Asymptotic behavior for a class of population dynamics. (English) Zbl 1484.92073
Summary: This paper investigates the asymptotic behavior for a class of n-dimensional population dynamics systems described by delay differential equations. With the help of technique of differential inequality, we show that each solution of the addressed systems tends to a constant vector as \(t \rightarrow \infty \), which includes many generalizations of Bernfeld-Haddock conjecture. By the way, our results extend some existing literatures.
MSC:
| 92D25 | Population dynamics (general) |
| 34K12 | Growth, boundedness, comparison of solutions to functional-differential equations |
| 34K25 | Asymptotic theory of functional-differential equations |
References:
| [1] | D. Yang; X. Li; J. Qiu, em>Output tracking control of delayed switched systems via state-dependent switching and dynamic output feedback</em, Nonlinear Anal. Hybrid Syst., 32, 294-305 (2019) · Zbl 1425.93149 · doi:10.1016/j.nahs.2019.01.006 |
| [2] | X. Yang; X. Li; Q. Xi, t al. <em>Review of stability and stabilization for impulsive delayed systems</em, Math. Biosci. Eng., 15, 1495-1515 (2018) · Zbl 1416.93159 · doi:10.3934/mbe.2018069 |
| [3] | X. Li; X. Yang; T. Huang, em>Persistence of delayed cooperative models: Impulsive control method</em, Appl. Math. Comput., 342, 130-146 (2019) · Zbl 1428.34113 |
| [4] | Y. Tan; C. Huang; B. Sun, t al. <em>Dynamics of a class of delayed reaction-diffusion systems with Neumann boundary condition</em, J. Math. Anal. Appl., 458, 1115-1130 (2018) · Zbl 1378.92077 · doi:10.1016/j.jmaa.2017.09.045 |
| [5] | C. Huang, X. Long, J. Cao, <em>Stability of anti-periodic recurrent neural networks with multiproportional delays</em>, Math. Method Appl. Sci., 2020. · Zbl 1456.34071 |
| [6] | J. Zhang; C. Huang, em>Dynamics analysis on a class of delayed neural networks involving inertial terms</em, Adv. Differ. Equations, 120, 1-12 (2020) · doi:10.1186/s13662-019-2438-0 |
| [7] | X. Long; S. Gong, em>New results on stability of Nicholson’s blowflies equation with multiple pairs of time-varying delays</em, Appl. Math. Lett., 100 (2020) · Zbl 1427.93207 · doi:10.1016/j.aml.2019.106027 |
| [8] | C. Huang; Y. Qiao; L. Huang, t al. <em>Dynamical behaviors of a food-chain model with stage structure and time delays</em, Adv. Differ. Equations, 186 (2018) · Zbl 1446.37083 |
| [9] | C. Huang; J. Cao; F. Wen, t al. <em>Stability Analysis of SIR Model with Distributed Delay on Complex Networks</em, Plos One, 11 (2016) |
| [10] | H. Hu; X. Yuan; L. Huang, t al. <em>Global dynamics of an SIRS model with demographics and transfer from infectious to susceptible on heterogeneous networks</em, Math. Biosci. Eng., 16, 5729-5749 (2019) · Zbl 1497.92262 · doi:10.3934/mbe.2019286 |
| [11] | H. Hu; X. Zou, em>Existence of an extinction wave in the fisher equation with a shifting habitat</em, Proc. Am. Math. Soc., 145, 4763-4771 (2017) · Zbl 1372.34057 · doi:10.1090/proc/13687 |
| [12] | H. Hu; T. Yi; X. Zou, em>On spatial-temporal dynamics of Fisher-KPP equation with a shifting environment</em, Proc. Amer. Math. Soc., 148, 213-221 (2020) · Zbl 1430.35140 · doi:10.1090/proc/14659 |
| [13] | J. Wang; C. Huang; L. Huang, em>Discontinuity-induced limit cycles in a general planar piecewise linear system of saddle-focus type</em, Nonlinear Anal. Hybrid Syst., 33, 162-178 (2019) · Zbl 1431.34020 · doi:10.1016/j.nahs.2019.03.004 |
| [14] | J. Wang; X. Chen; L. Huang, em>The number and stability of limit cycles for planar piecewise linear systems of nodeCsaddle type</em, J. Math. Anal. Appl., 469, 405-427 (2019) · Zbl 1429.34037 · doi:10.1016/j.jmaa.2018.09.024 |
| [15] | C. Huang; Z. Yang; T. Yi, t al. <em>On the basins of attraction for a class of delay differential equations with non-monotone bistable nonlinearities</em, J. Differ. Equations, 256, 2101-2114 (2014) · Zbl 1297.34084 · doi:10.1016/j.jde.2013.12.015 |
| [16] | C. Huang; H. Zhang; J. Cao, t al. <em>Stability and Hopf bifurcation of a delayed prey-predator model with disease in the predator</em, Int. J. Bifurcation Chaos, 29 (2019) · Zbl 1425.34093 |
| [17] | C. Huang; H. Zhang; L. Huang, em>Almost periodicity analysis for a delayed Nicholson’s blowflies model with nonlinear density-dependent mortality term</em, Commun. Pure Appl. Anal., 18, 3337-3349 (2019) · Zbl 1493.34221 · doi:10.3934/cpaa.2019150 |
| [18] | C. Qian; Y. Hu, em>Novel stability criteria on nonlinear density-dependent mortality Nicholson’s blowflies systems in asymptotically almost periodic environments</em, J. Inequal. Appl., 13, 1-18 (2020) · Zbl 1503.37094 |
| [19] | C. Huang, X. Long, L. Huang, et al. <em>Stability of almost periodic Nicholson’s blowflies model involving patch structure and mortality terms</em>, Can. Math. Bull., (2019), 1-18. |
| [20] | C. Huang, H. Yang, J. Cao, <em>Weighted Pseudo Almost Periodicity of Multi-Proportional Delayed Shunting Inhibitory Cellular Neural Networks with D operator</em>, Discrete Contin. Dyn. Syst. Ser. S, 2020. · Zbl 1475.92016 |
| [21] | S. R. Bernfeld, J. R. A. Haddock, <em>A variation of Razumikhin’s method for retarded functional equations, In: Nonlinear systems and applications</em>, An International Conference, New |
| [22] | C. Jehu, em>Comportement asymptotique des solutions de equation x</em>’(<em>t</em>) = -<em>f</em> (<em>t</em, x(t)) + f (t, x(t - 1)) + h(t) (in French), Ann. Soc. Sci. Brux. I, 92, 263-269 (1979) · Zbl 0436.34071 |
| [23] | T. Ding, em>Asymptotic behavior of solutions of some retarded differential equations</em, Sci. China Ser. A-Math., 25, 363-371 (1982) · Zbl 0498.34056 |
| [24] | T. Yi; L. Huang, em>Asymptotic behavior of solutions to a class of systems of delay differential equations</em, Acta Math. Sin. (Engl. Ser.), 23, 1375-1384 (2007) · Zbl 1152.34054 · doi:10.1007/s10114-005-0932-7 |
| [25] | M. Xu; W. Chen; X. Yi, em>New generalization of the two-dimensional Bernfeld-Haddock conjecture and its proof</em, Nonlinear Anal. Real World Appl., 11, 3413-3420 (2010) · Zbl 1206.34098 · doi:10.1016/j.nonrwa.2009.12.001 |
| [26] | Q. Zhou; W. Wang; Q. Fan, em>A generalization of the three-dimensional Bernfeld-Haddock conjecture and its proof</em, J. Comput. Appl. Math., 233, 473-481 (2009) · Zbl 1209.34092 · doi:10.1016/j.cam.2009.07.047 |
| [27] | B. S. Chen, em>Asymptotic behavior of solutions of some infinite retarded differential equations(in Chinese)</em, Acta Math. Sin. (Engl. Ser.), 3, 353-358 (1990) · Zbl 0729.34045 |
| [28] | T. Ding, <em>Applications of the qualitative methods in ordinary differential equations (in Chinese)</em> |
| [29] | T. Yi; L. Huang, em>Convergence of solution to a class of systems of delay differential equations</em, Nonlinear Dyn. Syst. Theory, 5, 189-200 (2005) · Zbl 1081.34075 |
| [30] | Q. Zhou, em>Convergence for a two-neuron network with delays</em, Appl. Math. Lett., 22, 1181-1184 (2009) · Zbl 1173.68656 · doi:10.1016/j.aml.2009.01.028 |
| [31] | S. Hu, L. Huang, T. Yi. <em>Convergence of bounded solutions for a class of systems of delay differential equations</em>, Nonlinear Anal., 61 (2005), 543-549. · Zbl 1075.34078 |
| [32] | B. S. Chen, em>Asymptotic behavior of a class of nonautonomous retarded differential equations (in Chinese)</em, Chinese Sci. Bull., 6, 413-415 (1988) |
| [33] | T. Yi; L. Huang, em>Convergence for pseudo monotone semi-flows on product ordered topological spaces</em, J. Differ. Equations, 214, 429-456 (2005) · Zbl 1066.37016 · doi:10.1016/j.jde.2005.02.005 |
| [34] | Q. Zhou, em>Asymptotic behavior of solutions to a first-order non-homogeneous delay differential equation</em, Electron. J. Differ. Equations, 103, 1-8 (2011) · Zbl 1230.34061 |
| [35] | B. Liu, em>Asymptotic behavior of solutions to a class of non-autonomous delay differential equations</em, J. Math. Anal. Appl., 446, 580-590 (2017) · Zbl 1356.34073 · doi:10.1016/j.jmaa.2016.09.001 |
| [36] | B. Liu, em>A generalization of the Bernfeld-Haddock conjecture</em, Appl. Math. Lett., 65, 7-13 (2017) · Zbl 1362.34115 · doi:10.1016/j.aml.2016.09.018 |
| [37] | S. Xiao, em>Asymptotic behavior of solutions to a non-autonomous system of two-dimensional differential equations</em, Electron. J. Differ. Equations, 2017, 1-12 (2017) · Zbl 1372.34117 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
