
AIMS Mathematics, 2020, 5(4): 33783390. doi: 10.3934/math.2020218.
Research article
Export file:
Format
 RIS(for EndNote,Reference Manager,ProCite)
 BibTex
 Text
Content
 Citation Only
 Citation and Abstract
Asymptotic behavior for a class of population dynamics
1 School of Mathematics and Statistics, Changsha University of Science and Technology; Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha 410114, China
2 School of Mathematics, Southeast University, Nanjing, 211189, China
Received: , Accepted: , Published:
Keywords: population dynamics; timevarying delay; asymptotic behavior; BernfeldHaddock conjecture
Citation: Chuangxia Huang, Luanshan Yang, Jinde Cao. Asymptotic behavior for a class of population dynamics. AIMS Mathematics, 2020, 5(4): 33783390. doi: 10.3934/math.2020218
References:
 1. D. Yang, X. Li, J. Qiu, Output tracking control of delayed switched systems via statedependent switching and dynamic output feedback, Nonlinear Anal. Hybrid Syst., 32 (2019), 294305.
 2. X. Yang, X. Li, Q. Xi, et al. Review of stability and stabilization for impulsive delayed systems, Math. Biosci. Eng., 15 (2018), 14951515.
 3. X. Li, X. Yang, T. Huang, Persistence of delayed cooperative models: Impulsive control method, Appl. Math. Comput., 342 (2019), 130146.
 4. Y. Tan, C. Huang, B. Sun, et al. Dynamics of a class of delayed reactiondiffusion systems with Neumann boundary condition, J. Math. Anal. Appl., 458 (2018), 11151130.
 5. C. Huang, X. Long, J. Cao, Stability of antiperiodic recurrent neural networks with multiproportional delays, Math. Method Appl. Sci., 2020.
 6. J. Zhang, C. Huang, Dynamics analysis on a class of delayed neural networks involving inertial terms, Adv. Differ. Equations, 120 (2020), 112.
 7. X. Long, S. Gong, New results on stability of Nicholson's blowflies equation with multiple pairs of timevarying delays, Appl. Math. Lett., 100 (2020), 106027.
 8. C. Huang, Y. Qiao, L. Huang, et al. Dynamical behaviors of a foodchain model with stage structure and time delays, Adv. Differ. Equations, 186 (2018).
 9. C. Huang, J. Cao, F. Wen, et al. Stability Analysis of SIR Model with Distributed Delay on Complex Networks, Plos One, 11 (2016), e0158813.
 10. H. Hu, X. Yuan, L. Huang, et al. Global dynamics of an SIRS model with demographics and transfer from infectious to susceptible on heterogeneous networks, Math. Biosci. Eng., 16 (2019), 57295749.
 11. H. Hu, X. Zou, Existence of an extinction wave in the fisher equation with a shifting habitat, Proc. Am. Math. Soc., 145 (2017), 47634771.
 12. H. Hu, T. Yi, X. Zou, On spatialtemporal dynamics of FisherKPP equation with a shifting environment, Proc. Amer. Math. Soc., 148 (2020), 213221.
 13. J. Wang, C. Huang, L. Huang, Discontinuityinduced limit cycles in a general planar piecewise linear system of saddlefocus type, Nonlinear Anal. Hybrid Syst., 33 (2019), 162178.
 14. J. Wang, X. Chen, L. Huang, The number and stability of limit cycles for planar piecewise linear systems of nodeCsaddle type, J. Math. Anal. Appl., 469 (2019), 405427.
 15. C. Huang, Z. Yang, T. Yi, et al. On the basins of attraction for a class of delay differential equations with nonmonotone bistable nonlinearities, J. Differ. Equations, 256 (2014), 21012114.
 16. C. Huang, H. Zhang, J. Cao, et al. Stability and Hopf bifurcation of a delayed preypredator model with disease in the predator, Int. J. Bifurcation Chaos, 29 (2019), 1950091.
 17. C. Huang, H. Zhang, L. Huang, Almost periodicity analysis for a delayed Nicholson's blowflies model with nonlinear densitydependent mortality term, Commun. Pure Appl. Anal., 18 (2019), 33373349.
 18. C. Qian, Y. Hu, Novel stability criteria on nonlinear densitydependent mortality Nicholson's blowflies systems in asymptotically almost periodic environments, J. Inequal. Appl., 13 (2020), 118.
 19. C. Huang, X. Long, L. Huang, et al. Stability of almost periodic Nicholson's blowflies model involving patch structure and mortality terms, Can. Math. Bull., (2019), 118.
 20. C. Huang, H. Yang, J. Cao, Weighted Pseudo Almost Periodicity of MultiProportional Delayed Shunting Inhibitory Cellular Neural Networks with D operator, Discrete Contin. Dyn. Syst. Ser. S, 2020.
 21. S. R. Bernfeld, J. R. A. Haddock, A variation of Razumikhin's method for retarded functional equations, In: Nonlinear systems and applications, An International Conference, New York: Academic Press, 1977, 561566.
 22. C. Jehu, Comportement asymptotique des solutions de equation x'(t) = f (t, x(t)) + f (t, x(t  1)) + h(t) (in French), Ann. Soc. Sci. Brux. I, 92 (1979), 263269.
 23. T. Ding, Asymptotic behavior of solutions of some retarded differential equations, Sci. China Ser. AMath., 25 (1982), 363371.
 24. T. Yi, L. Huang, Asymptotic behavior of solutions to a class of systems of delay differential equations, Acta Math. Sin. (Engl. Ser.), 23 (2007), 13751384.
 25. M. Xu, W. Chen, X. Yi, New generalization of the twodimensional BernfeldHaddock conjecture and its proof, Nonlinear Anal. Real World Appl., 11 (2010), 34133420.
 26. Q. Zhou, W. Wang, Q. Fan, A generalization of the threedimensional BernfeldHaddock conjecture and its proof, J. Comput. Appl. Math., 233 (2009), 473481.
 27. B. S. Chen, Asymptotic behavior of solutions of some infinite retarded differential equations(in Chinese), Acta Math. Sin. (Engl. Ser.), 3 (1990), 353358.
 28. T. Ding, Applications of the qualitative methods in ordinary differential equations (in Chinese), Peking: China Higher Education Press, 2004, 155163.
 29. T. Yi, L. Huang, Convergence of solution to a class of systems of delay differential equations, Nonlinear Dyn. Syst. Theory, 5 (2005), 189200.
 30. Q. Zhou, Convergence for a twoneuron network with delays, Appl. Math. Lett., 22 (2009), 11811184.
 31. S. Hu, L. Huang, T. Yi. Convergence of bounded solutions for a class of systems of delay differential equations, Nonlinear Anal., 61 (2005), 543549.
 32. B. S. Chen, Asymptotic behavior of a class of nonautonomous retarded differential equations (in Chinese), Chinese Sci. Bull., 6 (1988), 413415.
 33. T. Yi, L. Huang, Convergence for pseudo monotone semiflows on product ordered topological spaces, J. Differ. Equations, 214 (2005), 429456.
 34. Q. Zhou, Asymptotic behavior of solutions to a firstorder nonhomogeneous delay differential equation, Electron. J. Differ. Equations, 103 (2011), 18.
 35. B. Liu, Asymptotic behavior of solutions to a class of nonautonomous delay differential equations, J. Math. Anal. Appl., 446 (2017), 580590.
 36. B. Liu, A generalization of the BernfeldHaddock conjecture, Appl. Math. Lett., 65 (2017), 713.
 37. S. Xiao, Asymptotic behavior of solutions to a nonautonomous system of twodimensional differential equations, Electron. J. Differ. Equations, 2017 (2017), 112.
This article has been cited by:
 1. Hong Zhang, Qian Cao, Hedi Yang, Asymptotically almost periodic dynamics on delayed Nicholsontype system involving patch structure, Journal of Inequalities and Applications, 2020, 2020, 1, 10.1186/s13660020023660
 2. Xiaoling Zhang, Haijun Hu, Convergence in a system of critical neutral functional differential equations, Applied Mathematics Letters, 2020, 107, 106385, 10.1016/j.aml.2020.106385
 3. Hong Zhang, Chaofan Qian, Convergence analysis on inertial proportional delayed neural networks, Advances in Difference Equations, 2020, 2020, 1, 10.1186/s13662020027373
 4. Qian Cao, Xiaojin Guo, Antiperiodic dynamics on highorder inertial Hopfield neural networks involving timevarying delays, AIMS Mathematics, 2020, 5, 6, 5402, 10.3934/math.2020347
 5. Qian Cao, Xin Long, New convergence on inertial neural networks with timevarying delays and continuously distributed delays, AIMS Mathematics, 2020, 5, 6, 5955, 10.3934/math.2020381
 6. Luogen Yao, Qian Cao, Antiperiodicity on highorder inertial Hopfield neural networks involving mixed delays, Journal of Inequalities and Applications, 2020, 2020, 1, 10.1186/s13660020024443
 7. Xin Long, Novel stability criteria on a patch structure Nicholson’s blowflies model with multiple pairs of timevarying delays, AIMS Mathematics, 2020, 5, 6, 7387, 10.3934/math.2020473
 8. Chuangxia Huang, Xian Zhao, Jinde Cao, Fuad E Alsaadi, Global dynamics of neoclassical growth model with multiple pairs of variable delays, Nonlinearity, 2020, 33, 12, 6819, 10.1088/13616544/abab4e
 9. Gang Yang, Qian Cao, Stability for patch structure Nicholson’s blowflies systems involving distinctive maturation and feedback delays, Journal of Experimental & Theoretical Artificial Intelligence, 2020, 1, 10.1080/0952813X.2020.1836032
Reader Comments
© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)
Associated material
Metrics
Other articles by authors
Related pages
Tools
your name: * your email: *