29], [44], intraspecific competition [24].…”

Section: Introductionmentioning

confidence: 99%

Global stability for a model of competition in the chemostat with microbial inputs

Robledo¹,

Grognard²,

Gouzé³

2012

Nonlinear Analysis: Real World Applications

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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

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“…Due to the fact that the interaction of the populations in the ecosystem is very complex and lacks strict control, it is not possible to directly investigate the interrelationships among the various groups. The chemostat is a laboratory apparatus used for the continuous culture of microorganism, and it plays an important role in exploring the growth of microorganism in a deterministic environment [1][2][3][4][5][6][7][8][9]. By controlling the input and output rate of the chemostat, we can investigate the interaction between microorganisms and the dynamic behavior of microbial growth in nutrition conditions.…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis of multi-nutrient and single microorganism chemostat model in a polluted environment

Chi

Zhao

2018

Adv Differ Equ

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In this paper, we propose a multi-nutrient and single microorganism chemostat model with stochastic effect and impulsive toxicant input. Firstly, for the system neglecting stochastic effect, we investigate the global dynamics including the existence and global asymptotic stability of 'microorganism-extinction' periodic solution, as well as the permanence of the system. Then, for the stochastic differential system with impulsive effect, we discuss the persistence and extinction of microorganisms with stochastic effect in a polluted environment. Our results indicate that the stochastic disturbance can lead to microbial extinction. Moreover, the concentration of toxicant will also affect the survival of microorganisms. Finally, numerical simulations are carried out to illustrate our theoretical results. MSC: 60H10; 65C30; 91B70

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The effects of delayed growth response on the dynamic behaviors of the Monod type chemostat model with impulsive input nutrient concentration

Cited by 24 publications

References 25 publications

State estimation for complex-valued memristive neural networks with time-varying delays

State estimation for complex-valued memristive neural networks with time-varying delays

Global stability for a model of competition in the chemostat with microbial inputs

Dynamical analysis of multi-nutrient and single microorganism chemostat model in a polluted environment

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