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Applicable Analysis
An International Journal
Volume 31, 1988 - Issue 3
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Original Articles

Time lags in a “food–limited” population

K. Gopalsamy Department of Mathematics, The University of Rhode Island, Kingston, Rhode Island, 02881, U.S.A
,
M.R.S Kulenović Department of Mathematics, The University of Rhode Island, Kingston, Rhode Island, 02881, U.S.A
&
G. Ladas Department of Mathematics, The University of Rhode Island, Kingston, Rhode Island, 02881, U.S.A
Pages 225-237 | Published online: 02 May 2007

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Ying Su, Aying Wan & Junjie Wei. (2010) Bifurcation analysis in a diffusive ‘food-limited’ model with time delay. Applicable Analysis 89:7, pages 1161-1181.
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Yang Kuang. (1991) On neutral delay logistic gause-type predator-prey systems. Dynamics and Stability of Systems 6:2, pages 173-189.
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R. P. Gupta, Shristi Tiwari & Arun Kumar. (2024) A Comprehensive Study of Bifurcations in an Interactive Population Model with Food-Limited Growth. Differential Equations and Dynamical Systems.
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Yu Hu, Guohong Zhang & Xiaoli Wang. (2023) Spatio-temporal dynamics of a reaction–diffusion–advection food-limited system with nonlocal delayed competition and Dirichlet boundary condition. Nonlinear Analysis: Real World Applications 71, pages 103833.
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Ge Tian & Ruo-fan An. (2023) Spreading speed of a food-limited population model with delay. Applied Mathematics-A Journal of Chinese Universities 38:2, pages 264-273.
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Vsevolod G. Sorokin & Andrei V. Vyazmin. (2022) Nonlinear Reaction–Diffusion Equations with Delay: Partial Survey, Exact Solutions, Test Problems, and Numerical Integration. Mathematics 10:11, pages 1886.
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R. P. Gupta, Shristi Tiwari & Shivam Saxena. (2022) The qualitative behavior of a plankton-fish interaction model with food limited growth rate and non-constant fish harvesting. Discrete & Continuous Dynamical Systems - B 27:5, pages 2791.
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Antonio PalaciosAntonio Palacios. 2022. Mathematical Modeling. Mathematical Modeling 325 361 .
Honghua Bin, Hua Zhang & Junjie Wei. (2021) Bifurcation analysis in a delayed reaction–diffusion–advection food-limited system. Applied Mathematics Letters 120, pages 107332.
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Zhenliang Zhu, Mengxin He, Zhong Li & Fengde Chen. (2020) Stability and Bifurcation in a Logistic Model with Allee Effect and Feedback Control. International Journal of Bifurcation and Chaos 30:15, pages 2050231.
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Elena Trofimchuk, Manuel Pinto & Sergei Trofimchuk. (2019) Existence and uniqueness of monotone wavefronts in a nonlocal resource-limited model. Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150:5, pages 2462-2483.
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Wenzhen Gan, Peng Zhu, Zuhan Liu & Canrong Tian. (2020) Delay-driven instability and ecological control in a food-limited population networked system. Nonlinear Dynamics 100:4, pages 4031-4044.
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Andrey Perevaryukha. (2020) Modelling of Spatial Spreading of Invasions in the Discrete Homogeneous Environment. Mathematical Physics and Computer Simulation:1, pages 44-67.
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Ge Tian & Zhi-Cheng Wang. (2020) Spreading speed in a food-limited population model with nonlocal delay. Applied Mathematics Letters 102, pages 106121.
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Guangxun Sun & Binxiang Dai. (2020) Stability and bifurcation of a delayed diffusive predator-prey system with food-limited and nonlinear harvesting. Mathematical Biosciences and Engineering 17:4, pages 3520-3552.
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A. Yu. Perevaryukha. (2019) Continuous Model for the Devastating Oscillation Dynamics of Local Forest Pest Populations in Canada*. Cybernetics and Systems Analysis 55:1, pages 141-152.
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H. Y. Alfifi. (2017) Semi-analytical solutions for the delayed diffusive food-limited model. Semi-analytical solutions for the delayed diffusive food-limited model.
Jingdong Wei, Lixin Tian, Jiangbo Zhou, Zaili Zhen & Jing Xu. (2017) Existence and asymptotic behavior of traveling wave fronts for a food-limited population model with spatio-temporal delay. Japan Journal of Industrial and Applied Mathematics 34:1, pages 305-320.
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Cheng-Hsiung Hsu, Jian-Jhong Lin & Ting-Hui Yang. (2015) Travelling wave solutions for Kolmogorov-type delayed lattice reaction–diffusion systems. IMA Journal of Applied Mathematics 80:5, pages 1336-1367.
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Yuanyuan Wang & Xiaohua Ding. (2015) Numerical bifurcation of a delayed diffusive food‐limited model with Dirichlet boundary condition. Mathematical Methods in the Applied Sciences 38:13, pages 2888-2900.
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Zhong Li & Mengxin He. (2014) Hopf bifurcation in a delayed food-limited model with feedback control. Nonlinear Dynamics 76:2, pages 1215-1224.
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Yingguo Li. (2012) Dynamics of a discrete food-limited population model with time delay. Applied Mathematics and Computation 218:12, pages 6954-6962.
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Ravi P. Agarwal, Leonid Berezansky, Elena Braverman & Alexander DomoshnitskyRavi P. Agarwal, Leonid Berezansky, Elena Braverman & Alexander Domoshnitsky. 2012. Nonoscillation Theory of Functional Differential Equations with Applications. Nonoscillation Theory of Functional Differential Equations with Applications 1 21 .
Chuanxi Qian. (2011) Global attractivity in a delay differential equation with application in a commodity model. Applied Mathematics Letters 24:2, pages 116-121.
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Xiang-Ping Yan & Wan-Tong Li. (2010) Stability of bifurcating periodic solutions in a delayed reaction–diffusion population model. Nonlinearity 23:6, pages 1413-1431.
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Aying Wan & Junjie Wei. (2010) Hopf bifurcation analysis of a food-limited population model with delay. Nonlinear Analysis: Real World Applications 11:2, pages 1087-1095.
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Shuxia Pan & Shimin Wan. (2009) Traveling wave fronts in a delayed population model of Daphnia magna. Applied Mathematics and Computation 215:3, pages 1118-1123.
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Ying Su, Junjie Wei & Junping Shi. (2009) Hopf bifurcations in a reaction–diffusion population model with delay effect. Journal of Differential Equations 247:4, pages 1156-1184.
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Yanni Xiao, Roger G. Bowers & Sanyi Tang. (2009) The effect of delayed host self-regulation on host–pathogen population cycles in forest insects. Journal of Theoretical Biology 258:2, pages 240-249.
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Jianjie Wang & Jurang Yan. (2007) On oscillation of a food-limited population model with impulse and delay. Journal of Mathematical Analysis and Applications 334:1, pages 349-357.
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Zhi-Cheng Wang & Wan-Tong Li. (2007) Monotone travelling fronts of a food-limited population model with nonlocal delay. Nonlinear Analysis: Real World Applications 8:2, pages 699-712.
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Chuanxi Qian & Yijun Sun. (2007) Global attractivity of solutions of nonlinear delay differential equations with a forcing term. Nonlinear Analysis: Theory, Methods & Applications 66:3, pages 689-703.
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Chunhua Ou & Jianhong Wu. (2007) Traveling Wavefronts in a Delayed Food‐limited Population Model. SIAM Journal on Mathematical Analysis 39:1, pages 103-125.
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Jinliang Wang, Li Zhou & Yanbin Tang. (2006) Asymptotic periodicity of a food-limited diffusive population model with time-delay. Journal of Mathematical Analysis and Applications 313:2, pages 381-399.
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J. Arino & P. van den Driessche. 2006. Delay Differential Equations and Applications. Delay Differential Equations and Applications 539 578 .
Daqing Jiang, Ningzhong Shi & Yanan Zhao. (2005) Existence, uniqueness, and global stability of positive solutions to the food-limited population model with random perturbation. Mathematical and Computer Modelling 42:5-6, pages 651-658.
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Sanyi Tang & Lansun Chen. (2004) Global attractivity in a “food-limited” population model with impulsive effects. Journal of Mathematical Analysis and Applications 292:1, pages 211-221.
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Fengde Chen, Dexian Sun & Jinlin Shi. (2003) Periodicity in a food-limited population model with toxicants and state dependent delays. Journal of Mathematical Analysis and Applications 288:1, pages 136-146.
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Yuji Liu & Weigao Ge. (2003) Global attractivity in delay “food-limited” models with exponential impulses. Journal of Mathematical Analysis and Applications 287:1, pages 200-216.
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Meng Fan & Ke Wang. (2002) Periodicity in a “Food-limited” Population Model with Toxicants and Time Delays. Acta Mathematicae Applicatae Sinica, English Series 18:2, pages 309-314.
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S.A. Gourley. (2001) Wave front solutions of a diffusive delay model for populations of Daphnia magna. Computers & Mathematics with Applications 42:10-11, pages 1421-1430.
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F.A. Davidson & S.A. Gourley. (2001) The Effects of Temporal Delays in a Model for a Food-Limited, Diffusing Population. Journal of Mathematical Analysis and Applications 261:2, pages 633-648.
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Xianhua Tang & Jianshe Yu. (2001) 3–global attractivity of the zero solution of the “food limited” type functional differential equation. Science in China Series A: Mathematics 44:5, pages 610-618.
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Huaxing Xia & Jianhong Wu. (1996) Nonlinear oscillations in a discrete diffusive neutral logistic equation. Tohoku Mathematical Journal 48:3.
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Joseph W.-H. So & J. S. Yu. (2011) On the uniform stability for a ‘food-limited’ population model with time delay. Proceedings of the Royal Society of Edinburgh: Section A Mathematics 125:5, pages 991-1002.
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. 1993. Delay Differential Equations - With Applications in Population Dynamics. Delay Differential Equations - With Applications in Population Dynamics 353 373 .
Yang Kuang & Alan Feldstein. (1991) Boundedness of solutions of a nonlinear nonautonomous neutral delay equation. Journal of Mathematical Analysis and Applications 156:1, pages 293-304.
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Y. Kuang. (2009) On neutral-delay two-species Lotka-Volterra competitive systems. The Journal of the Australian Mathematical Society. Series B. Applied Mathematics 32:3, pages 311-326.
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K. Gopalsamy, M.R.S. Kulenović & G. Ladas. (1990) Environmental periodicity and time delays in a “food-limited” population model. Journal of Mathematical Analysis and Applications 147:2, pages 545-555.
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K. Gopalsamy, M. R. S. Kulenović & G. Ladas. (1990) Oscillations and global attractivity in models of hematopoiesis. Journal of Dynamics and Differential Equations 2:2, pages 117-132.
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