Pattern formation of a predator–prey model

Liu, Pan-Ping; Jin, Zhen

doi:10.1016/j.nahs.2008.12.004

Cited by 8 publications

(3 citation statements)

References 12 publications

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“…Recall the nonlinear discrete-time dynamical system described by (1) and (2). Assume that the last filtered state estimate O…”

Section: The Dynamics Of the First Phase Of The Modified Ekf With Uncmentioning

confidence: 99%

“…Most of the systems around us whether natural or man‐made are inherently nonlinear and are represented by nonlinear mathematical models. Examples of such models can be seen in biological systems , ecosystems , chemical and biochemical processes , nanotechnology , satellite dynamics , power systems , and so on. To devise suitable controllers for such systems that achieve realistic performances, a number of challenges must be taken into consideration.…”

Section: Introductionmentioning

confidence: 99%

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Observer-based controller for constrained uncertain stochastic nonlinear discrete-time systems

Hassan

Alrifai

Soliman

et al. 2015

Int. J. Robust. Nonlinear Control

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Summary In this paper, an observer‐based control approach is proposed for uncertain stochastic nonlinear discrete‐time systems with input constraints. The widely used extended Kalman filter (EKF) is well known to be inadequate for estimating the states of uncertain nonlinear dynamical systems with strong nonlinearities especially if the time horizon of the estimation process is relatively long. Instead, a modified version of the EKF with improved stability and robustness is proposed for estimating the states of such systems. A constrained observer‐based controller is then developed using the state‐dependent Riccati equation approach. Rigorous analysis of the stability of the developed stochastically controlled system is presented. The developed approach is applied to control the performance of a synchronous generator connected to an infinite bus and chaos in permanent magnet synchronous motor. Simulation results of the synchronous generator show that the estimated states resulting from the proposed estimator are stable, whereas those resulting from the EKF diverge. Moreover, satisfactory performance is achieved by applying the developed observer‐based control strategy on the two practical problems. Copyright © 2015 John Wiley & Sons, Ltd.

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“…Recall the nonlinear discrete-time dynamical system described by (1) and (2). Assume that the last filtered state estimate O…”

Section: The Dynamics Of the First Phase Of The Modified Ekf With Uncmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Observer-based controller for constrained uncertain stochastic nonlinear discrete-time systems

Hassan

Alrifai

Soliman

et al. 2015

Int. J. Robust. Nonlinear Control

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show abstract

“…Earlier Fan and Li [9] studied the global asymptotic stability of the unique positive constant equilibrium solution for the same type of ratiodependent prey-predator system with diffusion term. Recently Liu and Jin [13] analyze spatial pattern formation of a ratio-dependent predator-prey system with self diffusion. To the author's knowledge, the cross diffusion pattern generated by a ratio-dependent prey-predator model has not yet been reported by any researcher till date.…”

Section: Introductionmentioning

confidence: 99%

Pattern Formation for a Ratio-Dependent Predator-Prey Model With Cross Diffusion

Sambath¹,

Balachandran²

2012

Journal of the Korea Society for Industrial and Applied Mathema

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In this work, we analyze the spatial patterns of a predator-prey system with cross diffusion. First we get the critical lines of Hopf and Turing bifurcations in a spatial domain by using mathematical theory. More specifically, the exact Turing region is given in a two parameter space. Our results reveal that cross diffusion can induce stationary patterns which may be useful in understanding the dynamics of the real ecosystems better.

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Spatiotemporal dynamics of a predator–prey model

Liu

Xue

2011

Nonlinear Dyn

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Pattern formation of a predator–prey model

Cited by 8 publications

References 12 publications

Observer-based controller for constrained uncertain stochastic nonlinear discrete-time systems

Observer-based controller for constrained uncertain stochastic nonlinear discrete-time systems

Pattern Formation for a Ratio-Dependent Predator-Prey Model With Cross Diffusion

Spatiotemporal dynamics of a predator–prey model

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