Now showing items 1-9 of 9

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      A survey on Navier-Stokes models with delays: Existence, uniqueness and asymptotic behavior of solutions  [Article]

      Caraballo Garrido, Tomás; Xiaoying, Han (2015)
      In this survey paper we review several aspects related to Navier-Stokes models when some hereditary characteristics (constant, distributed or variable delay, memory, etc) appear in the formulation. First some results ...
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      Chemostats with random inputs and wall growth  [Article]

      Caraballo Garrido, Tomás; Xiaoying, Han; Kloeden, Peter E. (John Wiley & Sons, 2015-03-12)
      Chemostat refers to a laboratory device used for growing microorganisms in a cultured environment, and has been regarded as an idealization of nature to study competition modeling of mathematical biology. The simple form ...
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      Chemostats with time-dependent inputs and wall growth  [Article]

      Caraballo Garrido, Tomás; Xiaoying, Han; Kloeden, Peter E. (Natural Sciences Publishing Corporation, 2015)
      Traditional assumptions in the simple chemostat model include fixed availability of the nutrient and its supply rate, and fast flow rate to avoid wall growth. However, these assumptions become unrealistic when the availability ...
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      Dynamics of nonautonomous chemostat models  [Article]

      Caraballo Garrido, Tomás; Xiaoying, Han; Kloeden, Peter E.; Rapaport, Alain (2015)
      Chemostat models have a long history in the biological sciences as well as in biomathematics. Hitherto most investigations have focused on autonomous systems, that is, with constant parameters, inputs and outputs. In many ...
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      Nonautonomous chemostats with variable delays  [Article]

      Caraballo Garrido, Tomás; Xiaoying, Han; Kloeden, Peter E. (Society for Industrial and Applied Mathematics, 2015)
      The appearance of delay terms in a chemostat model can be fully justified since the future behavior of a dynamical system does not in general depend only on the present but also on its history. Sometimes only a short piece ...
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      On the stability of impulsive functional differential equations with infinite delays  [Article]

      Caraballo Garrido, Tomás; Xiaodi, Li; Rakkiyappan, R.; Xiaoying, Han (2015)
      In this paper, the stability problem of impulsive functional differential equations with infinite delays is considered. By using Lyapunov functions and the Razumikhin technique, some new theorems on the uniform stability ...
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      Predation with indirect effects in fluctuating environments  [Article]

      Caraballo Garrido, Tomás; Colucci, Renato; Xiaoying, Han (Springer, 2015-06-30)
      We investigate the long term dynamics for a predation model of Plankton community with indirect effects, under fluctuating environments. A random version and a stochastic version with multiplicative noise of the model ...
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      Random attractors for stochastic lattice dynamical systems with infinite multiplicative white noise  [Article]

      Caraballo Garrido, Tomás; Xiaoying, Han; Schmalfuss, Björn; Valero Cuadra, José (2016)
      In this paper we investigate the long term behavior of a stochastic lattice dynamical system with a diffusive nearest neighbor interaction, a dissipative nonlinear reaction term, and a different multiplicative white noise ...
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      Stability of stationary solutions to 2D-Navier-Stokes models with delays  [Article]

      Caraballo Garrido, Tomás; Xiaoying, Han (International Press, 2014)
      In this paper we establish some sufficient conditions for the exponential stability of the stationary solution to a two-dimensional Navier-Stokes model with delay in the forcing term. We are able to cover several situation ...