In this paper we study a new way to model noisy input flows in the chemostat model, based on Ornstein-Uhlenbeck process. We introduce parameter β as drift Langevin equation, that allows bridge gap between pure Wiener process, which is common random disturbances, and no noise at all. The value of related amplitude deviations observed realizations. show modeling approach well suited represent an variable has take non-negative values for almost any time.

In this paper we study two stochastic chemostat models, with and without wall growth, driven by a white noise. Specifically, analyze the existence uniqueness of solutions for these as well random attractor associated to dynamical system generated solution. The analysis will be carried out means well-known Ornstein-Uhlenbeck process, that allows us transform our models into ones.

We revisit the chemostat model with Haldane growth function, here subject to bounded random disturbances on input flow rate, as often met in biotechnological or waste-water industry. prove existence and uniqueness of global positive solution dynamics absorbing attracting sets that are independent realizations noise. study long-time behavior terms sets, provide first conditions under which biomass extinction cannot be avoided. for weak strong persistence microbial species lower bounds...

In this paper we analyze a chemostat model with wall growth where the input flow is affected by two different stochastic processes: well-known standard Wiener process, which leads into several drawbacks from biological point of view, and suitable Orsntein-Uhlenbeck process depending on some parameters allow us to control noise be bounded inside interval that can fixed previously practitioners. Thanks last approach, has already proved very realistic when modeling other simplest models, it...

<abstract> This paper investigates a chemostat model with wall growth and Haldane consumption kinetics. In addition, bounded random fluctuations on the input flow, which are modeled by means of well-known Ornstein-Uhlenbeck process, considered to obtain much more realistic fitting in better way phenomena observed practitioners real devices. Once existence uniqueness global positive solution has been proved, as well deterministic absorbing attracting sets, dynamics inside set is studied...

The chemostat model is used in many situations to represent biological systems which micro-organisms grow on abiotic resources. Nevertheless, most of the times, deterministic versions this are analyzed spite random fluctuations that frequently appear real life ecosystems. We and analyze input flow model, bounded inside a given interval could be provided by practitioners. use Ornstein-Uhlenbeck process has already proved suitable tool when modeling systems. In present work, we consider with...

This paper investigates the dynamics of a model two chemostats connected by Fickian diffusion with bounded random fluctuations. We prove existence and uniqueness non-negative global solution as well compact absorbing attracting sets for solutions corresponding system. After that, we study internal structure set to obtain more detailed information about long-time behavior state variables. In such way, provide conditions under which extinction species cannot be avoided ensure persistence...

In this paper, we study the asymptotic dynamics of two chemostat models with random environmental fluctuations modeled by means real noise, where different consumption functions for consumer species (Monod and Haldane) are taking into account. For each model, our main goal is to investigate existence deterministic attracting sets. This allows us provide conditions under which become extinct or persist, in industrial setup. addition, depict numerical simulations support theoretical results....

<abstract> In this paper we study some chemostat models with random bounded fluctuations on the input flow. We start classical system and obtain new incorporating, for instance, wall growth different consumption functions, motivated by phenomena in real devices. every case, prove existence uniqueness of positive global solution, deterministic absorbing attracting sets investigate internal structure to detailed information about long-time dynamics systems. This allows us provide conditions...

We investigate SIR models with vital dynamics, reinfection, and randomness at the transmission coefficient recruitment rate. Initially, we conduct an extensive analysis of autonomous scenario, covering aspects such as local global well-posedness, existence internal structure attractors, presence gradient dynamics. Subsequently, explore implications small nonautonomous random perturbations, establishing continuity attractors ensuring their topological structural stability. Additionally, study...

In this paper we correct an error made in a previous work, where misleading stochastic system was obtained due to lapse concerning sign one of the equations at beginning work such that results are quite different ones developed throughout since required conditions, and also results, substantially change. Then, repair analysis carried out there, studied simple chemostat model influenced by white noise making use theory random attractors. Even though changes minor, have chosen provide new...

In this work we consider two classical mathematical models of wine fermentation. The first model describes the wine-making process that is used to produce dry wine. second obtained by introducing a term in equation dynamics yeast. Thanks change it will be possible inhibit fermentation sugar and as consequence sweet obtained. We prove existence, uniqueness, positiveness boundedness solutions for both models. Then pass analyse long-time dynamics. For also provide estimates concentration...

In this paper, we investigate four non-autonomous chemostat models with non-monotonic consumption function, where wall growth and nutrient recycling are also taken into account. each case, prove the existence uniqueness of non-negative global solution that generates a dynamical system. addition, unique (global) pullback attractor whose internal structure provides detailed information about long-time behaviour state variables, for instance, conditions to ensure extinction persistence species....