×

New results on global exponential stability for a periodic Nicholson’s blowflies model involving time-varying delays. (English) Zbl 1487.34137


MSC:

34K20 Stability theory of functional-differential equations
34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K13 Periodic solutions to functional-differential equations
37N25 Dynamical systems in biology
92D25 Population dynamics (general)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Liu, B., Global exponential stability of positive periodic solutions for a delayed Nicholson’s blowflies model, J. Math. Anal. Appl., 412, 212-221 (2014) · Zbl 1308.34096 · doi:10.1016/j.jmaa.2013.10.049
[2] Liu, B., New results on global exponential stability of almost periodic solutions for a delayed Nicholson’s blowflies model, Ann. Pol. Math., 113, 2, 191-208 (2015) · Zbl 1327.34130 · doi:10.4064/ap113-2-6
[3] Xiong, W., New results on positive pseudo-almost periodic solutions for a delayed Nicholson’s blowflies model, Nonlinear Dyn., 85, 563-571 (2016) · Zbl 1349.92134 · doi:10.1007/s11071-016-2706-4
[4] Xu, Y., New stability theorem for periodic Nicholson’s model with mortality term, Appl. Math. Lett., 94, 59-65 (2019) · Zbl 1412.34232 · doi:10.1016/j.aml.2019.02.021
[5] Son, D. T.; Hien, L. V.; Anh, T. T., Global attractivity of positive periodic solution of a delayed Nicholson model with nonlinear density-dependent mortality term, J. Qual. Theory Differ. Equ., 8, 1-21 (2019) · Zbl 1424.34281
[6] Ding, H.; Fu, S., Periodicity on Nicholson’s blowflies systems involving patch structure and mortality terms, J. Exp. Theor. Artif. Intell. (2019) · doi:10.1080/0952813X.2019.1647567
[7] Smith, H. L., Monotone Dynamical Systems (1995), Providence: Amer. Math. Soc., Providence · Zbl 0821.34003
[8] Hale, J. K.; Verduyn Lunel, S. M., Introduction to Functional Differential Equations (1993), New York: Springer, New York · Zbl 0787.34002
[9] Smith, H. L., An Introduction to Delay Differential Equations with Applications to the Life Sciences (2011), New York: Springer, New York · Zbl 1227.34001
[10] Liz, E.; Tkachenko, V.; Trofimchuk, S., A global stability criterion for scalar functional differential equation, SIAM J. Math. Anal., 35, 3, 596-622 (2003) · Zbl 1069.34109 · doi:10.1137/S0036141001399222
[11] Berezansky, L.; Braverman, E.; Idels, L., Nicholson’s blowflies differential equations revisited: main results and open problems, Appl. Math. Model., 34, 1405-1417 (2010) · Zbl 1193.34149 · doi:10.1016/j.apm.2009.08.027
[12] Huang, C.; Yang, Z.; Yi, T.; Zou, X., On the basins of attraction for a class of delay differential equations with non-monotone bistable nonlinearities, J. Differ. Equ., 256, 2101-2114 (2014) · Zbl 1297.34084 · doi:10.1016/j.jde.2013.12.015
[13] Huang, C.; Qiao, Y.; Huang, L.; Agarwal, R., Dynamical behaviors of a food-chain model with stage structure and time delays, Adv. Differ. Equ., 2018 (2018) · Zbl 1446.37083 · doi:10.1186/s13662-018-1589-8
[14] Huang, C.; Zhang, H.; Huang, L., Almost periodicity analysis for a delayed Nicholson’s blowflies model with nonlinear density-dependent mortality term, Commun. Pure Appl. Anal., 18, 6, 3337-3349 (2019) · Zbl 1493.34221 · doi:10.3934/cpaa.2019150
[15] Huang, C.; Zhang, H.; Cao, J.; Hu, H., Stability and Hopf bifurcation of a delayed prey-predator model with disease in the predator, Int. J. Bifurc. Chaos, 29, 7 (2019) · Zbl 1425.34093 · doi:10.1142/S0218127419500913
[16] Long, X.; Gong, S., New results on stability of Nicholson’s blowflies equation with multiple pairs of time-varying delays, Appl. Math. Lett., 100 (2020) · Zbl 1427.93207 · doi:10.1016/j.aml.2019.106027
[17] Huang, C.; Yang, X.; Cao, J., Stability analysis of Nicholson’s blowflies equation with two different delays, Math. Comput. Simul. (2019) · Zbl 1510.92163 · doi:10.1016/j.matcom.2019.09.023
[18] Tan, Y.; Huang, C.; Sun, B.; Wang, T., Dynamics of a class of delayed reaction-diffusion systems with Neumann boundary condition, J. Math. Anal. Appl., 458, 2, 1115-1130 (2018) · Zbl 1378.92077 · doi:10.1016/j.jmaa.2017.09.045
[19] Duan, L.; Fang, X.; Huang, C., Global exponential convergence in a delayed almost periodic Nicholson’s blowflies model with discontinuous harvesting, Math. Methods Appl. Sci., 41, 5, 1954-1965 (2018) · Zbl 1446.65033 · doi:10.1002/mma.4722
[20] Hu, H.; Zou, X., Existence of an extinction wave in the Fisher equation with a shifting habitat, Proc. Am. Math. Soc., 145, 11, 4763-4771 (2017) · Zbl 1372.34057 · doi:10.1090/proc/13687
[21] Wang, J.; Huang, C.; Huang, L., Discontinuity-induced limit cycles in a general planar piecewise linear system of saddle-focus type, Nonlinear Anal. Hybrid Syst., 33, 162-178 (2019) · Zbl 1431.34020 · doi:10.1016/j.nahs.2019.03.004
[22] Wang, J.; Chen, X.; Huang, L., The number and stability of limit cycles for planar piecewise linear systems of node-saddle type, J. Math. Anal. Appl., 469, 1, 405-427 (2019) · Zbl 1429.34037 · doi:10.1016/j.jmaa.2018.09.024
[23] Cai, Z.; Huang, J.; Huang, L., Periodic orbit analysis for the delayed Filippov system, Proc. Am. Math. Soc., 146, 11, 4667-4682 (2018) · Zbl 1400.34108 · doi:10.1090/proc/13883
[24] Liu, J.; Yan, L.; Xu, F.; Lai, M., Homoclinic solutions for Hamiltonian system with impulsive effects, Adv. Differ. Equ., 2018, 1 (2018) · Zbl 1448.37073 · doi:10.1186/s13662-018-1774-9
[25] Chen, T.; Huang, L.; Yu, P.; Huang, W., Bifurcation of limit cycles at infinity in piecewise polynomial systems, Nonlinear Anal., Real World Appl., 41, 82-106 (2018) · Zbl 1387.34059 · doi:10.1016/j.nonrwa.2017.10.003
[26] Yang, X.; Wen, S.; Liu, Z.; Li, C.; Huang, C., Dynamic properties of foreign exchange complex network, Mathematics, 7 (2019) · doi:10.3390/math7090832
[27] Iswarya, M.; Raja, R.; Rajchakit, G.; Cao, J.; Alzabut, J.; Huang, C., Existence, uniqueness and exponential stability of periodic solution for discrete-time delayed BAM neural networks based on coincidence degree theory and graph theoretic method, Mathematics, 7, 11 (2019) · Zbl 1487.34161 · doi:10.3390/mathxx010005
[28] Li, J.; Ying, J.; Xie, D., On the analysis and application of an ion size-modified Poisson-Boltzmann equation, Nonlinear Anal., Real World Appl., 47, 188-203 (2019) · Zbl 1412.78003 · doi:10.1016/j.nonrwa.2018.10.011
[29] Li, X.; Liu, Z.; Li, J., Existence and controllability for nonlinear fractional control systems with damping in Hilbert spaces, Acta Mech. Sin. Engl. Ser., 39, 1, 229-242 (2019) · Zbl 1499.34392
[30] Zhu, K.; Xie, Y.; Zhou, F., Pullback attractors for a damped semilinear wave equation with delays, Acta Math. Sin. Engl. Ser., 34, 7, 1131-1150 (2018) · Zbl 1392.35046 · doi:10.1007/s10114-018-7420-3
[31] Zhao, J.; Liu, J.; Fang, L., Anti-periodic boundary value problems of second-order functional differential equations, Bull. Malays. Math. Sci. Soc., 37, 2, 311-320 (2014) · Zbl 1306.34098
[32] Huang, C.; Yang, L.; Liu, B., New results on periodicity of non-autonomous inertial neural networks involving non-reduced order method, Neural Process. Lett., 50, 595-606 (2019) · doi:10.1007/s11063-019-10055-3
[33] Huang, C., Exponential stability of inertial neural networks involving proportional delays and non-reduced order method, J. Exp. Theor. Artif. Intell. (2019) · doi:10.1080/0952813X.2019.1635654
[34] Huang, C.; Wen, S.; Huang, L., Dynamics of anti-periodic solutions on shunting inhibitory cellular neural networks with multi-proportional delays, Neurocomputing, 357, 47-52 (2019) · doi:10.1016/j.neucom.2019.05.022
[35] Huang, C.; Zhang, H., Periodicity of non-autonomous inertial neural networks involving proportional delays and non-reduced order method, Int. J. Biomath., 12, 2 (2019) · Zbl 1409.34038 · doi:10.1142/S1793524519500165
[36] Huang, C.; Liu, B., New studies on dynamic analysis of inertial neural networks involving non-reduced order method, Neurocomputing, 325, 24, 283-287 (2019) · doi:10.1016/j.neucom.2018.09.065
[37] Zhang, H., Global large smooth solutions for 3-D hall-magnetohydrodynamics, Discrete Contin. Dyn. Syst., 39, 11, 6669-6682 (2019) · Zbl 1428.35411 · doi:10.3934/dcds.2019290
[38] Li, W.; Huang, L.; Ji, J., Periodic solution and its stability of a delayed Beddington-DeAngelis type predator-prey system with discontinuous control strategy, Math. Methods Appl. Sci., 42, 13, 4498-4515 (2019) · Zbl 1427.34110 · doi:10.1002/mma.5673
[39] Qian, C.; Hu, Y., Novel stability criteria on nonlinear density-dependent mortality Nicholson’s blowflies systems in asymptotically almost periodic environments, J. Inequal. Appl. (2020) · Zbl 1503.37094 · doi:10.1186/s13660-019-2275-4
[40] Huang, C.; Long, X.; Huang, L.; Fu, S., Stability of almost periodic Nicholson’s blowflies model involving patch structure and mortality terms, Can. Math. Bull. (2019) · Zbl 1441.34088 · doi:10.4153/S0008439519000511
[41] Hu, H.; Yi, T.; Zou, X., On spatial-temporal dynamics of Fisher-KPP equation with a shifting environment, Proc. Am. Math. Soc., 148, 1, 213-221 (2020) · Zbl 1430.35140 · doi:10.1090/proc/14659
[42] Wang, F.; Yao, Z., Approximate controllability of fractional neutral differential systems with bounded delay, Fixed Point Theory, 17, 495-508 (2016) · Zbl 1386.47014
[43] Hu, H.; Yuan, X.; Huang, L.; Huang, C., Global dynamics of an SIRS model with demographics and transfer from infectious to susceptible on heterogeneous networks, Math. Biosci. Eng., 16, 5, 5729-5749 (2019) · Zbl 1497.92262 · doi:10.3934/mbe.2019286
[44] Wei, Y.; Yin, L.; Long, X., The coupling integrable couplings of the generalized coupled Burgers equation hierarchy and its Hamiltonian structure, Adv. Differ. Equ., 2019 (2019) · Zbl 1458.37071 · doi:10.1186/s13662-019-2004-9
[45] Zhang, J.; Lu, C.; Li, X.; Kim, H.-J.; Wang, J., A full convolutional network based on DenseNet for remote sensing scene classification, Math. Biosci. Eng., 16, 5, 3345-3367 (2019) · doi:10.3934/mbe.2019167
[46] Hu, H.; Liu, L., Weighted inequalities for a general commutator associated to a singular integral operator satisfying a variant of Hormander’s condition, Math. Notes, 101, 5-6, 830-840 (2017) · Zbl 1373.42015 · doi:10.1134/S0001434617050091
[47] Huang, C.; Liu, L., Boundedness of multilinear singular integral operator with non-smooth kernels and mean oscillation, Quaest. Math., 40, 3, 295-312 (2017) · Zbl 1423.42027 · doi:10.2989/16073606.2017.1287136
[48] Huang, C.; Cao, J.; Wen, F.; Yang, X., Stability analysis of SIR model with distributed delay on complex networks, PLoS ONE, 11, 8 (2016) · doi:10.1371/journal.pone.0158813
[49] Li, X.; Liu, Y.; Wu, J., Flocking and pattern motion in a modified Cucker-Smale model, Bull. Korean Math. Soc., 53, 5, 1327-1339 (2016) · Zbl 1355.34033 · doi:10.4134/BKMS.b150629
[50] Xie, Y.; Li, Q.; Zhu, K., Attractors for nonclassical diffusion equations with arbitrary polynomial growth nonlinearity, Nonlinear Anal., Real World Appl., 31, 23-37 (2016) · Zbl 1338.35066 · doi:10.1016/j.nonrwa.2016.01.004
[51] Xie, Y.; Li, Y.; Zeng, Y., Uniform attractors for nonclassical diffusion equations with memory, J. Funct. Spaces, 2016 (2016) · Zbl 1343.35038 · doi:10.1155/2016/5340489
[52] Wang, F.; Wang, P.; Yao, Z., Approximate controllability of fractional partial differential equation, Adv. Differ. Equ., 2015 (2015) · Zbl 1422.35177 · doi:10.1186/s13662-015-0692-3
[53] Liu, Y.; Wu, J., Multiple solutions of ordinary differential systems with min-max terms and applications to the fuzzy differential equations, Adv. Differ. Equ., 2015 (2015) · Zbl 1422.34004 · doi:10.1186/s13662-015-0708-z
[54] Yan, L.; Liu, J.; Luo, Z., Existence and multiplicity of solutions for second-order impulsive differential equations on the half-line, Adv. Differ. Equ., 2013 (2013) · Zbl 1391.34030 · doi:10.1186/1687-1847-2013-293
[55] Liu, Y.; Wu, J., Fixed point theorems in piecewise continuous function spaces and applications to some nonlinear problems, Math. Methods Appl. Sci., 37, 4, 508-517 (2014) · Zbl 1524.47065 · doi:10.1002/mma.2809
[56] Zhou, S.; Jiang, Y., Finite volume methods for N-dimensional time fractional Fokker-Planck equations, Bull. Malays. Math. Sci. Soc., 42, 6, 3167-3186 (2019) · Zbl 1426.65141 · doi:10.1007/s40840-018-0652-7
[57] Liu, F.; Feng, L.; Vo, A.; Li, J., Unstructured-mesh Galerkin finite element method for the two-dimensional multi-term time-space fractional Bloch-Torrey equations on irregular convex domains, Comput. Math. Appl., 78, 5, 1637-1650 (2019) · Zbl 1442.65268 · doi:10.1016/j.camwa.2019.01.007
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.