
-
Previous Article
A note on multiplicity of solutions near resonance of semilinear elliptic equations
- CPAA Home
- This Issue
-
Next Article
The regularity of a degenerate Goursat problem for the 2-D isothermal Euler equations
Almost periodicity analysis for a delayed Nicholson's blowflies model with nonlinear density-dependent mortality term
1. | School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114, Hunan, China |
2. | Hunan Provincial Key Laboratory of Mathematical Modeling, and Analysis in Engineering, Changsha 410114, Hunan, China |
This paper mainly investigates a class of almost periodic Nicholson's blowflies model involving a nonlinear density-dependent mortality term and time-varying delays. Combining Lyapunov function method and differential inequality approach, some novel assertions are established to guarantee the existence and exponential stability of positive almost periodic solutions for the addressed model, which generalize and refine the corresponding results in some recent published literatures. Particularly, an example and its numerical simulations are given to support the proposed approach.
References:
[1] |
A. M. Fink, Almost Periodic Differential Equations, Lecture Notes in Mathematics, Vol. 377, Springer-Verlag, Berlin, 1974. |
[2] |
C. Huang and H. Zhang, Periodicity of non-autonomous inertial neural networks involving proportional delays and non-reduced order method, International Journal of Biomathematics, 12 (2019), 1950016.
doi: 10.1142/S1793524519500165. |
[3] |
C. Zhang, Almost Periodic Type Functions and Ergodicity, Kluwer Academic/Science Press, Beijing, 2003.
doi: 10.1007/978-94-007-1073-3.![]() ![]() |
[4] |
T. M. Touaoula,
Global stability for a class of functional differential equations (Application to Nicholson's blowflies and Mackey-Glass models), Discrete & Continuous Dynamical Systems -A, 38 (2018), 4391-4419.
doi: 10.3934/dcds.2018191. |
[5] |
S. Chen and J. Yu,
Stability and bifurcation on predator-prey systems with nonlocal prey competition, Discrete & Continuous Dynamical Systems -A, 38 (2018), 43-62.
doi: 10.3934/dcds.2018002. |
[6] |
T. Shibata,
Global behavior of bifurcation curves for the nonlinear eigenvalue problems with periodic nonlinear terms, Communications on Pure & Applied Analysis, 17 (2018), 2139-2147.
doi: 10.3934/cpaa.2018102. |
[7] |
C. Huang, Y. Qiao, L. Huang and R. Agarwal,
Dynamical behaviors of a food-chain model with stage structure and time delays, Advances in Difference Equations, 186 (2018), 1-26.
doi: 10.1186/s13662-018-1589-8. |
[8] |
Z. Yang, C. Huang and X. Zou,
Effect of impulsive controls in a model system for age-structured population over a patchy environment, Journal of Mathematical Biology, 76 (2018), 1387-1419.
doi: 10.1007/s00285-017-1172-z. |
[9] |
C. Huang, Z. Yang, T. Yi and X. Zou,
On the basins of attraction for a class of delay differential equations with non-monotone bistable nonlinearities, Journal of Differential Equations, 256 (2014), 2101-2114.
doi: 10.1016/j.jde.2013.12.015. |
[10] |
B. Liu,
Global exponential stability of positive periodic solutions for a delayed Nicholsons blowflies model, Journal of Mathematical Analysis and Applications, 412 (2014), 212-221.
doi: 10.1016/j.jmaa.2013.10.049. |
[11] |
B. Liu,
New results on global exponential stability of almost periodic solutions for a delayed Nicholson blowflies model, Annales Polonici Mathematici, 113 (2015), 191-208.
doi: 10.4064/ap113-2-6. |
[12] |
W. Xiong,
New results on positive pseudo-almost periodic solutions for a delayed Nicholson's blowflies model, Nonlinear Dynamics, 85 (2016), 563-571.
doi: 10.1007/s11071-016-2706-4. |
[13] |
Y. Xu, New stability theorem for periodic Nicholson's model with mortality term, Applied Mathematics Letters, (2019).
doi: 10.1016/j.aml.2019.02.021. |
[14] |
B. Liu,
Almost periodic solutions for a delayed Nicholson's blowflies model with a nonlinear density-dependent mortality term, Advances in Difference Equations, 72 (2014), 1-16.
doi: 10.1186/1687-1847-2014-72. |
[15] |
B. Liu,
Positive periodic solutions for a nonlinear density-dependent mortality Nicholson's blowflies model, Kodai Mathematical Journal, 37 (2014), 157-173.
doi: 10.2996/kmj/1396008252. |
[16] |
L. Yao,
Dynamics of Nicholson's blowflies models with a nonlinear density-dependent mortality, Applied Mathematical Modelling, 64 (2018), 185-195.
doi: 10.1016/j.apm.2018.07.007. |
[17] |
Y. Tang, Global attractivity of asymptotically almost periodic Nicholson's blowflies models with a nonlinear density-dependent mortality term, International Journal of Biomathematics, 11 (2018), 1850079.
doi: 10.1142/S1793524518500791. |
[18] |
Y. Xu,
Existence and global exponential stability of positive almost periodic solutions for a delayed Nicholson's blowflies model, Journal of the Korean Mathematical Society, 51 (2014), 473-493.
doi: 10.4134/JKMS.2014.51.3.473. |
[19] |
W. Chen and W. Wang,
Almost periodic solutions for a delayed Nicholson's blowflies system with nonlinear density-dependent mortality terms and patch structure, Advances in Difference Equations, 205 (2014), 1-19.
doi: 10.1186/1687-1847-2014-205. |
[20] |
P. Liu, L. Zhang and et al,
Global exponential stability of almost periodic solutions for Nicholson's Blowflies system with nonlinear density-dependent mortality terms and patch structure, Mathematical Modelling and Analysis, 22 (2017), 484-502.
doi: 10.3846/13926292.2017.1329171. |
[21] |
L. Berezansky, E. Braverman and L. Idels,
Nicholson's blowflies differential equations revisited: Main results and open problems, Applied Mathematical Modelling, 34 (2010), 1405-1417.
doi: 10.1016/j.apm.2009.08.027. |
[22] |
J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional Differential Equations, Springer-Verlag, New York, 1993.
doi: 10.1007/978-1-4612-4342-7. |
[23] |
H. Smith, An Introduction to Delay Differential Equations with Applications to the Life Sciences, Springer-Verlag, New York, 2011.
doi: 10.1007/978-1-4419-7646-8. |
[24] |
L. Duan, X. Fang and C. Huang,
Global exponential convergence in a delayed almost periodic Nicholson's blowflies model with discontinuous harvesting, Mathematical Methods in the Applied Sciences, 41 (2018), 1954-1965.
doi: 10.1002/mma.4722. |
[25] |
L. Duan and C. Huang,
Existence and global attractivity of almost periodic solutions for a delayed differential neoclassical growth model, Mathematical Methods in the Applied Sciences, 40 (2017), 814-822.
doi: 10.1002/mma.4019. |
show all references
References:
[1] |
A. M. Fink, Almost Periodic Differential Equations, Lecture Notes in Mathematics, Vol. 377, Springer-Verlag, Berlin, 1974. |
[2] |
C. Huang and H. Zhang, Periodicity of non-autonomous inertial neural networks involving proportional delays and non-reduced order method, International Journal of Biomathematics, 12 (2019), 1950016.
doi: 10.1142/S1793524519500165. |
[3] |
C. Zhang, Almost Periodic Type Functions and Ergodicity, Kluwer Academic/Science Press, Beijing, 2003.
doi: 10.1007/978-94-007-1073-3.![]() ![]() |
[4] |
T. M. Touaoula,
Global stability for a class of functional differential equations (Application to Nicholson's blowflies and Mackey-Glass models), Discrete & Continuous Dynamical Systems -A, 38 (2018), 4391-4419.
doi: 10.3934/dcds.2018191. |
[5] |
S. Chen and J. Yu,
Stability and bifurcation on predator-prey systems with nonlocal prey competition, Discrete & Continuous Dynamical Systems -A, 38 (2018), 43-62.
doi: 10.3934/dcds.2018002. |
[6] |
T. Shibata,
Global behavior of bifurcation curves for the nonlinear eigenvalue problems with periodic nonlinear terms, Communications on Pure & Applied Analysis, 17 (2018), 2139-2147.
doi: 10.3934/cpaa.2018102. |
[7] |
C. Huang, Y. Qiao, L. Huang and R. Agarwal,
Dynamical behaviors of a food-chain model with stage structure and time delays, Advances in Difference Equations, 186 (2018), 1-26.
doi: 10.1186/s13662-018-1589-8. |
[8] |
Z. Yang, C. Huang and X. Zou,
Effect of impulsive controls in a model system for age-structured population over a patchy environment, Journal of Mathematical Biology, 76 (2018), 1387-1419.
doi: 10.1007/s00285-017-1172-z. |
[9] |
C. Huang, Z. Yang, T. Yi and X. Zou,
On the basins of attraction for a class of delay differential equations with non-monotone bistable nonlinearities, Journal of Differential Equations, 256 (2014), 2101-2114.
doi: 10.1016/j.jde.2013.12.015. |
[10] |
B. Liu,
Global exponential stability of positive periodic solutions for a delayed Nicholsons blowflies model, Journal of Mathematical Analysis and Applications, 412 (2014), 212-221.
doi: 10.1016/j.jmaa.2013.10.049. |
[11] |
B. Liu,
New results on global exponential stability of almost periodic solutions for a delayed Nicholson blowflies model, Annales Polonici Mathematici, 113 (2015), 191-208.
doi: 10.4064/ap113-2-6. |
[12] |
W. Xiong,
New results on positive pseudo-almost periodic solutions for a delayed Nicholson's blowflies model, Nonlinear Dynamics, 85 (2016), 563-571.
doi: 10.1007/s11071-016-2706-4. |
[13] |
Y. Xu, New stability theorem for periodic Nicholson's model with mortality term, Applied Mathematics Letters, (2019).
doi: 10.1016/j.aml.2019.02.021. |
[14] |
B. Liu,
Almost periodic solutions for a delayed Nicholson's blowflies model with a nonlinear density-dependent mortality term, Advances in Difference Equations, 72 (2014), 1-16.
doi: 10.1186/1687-1847-2014-72. |
[15] |
B. Liu,
Positive periodic solutions for a nonlinear density-dependent mortality Nicholson's blowflies model, Kodai Mathematical Journal, 37 (2014), 157-173.
doi: 10.2996/kmj/1396008252. |
[16] |
L. Yao,
Dynamics of Nicholson's blowflies models with a nonlinear density-dependent mortality, Applied Mathematical Modelling, 64 (2018), 185-195.
doi: 10.1016/j.apm.2018.07.007. |
[17] |
Y. Tang, Global attractivity of asymptotically almost periodic Nicholson's blowflies models with a nonlinear density-dependent mortality term, International Journal of Biomathematics, 11 (2018), 1850079.
doi: 10.1142/S1793524518500791. |
[18] |
Y. Xu,
Existence and global exponential stability of positive almost periodic solutions for a delayed Nicholson's blowflies model, Journal of the Korean Mathematical Society, 51 (2014), 473-493.
doi: 10.4134/JKMS.2014.51.3.473. |
[19] |
W. Chen and W. Wang,
Almost periodic solutions for a delayed Nicholson's blowflies system with nonlinear density-dependent mortality terms and patch structure, Advances in Difference Equations, 205 (2014), 1-19.
doi: 10.1186/1687-1847-2014-205. |
[20] |
P. Liu, L. Zhang and et al,
Global exponential stability of almost periodic solutions for Nicholson's Blowflies system with nonlinear density-dependent mortality terms and patch structure, Mathematical Modelling and Analysis, 22 (2017), 484-502.
doi: 10.3846/13926292.2017.1329171. |
[21] |
L. Berezansky, E. Braverman and L. Idels,
Nicholson's blowflies differential equations revisited: Main results and open problems, Applied Mathematical Modelling, 34 (2010), 1405-1417.
doi: 10.1016/j.apm.2009.08.027. |
[22] |
J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional Differential Equations, Springer-Verlag, New York, 1993.
doi: 10.1007/978-1-4612-4342-7. |
[23] |
H. Smith, An Introduction to Delay Differential Equations with Applications to the Life Sciences, Springer-Verlag, New York, 2011.
doi: 10.1007/978-1-4419-7646-8. |
[24] |
L. Duan, X. Fang and C. Huang,
Global exponential convergence in a delayed almost periodic Nicholson's blowflies model with discontinuous harvesting, Mathematical Methods in the Applied Sciences, 41 (2018), 1954-1965.
doi: 10.1002/mma.4722. |
[25] |
L. Duan and C. Huang,
Existence and global attractivity of almost periodic solutions for a delayed differential neoclassical growth model, Mathematical Methods in the Applied Sciences, 40 (2017), 814-822.
doi: 10.1002/mma.4019. |
[1] |
Tong Tang, Jianzhu Sun. Local well-posedness for the density-dependent incompressible magneto-micropolar system with vacuum. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020377 |
[2] |
Yang Liu. Global existence and exponential decay of strong solutions to the cauchy problem of 3D density-dependent Navier-Stokes equations with vacuum. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1291-1303. doi: 10.3934/dcdsb.2020163 |
[3] |
Mengyu Cheng, Zhenxin Liu. Periodic, almost periodic and almost automorphic solutions for SPDEs with monotone coefficients. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021026 |
[4] |
Jiangtao Yang. Permanence, extinction and periodic solution of a stochastic single-species model with Lévy noises. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020371 |
[5] |
Amira M. Boughoufala, Ahmed Y. Abdallah. Attractors for FitzHugh-Nagumo lattice systems with almost periodic nonlinear parts. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1549-1563. doi: 10.3934/dcdsb.2020172 |
[6] |
Skyler Simmons. Stability of Broucke's isosceles orbit. Discrete & Continuous Dynamical Systems - A, 2021 doi: 10.3934/dcds.2021015 |
[7] |
Wenbin Lv, Qingyuan Wang. Global existence for a class of Keller-Segel models with signal-dependent motility and general logistic term. Evolution Equations & Control Theory, 2021, 10 (1) : 25-36. doi: 10.3934/eect.2020040 |
[8] |
Yi Guan, Michal Fečkan, Jinrong Wang. Periodic solutions and Hyers-Ulam stability of atmospheric Ekman flows. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1157-1176. doi: 10.3934/dcds.2020313 |
[9] |
Hui Zhao, Zhengrong Liu, Yiren Chen. Global dynamics of a chemotaxis model with signal-dependent diffusion and sensitivity. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2021011 |
[10] |
Chao Wang, Qihuai Liu, Zhiguo Wang. Periodic bouncing solutions for Hill's type sub-linear oscillators with obstacles. Communications on Pure & Applied Analysis, 2021, 20 (1) : 281-300. doi: 10.3934/cpaa.2020266 |
[11] |
Eduard Feireisl, Elisabetta Rocca, Giulio Schimperna, Arghir Zarnescu. Weak sequential stability for a nonlinear model of nematic electrolytes. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 219-241. doi: 10.3934/dcdss.2020366 |
[12] |
Zhihua Liu, Yayun Wu, Xiangming Zhang. Existence of periodic wave trains for an age-structured model with diffusion. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2021009 |
[13] |
Ran Zhang, Shengqiang Liu. On the asymptotic behaviour of traveling wave solution for a discrete diffusive epidemic model. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 1197-1204. doi: 10.3934/dcdsb.2020159 |
[14] |
Yoichi Enatsu, Emiko Ishiwata, Takeo Ushijima. Traveling wave solution for a diffusive simple epidemic model with a free boundary. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 835-850. doi: 10.3934/dcdss.2020387 |
[15] |
Mohammad Ghani, Jingyu Li, Kaijun Zhang. Asymptotic stability of traveling fronts to a chemotaxis model with nonlinear diffusion. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021017 |
[16] |
Yi-Ming Tai, Zhengyang Zhang. Relaxation oscillations in a spruce-budworm interaction model with Holling's type II functional response. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021027 |
[17] |
Hai-Feng Huo, Shi-Ke Hu, Hong Xiang. Traveling wave solution for a diffusion SEIR epidemic model with self-protection and treatment. Electronic Research Archive, , () : -. doi: 10.3934/era.2020118 |
[18] |
Thazin Aye, Guanyu Shang, Ying Su. On a stage-structured population model in discrete periodic habitat: III. unimodal growth and delay effect. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2021005 |
[19] |
Yan'e Wang, Nana Tian, Hua Nie. Positive solution branches of two-species competition model in open advective environments. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2021006 |
[20] |
Yongjie Wang, Nan Gao. Some properties for almost cellular algebras. Electronic Research Archive, 2021, 29 (1) : 1681-1689. doi: 10.3934/era.2020086 |
2019 Impact Factor: 1.105
Tools
Metrics
Other articles
by authors
[Back to Top]