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Rocky Mountain Journal of Mathematics
VOL. 38 · NO. 5 | 2008
 
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Front Matter
Table of Contents, Rocky Mountain Journal of Mathematics, vol. 38, no. 5, (2008)
Rocky Mountain J. Math. 38 (5), (2008) Open Access
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Preface toProceedings of the4th International Conference on Mathematical Biology
L. Chen, M. Fan, Y. Kuang, H. Zhu
Rocky Mountain J. Math. 38 (5), 1303-1305, (2008) DOI: 10.1216/RMJ-2008-38-5-1303 Open Access
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Articles
Four Periodic Solutions of a Generalized Delayed Predator-Prey System on Time Scales
Xiaoxing Chen, Haijun Guo
Rocky Mountain J. Math. 38 (5), 1307-1322, (2008) DOI: 10.1216/RMJ-2008-38-5-1307 Open Access
KEYWORDS: Time scales, four positive periodic solutions, Delay, predator-prey system, Coincidence degree, 34K15, 34C25, 34K20, 92D25
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An SIS Infection Model Incorporating Media Coverage
Jing-An Cui, Xin Tao, Huaiping Zhu
Rocky Mountain J. Math. 38 (5), 1323-1334, (2008) DOI: 10.1216/RMJ-2008-38-5-1323 Open Access
KEYWORDS: SIS infection model, media coverage, Basic reproduction number, global stability, 54B20, 54F15
No abstract available
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Global Behavior of a Reaction-Diffusion Volterra Equation With Variable Coefficients
Yong-Hong Fan, Lin-Lin Wang
Rocky Mountain J. Math. 38 (5), 1335-1354, (2008) DOI: 10.1216/RMJ-2008-38-5-1335 Open Access
KEYWORDS: Reaction-diffusion Volterra equation, sub- and supersolutions, Lyapunov functional method, global stability
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Permanence for Nonautonomous $N$-Species Lotka-Volterra Competitive Systems with Feedback Controls
Xiaomei Feng, Zhidong Teng, Long Zhang
Rocky Mountain J. Math. 38 (5), 1355-1376, (2008) DOI: 10.1216/RMJ-2008-38-5-1355 Open Access
KEYWORDS: permanence, competition, nonautonomous LotkaVolterra system, feedback control, 34D25, 92D25
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Stability Analysis of the Nonlinear Impulsive System in Microbial Fed-Batch Fermentation
Caixia Gao, Enmin Feng
Rocky Mountain J. Math. 38 (5), 1377-1384, (2008) DOI: 10.1216/RMJ-2008-38-5-1377 Open Access
KEYWORDS: stability, Lyapunov function, nonlinear impulsive system, 34K45, 49N25, 49N90
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Analysis of an SEIRS Epidemic Model with Time Delays And Pulse Vaccination
Shujing Gao, Lansun Chen, Zhidong Teng
Rocky Mountain J. Math. 38 (5), 1385-1402, (2008) DOI: 10.1216/RMJ-2008-38-5-1385 Open Access
KEYWORDS: time delay, pulse vaccination, SEIRS epidemic model, global attractivity, permanence
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Time-Limited Management Strategies of a Single-Species With Allee Effect
Hongjian Guo, Lansun Chen, Xinyu Song
Rocky Mountain J. Math. 38 (5), 1403-1420, (2008) DOI: 10.1216/RMJ-2008-38-5-1403 Open Access
KEYWORDS: impulsive effect, boundary value problem, Impulsive differential equation, single species, Allee effect, 54B20, 54F15
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The Analysis of Two Epidemic Models with Constant Immigration and Quarantine
Zhixing Hu, Yang Yu, Wanbiao Ma
Rocky Mountain J. Math. 38 (5), 1421-1436, (2008) DOI: 10.1216/RMJ-2008-38-5-1421 Open Access
KEYWORDS: Epidemiological models, quarantine, immigration, endemic equilibrium, global stability
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The Effect of Constant and Mixed Impulsive Vaccination on SIS Epidemic Models Incorporating Media Coverage
Yongfeng Li, Chaoqun Ma, Jingan Cui
Rocky Mountain J. Math. 38 (5), 1437-1455, (2008) DOI: 10.1216/RMJ-2008-38-5-1437 Open Access
KEYWORDS: vaccination, vertical transmission, impulsive effect, media coverage, 34C05, 92D25
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Dynamical Behavior of an Epidemic Model with Coinfection Of Two Diseases
Jianquan Li, Ladi Wang, Huiwen Zhao, Zhien Ma
Rocky Mountain J. Math. 38 (5), 1457-1479, (2008) DOI: 10.1216/RMJ-2008-38-5-1457 Open Access
KEYWORDS: Epidemic model, age of infection, Equilibrium, stability
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Optimization Algorithm and its Convergence for Microbial Continuous Fermentation
Xiaohong Li, Enmin Feng, Zhilong Xiu
Rocky Mountain J. Math. 38 (5), 1481-1491, (2008) DOI: 10.1216/RMJ-2008-38-5-1481 Open Access
KEYWORDS: Optimality function, optimization algorithm, convergence
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Stability of the $T$ -Periodic Solution on the ES-S Model
J.G. Lian, H.K. Zhang
Rocky Mountain J. Math. 38 (5), 1493-1504, (2008) DOI: 10.1216/RMJ-2008-38-5-1493 Open Access
KEYWORDS: ES-S model, periodic solution, existence, uniqueness, stability
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Modeling and Analysis of a Delayed Competitive System With Impulsive Perturbations
Zhijun Liu, Ronghua Tan, Yiping Chen
Rocky Mountain J. Math. 38 (5), 1505-1523, (2008) DOI: 10.1216/RMJ-2008-38-5-1505 Open Access
KEYWORDS: Delay, impulse, competitive system, permanence, periodic solution
No abstract available
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Modeling Disease Spread via Transport-Related Infection By a Delay Differential Equation
Junli Liu, Jianhong Wu, Yicang Zhou
Rocky Mountain J. Math. 38 (5), 1525-1540, (2008) DOI: 10.1216/RMJ-2008-38-5-1525 Open Access
KEYWORDS: Transport-related infection, stability, Delay, permanence
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Global Dynamics in a TB Model Incorporating Case Detection And Two Treatment Stages
Luju Liu, Yicang Zhou, Jianhong Wu
Rocky Mountain J. Math. 38 (5), 1541-1559, (2008) DOI: 10.1216/RMJ-2008-38-5-1541 Open Access
KEYWORDS: TB model, case detection, relapse, treatment, M. tuberculosis
No abstract available
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The Analysis of an HIV/AIDS Model with Vaccination
Liu Maoxing, Jin Zhen
Rocky Mountain J. Math. 38 (5), 1561-1572, (2008) DOI: 10.1216/RMJ-2008-38-5-1561 Open Access
KEYWORDS: HIV/AIDS, vaccination, stability, Hopf bifurcation
No abstract available
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Mathematical Analysis of a Basic Virus Infection Model With Application to HBV Infection
Lequan Min, Yongmei Su, Yang Kuang
Rocky Mountain J. Math. 38 (5), 1573-1585, (2008) DOI: 10.1216/RMJ-2008-38-5-1573 Open Access
KEYWORDS: Basic model of virus infection, basic infection reproduction number, equilibrium point, basin of global attraction
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Waning Herd Immunity: A Challenge for Eradication of Measles
Seyed M. Moghadas, Murray E. Alexander, Beni M. Sahai
Rocky Mountain J. Math. 38 (5), 1587-1607, (2008) DOI: 10.1216/RMJ-2008-38-5-1587 Open Access
KEYWORDS: adaptive dynamics, herd immunity, vaccination, epidemic patterns
No abstract available
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Permanence in Multi-Species Competitive Systems with Delays And Feedback Controls
Linfei Nie, Jigen Peng, Zhidong Teng
Rocky Mountain J. Math. 38 (5), 1609-1631, (2008) DOI: 10.1216/RMJ-2008-38-5-1609 Open Access
KEYWORDS: Kolomogorov, Lotka-Volterra system, competitive system, Delay, feedback control, Ultimate boundedness, permanence
No abstract available
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The Effect of Partial Crop Harvest on Biological Pest Control
S. Nundloll, L. Mailleret, F. Grognard
Rocky Mountain J. Math. 38 (5), 1633-1661, (2008) DOI: 10.1216/RMJ-2008-38-5-1633 Open Access
No abstract available
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Dynamic Behaviors of a Single-Species Population Model With Birth Pulses in a Polluted Environment
Fengmei Tao, Bing Liu
Rocky Mountain J. Math. 38 (5), 1663-1684, (2008) DOI: 10.1216/RMJ-2008-38-5-1663 Open Access
KEYWORDS: Birth pulse, pulse harvesting, pulse toxicant input, bifurcation, chaos
No abstract available
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Global Stability and Hopf Bifurcation on a Predator-Prey System with Diffusion and Delays
Yuquan Wang
Rocky Mountain J. Math. 38 (5), 1685-1703, (2008) DOI: 10.1216/RMJ-2008-38-5-1685 Open Access
KEYWORDS: Holling II functional response, Delay, permanence, global stability, Hopf bifurcation, 34C25, 34K15, 92D25
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Periodic Solutions in a Delayed Predator-Prey Model with Nonmonotonic Functional Response
Lin-Lin Wang, Yong-Hong Fan, Wei-Gao Ge
Rocky Mountain J. Math. 38 (5), 1705-1719, (2008) DOI: 10.1216/RMJ-2008-38-5-1705 Open Access
KEYWORDS: predator-prey model, nonmonotonic functional response, positive periodic solution, Coincidence degree, 34K15, 92D25, 34C25
No abstract available
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A Stage Structured Predator-Prey Model with Time Delays
Yan Wang, Jianhong Wu, Yanni Xiao
Rocky Mountain J. Math. 38 (5), 1721-1743, (2008) DOI: 10.1216/RMJ-2008-38-5-1721 Open Access
KEYWORDS: Predator-prey, stage-structured, time delay, global stability, Hopf bifurcation
No abstract available
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A Class of Nonlinear Multistage Dynamical System and its Optimal Control
Huiyuan Wang, Enmin Feng, Zhilong Xiu
Rocky Mountain J. Math. 38 (5), 1745-1760, (2008) DOI: 10.1216/RMJ-2008-38-5-1745 Open Access
KEYWORDS: Bio-dissimilation, nonlinear multistage dynamical system, batch fermentation, optimal control
No abstract available
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Stability and Bifurcation in a Beddington-Deangelis Type Predator-Prey Model with Prey Dispersal
Rui Xu, Zhien Ma, Qintao Gan
Rocky Mountain J. Math. 38 (5), 1761-1783, (2008) DOI: 10.1216/RMJ-2008-38-5-1761 Open Access
KEYWORDS: predator-prey model, dispersal, time delay, stability, 34K20, 34K60, 92D25
No abstract available
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Global Solutions for a Tritrophic Food Chain Model with Diffusion
Fang Yang, Shengmao Fu
Rocky Mountain J. Math. 38 (5), 1785-1812, (2008) DOI: 10.1216/RMJ-2008-38-5-1785 Open Access
KEYWORDS: diffusion, cross-diffusion, global solution, equilibrium point, stability, 35K57, 35B35, 92D25
No abstract available
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Simple Models for Avian Influenza
Xingyang Ye, Xuepeng Li
Rocky Mountain J. Math. 38 (5), 1813-1828, (2008) DOI: 10.1216/RMJ-2008-38-5-1813 Open Access
KEYWORDS: avian influenza, Epidemic model, global stability, 34D23, 92D30
No abstract available
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Necessary and Sufficient Conditions for Global Attractivity of Hopfield-Type Neural Networks with Time Delays
Shangguo Zhang, Wanbiao Ma, Yang Kuang
Rocky Mountain J. Math. 38 (5), 1829-1840, (2008) DOI: 10.1216/RMJ-2008-38-5-1829 Open Access
KEYWORDS: Hopfield-type neural networks, time delays, global attractivity, 34K20, 92B20
No abstract available
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Dynamic Behavior of a Delayed Impulsive SEIRS Model In Epidemiology
Tailei Zhang, Zhidong Teng
Rocky Mountain J. Math. 38 (5), 1841-1862, (2008) DOI: 10.1216/RMJ-2008-38-5-1841 Open Access
KEYWORDS: Krasnoselskii's fixed-point theorem, time delay, pulse vaccination, threshold value
No abstract available
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Maximum Likelihood Estimation for Simplex Distribution Nonlinear Mixed Models via the Stochastic Approximation Algorithm
Wenzhuan Zhang, Hongjie Wei
Rocky Mountain J. Math. 38 (5), 1863-1875, (2008) DOI: 10.1216/RMJ-2008-38-5-1863 Open Access
KEYWORDS: simplex distribution, nonlinear mixed models, maximum likelihood estimates, stochastic approximation algorithm, M-H algorithm, longitudinal continuous proportional data
No abstract available
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Analysis of an Eco-Epidemiological Model with Time Delay
Hui Zhu, Zuoliang Xiong, Xin Wang
Rocky Mountain J. Math. 38 (5), 1877-1886, (2008) DOI: 10.1216/RMJ-2008-38-5-1877 Open Access
KEYWORDS: Eco-epidemiological model, stability, Hopf bifurcation, time delay
No abstract available
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