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Lansun Chen - One of the best experts on this subject based on the ideXlab platform.
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A single stage-structured Population Model with mature individuals in a polluted environment and pulse input of environmental toxin
Nonlinear Analysis: Real World Applications, 2009Co-Authors: Jianjun Jiao, Wen Long, Lansun ChenAbstract:In this paper, we concentrates on the study of a single stage-structured Population Model with mature individuals in a polluted environment and pulse input of environmental toxin. A globally attractive condition for the Population-extinction boundary periodic solution of the investigated system is obtained. Sufficient criteria on the permanence of the Population are derived.
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the extinction threshold on a single Population Model with pulse input of environmental toxin in a polluted environment
Mathematica Applicata, 2009Co-Authors: Jianjun Jiao, Lansun ChenAbstract:We investigate a single Population Model with pulse input of environmental toxin in a polluted environment. By using Floquet theorem and small amplitude perturbation skills, we show that there exists a globally asymptotically stable Population-extinction periodic solution when the period of impulsive effect is less than some critical value. The condition for the Population s permanence is also given. From the biological point of view, it is easy to protect species by changing impulsive period of the exogenous input of toxicant input amount, etc. Our results provide tactic base for biological source management in a polluted environment.
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Harvesting on a stage-structured single Population Model with mature individuals in a polluted environment and pulse input of environmental toxin.
Biosystems, 2009Co-Authors: Jianjun Jiao, Xiao-song Yang, Lansun ChenAbstract:In the natural world, there are many species whose individual members have a life history that they take them with two distinct stages: immaturity and maturity. In particular, we have in mind mammalian Populations and some amphibious animals. We improve the assumption of a single Population as a whole. It is assumed that the immature individuals and mature individuals are divided by a fixed period. This paper concentrates on the study of a stage-structured single Population Model with mature individuals in a polluted environment and pulse input of environmental toxin at fixed moments. Furthermore, the mature individuals are harvested continuously. We show that the Population goes extinct if the harvesting rate is beyond a critical threshold. Conditions for the extended permanence of the Population are also examined. From the biological point of view, it is easy to protect species by controlling the harvesting amount, impulsive period of the exogenous input of toxin and toxin impulsive input amount, etc. Our results provide reasonable tactics for biological resource management.
Jianjun Jiao - One of the best experts on this subject based on the ideXlab platform.
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A single stage-structured Population Model with mature individuals in a polluted environment and pulse input of environmental toxin
Nonlinear Analysis: Real World Applications, 2009Co-Authors: Jianjun Jiao, Wen Long, Lansun ChenAbstract:In this paper, we concentrates on the study of a single stage-structured Population Model with mature individuals in a polluted environment and pulse input of environmental toxin. A globally attractive condition for the Population-extinction boundary periodic solution of the investigated system is obtained. Sufficient criteria on the permanence of the Population are derived.
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the extinction threshold on a single Population Model with pulse input of environmental toxin in a polluted environment
Mathematica Applicata, 2009Co-Authors: Jianjun Jiao, Lansun ChenAbstract:We investigate a single Population Model with pulse input of environmental toxin in a polluted environment. By using Floquet theorem and small amplitude perturbation skills, we show that there exists a globally asymptotically stable Population-extinction periodic solution when the period of impulsive effect is less than some critical value. The condition for the Population s permanence is also given. From the biological point of view, it is easy to protect species by changing impulsive period of the exogenous input of toxicant input amount, etc. Our results provide tactic base for biological source management in a polluted environment.
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Harvesting on a stage-structured single Population Model with mature individuals in a polluted environment and pulse input of environmental toxin.
Biosystems, 2009Co-Authors: Jianjun Jiao, Xiao-song Yang, Lansun ChenAbstract:In the natural world, there are many species whose individual members have a life history that they take them with two distinct stages: immaturity and maturity. In particular, we have in mind mammalian Populations and some amphibious animals. We improve the assumption of a single Population as a whole. It is assumed that the immature individuals and mature individuals are divided by a fixed period. This paper concentrates on the study of a stage-structured single Population Model with mature individuals in a polluted environment and pulse input of environmental toxin at fixed moments. Furthermore, the mature individuals are harvested continuously. We show that the Population goes extinct if the harvesting rate is beyond a critical threshold. Conditions for the extended permanence of the Population are also examined. From the biological point of view, it is easy to protect species by controlling the harvesting amount, impulsive period of the exogenous input of toxin and toxin impulsive input amount, etc. Our results provide reasonable tactics for biological resource management.
Jian-feng Yao - One of the best experts on this subject based on the ideXlab platform.
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on sample eigenvalues in a generalized spiked Population Model
Journal of Multivariate Analysis, 2012Co-Authors: Zhidong Bai, Jian-feng YaoAbstract:In the spiked Population Model introduced by Johnstone (2001) [11], the Population covariance matrix has all its eigenvalues equal to unit except for a few fixed eigenvalues (spikes). The question is to quantify the effect of the perturbation caused by the spike eigenvalues. Baik and Silverstein (2006) [5] establishes the almost sure limits of the extreme sample eigenvalues associated to the spike eigenvalues when the Population and the sample sizes become large. In a recent work Bai and Yao (2008) [4], we have provided the limiting distributions for these extreme sample eigenvalues. In this paper, we extend this theory to a generalized spiked Population Model where the base Population covariance matrix is arbitrary, instead of the identity matrix as in Johnstone's case. As the limiting spectral distribution is arbitrary here, new mathematical tools, different from those in Baik and Silverstein (2006) [5], are introduced for establishing the almost sure convergence of the sample eigenvalues generated by the spikes.
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On determining the number of spikes in a high-dimensional spiked Population Model
Random Matrices. Theory and Applications, 2012Co-Authors: Damien Passemier, Jian-feng YaoAbstract:In a spiked Population Model, the Population covariance matrix has all its eigenvalues equal to units except for a few fixed eigenvalues (spikes). Determining the number of spikes is a fundamental problem which appears in many scientific fields, including signal processing (linear mixture Model) or economics (factor Model). Several recent papers studied the asymptotic behavior of the eigenvalues of the sample covariance matrix (sample eigenvalues) when the dimension of the observations and the sample size both grow to infinity so that their ratio converges to a positive constant. Using these results, we propose a new estimator based on the difference between two consecutive sample eigenvalues.
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Limit theorems for sample eigenvalues in a generalized spiked Population Model
2008Co-Authors: Zhidong Bai, Jian-feng YaoAbstract:In the spiked Population Model introduced by Johnstone (2001),the Population covariance matrix has all its eigenvalues equal to unit except for a few fixed eigenvalues (spikes). The question is to quantify the effect of the perturbation caused by the spike eigenvalues. Baik and Silverstein (2006) establishes the almost sure limits of the extreme sample eigenvalues associated to the spike eigenvalues when the Population and the sample sizes become large. In a recent work (Bai and Yao, 2008), we have provided the limiting distributions for these extreme sample eigenvalues. In this paper, we extend this theory to a {\em generalized} spiked Population Model where the base Population covariance matrix is arbitrary, instead of the identity matrix as in Johnstone's case. New mathematical tools are introduced for establishing the almost sure convergence of the sample eigenvalues generated by the spikes.
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Central limit theorems for eigenvalues in a spiked Population Model
Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2008Co-Authors: Zhidong Bai, Jian-feng YaoAbstract:In a spiked Population Model, the Population covariance matrix has all its eigenvalues equal to unit except for a few fixed eigenvalues (spikes). This Model is proposed by Johnstone to cope with empirical findings on various data sets. The question is to quantify the effect of the perturbation caused by the spike eigenvalues. A recent work by Baik and Silverstein establishes the almost sure limits of the extreme sample eigenvalues associated to the spike eigenvalues when the Population and the sample sizes become large. This paper establishes the limiting distributions of these extreme sample eigenvalues. As another important result of the paper, we provide a central limit theorem on random sesquilinear forms.
Wen Long - One of the best experts on this subject based on the ideXlab platform.
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A single stage-structured Population Model with mature individuals in a polluted environment and pulse input of environmental toxin
Nonlinear Analysis: Real World Applications, 2009Co-Authors: Jianjun Jiao, Wen Long, Lansun ChenAbstract:In this paper, we concentrates on the study of a single stage-structured Population Model with mature individuals in a polluted environment and pulse input of environmental toxin. A globally attractive condition for the Population-extinction boundary periodic solution of the investigated system is obtained. Sufficient criteria on the permanence of the Population are derived.
W. Robertson - One of the best experts on this subject based on the ideXlab platform.
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The seasonal dynamics of Calanus finmarchicus: development of a three-dimensional structured Population Model and application to the northern North Sea
Journal of Sea Research, 1997Co-Authors: A.d. Bryant, M. Heath, W.s.g. Gurney, D.j. Beare, W. RobertsonAbstract:A weight-structured Population Model is described for Calanus finmarchicus. Results are presented for an area of the northern North Sea for which detailed stage succession data exist, and are discussed in the context of other Models of zooplankton Population dynamics for that area. The essential simplicity of the Model enables embedding in a three-dimensional hydrodynamic scheme representing the northern North Sea (1° × 1° boxes, split into upper 30 m and below). Results of this spatially-resolved Model are discussed in the context of a new statistical analysis of C. finmarchicus late-copepodites from the continuous plankton recorder