- Previous Article
- DCDS-B Home
- This Issue
-
Next Article
A study on the positive nonconstant steady states of nonlocal chemotaxis systems
On positive solutions and the Omega limit set for a class of delay differential equations
1. | Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing, 100084, China |
2. | School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China |
3. | Zhou Pei-Yuan Center for Applied Mathematics, MOE Key Laboratory of Bioinformatics, Tsinghua University, Beijing, 100084, China |
References:
[1] |
J. Adamson, The relationship of erythropoietin and iron metabolism to red blood cell production in humans, Semin. Oncol., 21 (1974), 9-15. |
[2] |
J. Bélair and M. C. Mackey, Consumer memory and price fluctuations in commodity markets: An integrodifferential model, Journal of Dynamics and Differential Equations, 1 (1989), 299-325.
doi: 10.1007/BF01053930. |
[3] |
D. L. Bellman and S. A. Gourley, Asymptotic properties of a delay differential equation model for the interaction of glucose with plasma and interstitial insulin, Applied Mathematics and Computation, 151 (2004), 189-207.
doi: 10.1016/S0096-3003(03)00332-1. |
[4] |
S. Bernard, J. Bélair and M. C. Mackey, Oscillations in cyclical neutropenia: New evidence based on mathematical modeling, Journal of Theoretical Biology, 223 (2003), 283-298.
doi: 10.1016/S0022-5193(03)00090-0. |
[5] |
C. Colijn and M. C. Mackey, A mathematical model of hematopoiesis-I. Periodic chronic myelogenous leukemia, Journal of Theoretical Biology, 237 (2005), 117-132.
doi: 10.1016/j.jtbi.2005.03.033. |
[6] |
C. Colijn and M. C. Mackey, A mathematical model of hematopoiesis: II. Cyclical neutropenia, Journal of Theoretical Biology, 237 (2005), 133-146.
doi: 10.1016/j.jtbi.2005.03.034. |
[7] |
C. Colijn and M. C. Mackey, Bifurcation and bistability in a model of hematopoietic regulation, SIAM Journal on Applied Dynamical Systems, 6 (2007), 378-394.
doi: 10.1137/050640072. |
[8] |
B. Dorizzi, B. Grammaticos, M. Le Berre, Y. Pomeau, E. Ressayre and A. Tallet, Statistics and dimension of chaos in differential delay systems, Physical Review A, 35 (1987), 328-339.
doi: 10.1103/PhysRevA.35.328. |
[9] |
S. A. Gourley and Y. Kuang, A delay reaction-diffusion model of the spread of bacteriophage infection, SIAM Journal on Applied Mathematics, 65 (2005), 550-566.
doi: 10.1137/S0036139903436613. |
[10] |
J. Lei and M. C. Mackey, Stochastic differential delay equation, moment stability, and application to hematopoietic stem cell regulation system, SIAM Journal on Applied Mathematics, 67 (2007), 387-407.
doi: 10.1137/060650234. |
[11] |
J. Lei and M. C. Mackey, Deterministic Brownian motion generated from differential delay equations, Physical Review E, 84 (2011), 041105.
doi: 10.1103/PhysRevE.84.041105. |
[12] |
J. Lei and M. C. Mackey, Multistability in an age-structured model of hematopoiesis: Cyclical neutropenia, Journal of Theoretical Biology, 270 (2011), 143-153.
doi: 10.1016/j.jtbi.2010.11.024. |
[13] |
M. C. Mackey and L. Glass, Oscillation and chaos in physiological control systems, Science, 197 (1977), 287-289.
doi: 10.1126/science.267326. |
[14] |
J. Mahaffy, J. Bélair and M. C. Mackey, Hematopoietic model with moving boundary condition and state dependent delay: Applications in erythropoiesis, Journal of Theoretical Biology, 190 (1998), 135-146.
doi: 10.1006/jtbi.1997.0537. |
[15] |
M. Silva, D. Grillot, A. Benito, C. Richard, G. Nunez and J. Fernandez-Luna, Erythropoietin can promote erythroid progenitor survival by repressing apoptosis through bcl-1 and bcl-2, Blood, 88 (1996), 1576-1582. |
[16] |
J. C. Sprott, A simple chaotic delay differential equation, Physics Letters A, 366 (2007), 397-402.
doi: 10.1016/j.physleta.2007.01.083. |
show all references
References:
[1] |
J. Adamson, The relationship of erythropoietin and iron metabolism to red blood cell production in humans, Semin. Oncol., 21 (1974), 9-15. |
[2] |
J. Bélair and M. C. Mackey, Consumer memory and price fluctuations in commodity markets: An integrodifferential model, Journal of Dynamics and Differential Equations, 1 (1989), 299-325.
doi: 10.1007/BF01053930. |
[3] |
D. L. Bellman and S. A. Gourley, Asymptotic properties of a delay differential equation model for the interaction of glucose with plasma and interstitial insulin, Applied Mathematics and Computation, 151 (2004), 189-207.
doi: 10.1016/S0096-3003(03)00332-1. |
[4] |
S. Bernard, J. Bélair and M. C. Mackey, Oscillations in cyclical neutropenia: New evidence based on mathematical modeling, Journal of Theoretical Biology, 223 (2003), 283-298.
doi: 10.1016/S0022-5193(03)00090-0. |
[5] |
C. Colijn and M. C. Mackey, A mathematical model of hematopoiesis-I. Periodic chronic myelogenous leukemia, Journal of Theoretical Biology, 237 (2005), 117-132.
doi: 10.1016/j.jtbi.2005.03.033. |
[6] |
C. Colijn and M. C. Mackey, A mathematical model of hematopoiesis: II. Cyclical neutropenia, Journal of Theoretical Biology, 237 (2005), 133-146.
doi: 10.1016/j.jtbi.2005.03.034. |
[7] |
C. Colijn and M. C. Mackey, Bifurcation and bistability in a model of hematopoietic regulation, SIAM Journal on Applied Dynamical Systems, 6 (2007), 378-394.
doi: 10.1137/050640072. |
[8] |
B. Dorizzi, B. Grammaticos, M. Le Berre, Y. Pomeau, E. Ressayre and A. Tallet, Statistics and dimension of chaos in differential delay systems, Physical Review A, 35 (1987), 328-339.
doi: 10.1103/PhysRevA.35.328. |
[9] |
S. A. Gourley and Y. Kuang, A delay reaction-diffusion model of the spread of bacteriophage infection, SIAM Journal on Applied Mathematics, 65 (2005), 550-566.
doi: 10.1137/S0036139903436613. |
[10] |
J. Lei and M. C. Mackey, Stochastic differential delay equation, moment stability, and application to hematopoietic stem cell regulation system, SIAM Journal on Applied Mathematics, 67 (2007), 387-407.
doi: 10.1137/060650234. |
[11] |
J. Lei and M. C. Mackey, Deterministic Brownian motion generated from differential delay equations, Physical Review E, 84 (2011), 041105.
doi: 10.1103/PhysRevE.84.041105. |
[12] |
J. Lei and M. C. Mackey, Multistability in an age-structured model of hematopoiesis: Cyclical neutropenia, Journal of Theoretical Biology, 270 (2011), 143-153.
doi: 10.1016/j.jtbi.2010.11.024. |
[13] |
M. C. Mackey and L. Glass, Oscillation and chaos in physiological control systems, Science, 197 (1977), 287-289.
doi: 10.1126/science.267326. |
[14] |
J. Mahaffy, J. Bélair and M. C. Mackey, Hematopoietic model with moving boundary condition and state dependent delay: Applications in erythropoiesis, Journal of Theoretical Biology, 190 (1998), 135-146.
doi: 10.1006/jtbi.1997.0537. |
[15] |
M. Silva, D. Grillot, A. Benito, C. Richard, G. Nunez and J. Fernandez-Luna, Erythropoietin can promote erythroid progenitor survival by repressing apoptosis through bcl-1 and bcl-2, Blood, 88 (1996), 1576-1582. |
[16] |
J. C. Sprott, A simple chaotic delay differential equation, Physics Letters A, 366 (2007), 397-402.
doi: 10.1016/j.physleta.2007.01.083. |
[1] |
Yukihiko Nakata. Existence of a period two solution of a delay differential equation. Discrete and Continuous Dynamical Systems - S, 2021, 14 (3) : 1103-1110. doi: 10.3934/dcdss.2020392 |
[2] |
Artem Dudko. Computability of the Julia set. Nonrecurrent critical orbits. Discrete and Continuous Dynamical Systems, 2014, 34 (7) : 2751-2778. doi: 10.3934/dcds.2014.34.2751 |
[3] |
Qianqian Han, Bo Deng, Xiao-Song Yang. The existence of $ \omega $-limit set for a modified Nosé-Hoover oscillator. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022043 |
[4] |
Josef Diblík. Long-time behavior of positive solutions of a differential equation with state-dependent delay. Discrete and Continuous Dynamical Systems - S, 2020, 13 (1) : 31-46. doi: 10.3934/dcdss.2020002 |
[5] |
Jaume Llibre, Ana Rodrigues. On the limit cycles of the Floquet differential equation. Discrete and Continuous Dynamical Systems - B, 2014, 19 (4) : 1129-1136. doi: 10.3934/dcdsb.2014.19.1129 |
[6] |
Carlos Arnoldo Morales, M. J. Pacifico. Lyapunov stability of $\omega$-limit sets. Discrete and Continuous Dynamical Systems, 2002, 8 (3) : 671-674. doi: 10.3934/dcds.2002.8.671 |
[7] |
Zhiming Guo, Zhi-Chun Yang, Xingfu Zou. Existence and uniqueness of positive solution to a non-local differential equation with homogeneous Dirichlet boundary condition---A non-monotone case. Communications on Pure and Applied Analysis, 2012, 11 (5) : 1825-1838. doi: 10.3934/cpaa.2012.11.1825 |
[8] |
Liangwei Wang, Jingxue Yin, Chunhua Jin. $\omega$-limit sets for porous medium equation with initial data in some weighted spaces. Discrete and Continuous Dynamical Systems - B, 2013, 18 (1) : 223-236. doi: 10.3934/dcdsb.2013.18.223 |
[9] |
Pablo Amster, Alberto Déboli, Manuel Pinto. Hartman and Nirenberg type results for systems of delay differential equations under $ (\omega,Q) $-periodic conditions. Discrete and Continuous Dynamical Systems - B, 2022, 27 (6) : 3019-3037. doi: 10.3934/dcdsb.2021171 |
[10] |
István Győri, Ferenc Hartung, Nahed A. Mohamady. Boundedness of positive solutions of a system of nonlinear delay differential equations. Discrete and Continuous Dynamical Systems - B, 2018, 23 (2) : 809-836. doi: 10.3934/dcdsb.2018044 |
[11] |
Teresa Faria, Rubén Figueroa. Positive periodic solutions for systems of impulsive delay differential equations. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022070 |
[12] |
Andrew D. Barwell, Chris Good, Piotr Oprocha, Brian E. Raines. Characterizations of $\omega$-limit sets in topologically hyperbolic systems. Discrete and Continuous Dynamical Systems, 2013, 33 (5) : 1819-1833. doi: 10.3934/dcds.2013.33.1819 |
[13] |
Hongyong Cui, Peter E. Kloeden, Meihua Yang. Forward omega limit sets of nonautonomous dynamical systems. Discrete and Continuous Dynamical Systems - S, 2020, 13 (4) : 1103-1114. doi: 10.3934/dcdss.2020065 |
[14] |
Bruce Kitchens, Michał Misiurewicz. Omega-limit sets for spiral maps. Discrete and Continuous Dynamical Systems, 2010, 27 (2) : 787-798. doi: 10.3934/dcds.2010.27.787 |
[15] |
P. Dormayer, A. F. Ivanov. Symmetric periodic solutions of a delay differential equation. Conference Publications, 1998, 1998 (Special) : 220-230. doi: 10.3934/proc.1998.1998.220 |
[16] |
Yihong Du, Yoshio Yamada. On the long-time limit of positive solutions to the degenerate logistic equation. Discrete and Continuous Dynamical Systems, 2009, 25 (1) : 123-132. doi: 10.3934/dcds.2009.25.123 |
[17] |
Galina V. Grishina. On positive solution to a second order elliptic equation with a singular nonlinearity. Communications on Pure and Applied Analysis, 2010, 9 (5) : 1335-1343. doi: 10.3934/cpaa.2010.9.1335 |
[18] |
Xiang-Dong Fang. A positive solution for an asymptotically cubic quasilinear Schrödinger equation. Communications on Pure and Applied Analysis, 2019, 18 (1) : 51-64. doi: 10.3934/cpaa.2019004 |
[19] |
István Győri, Yukihiko Nakata, Gergely Röst. Unbounded and blow-up solutions for a delay logistic equation with positive feedback. Communications on Pure and Applied Analysis, 2018, 17 (6) : 2845-2854. doi: 10.3934/cpaa.2018134 |
[20] |
Chunhua Jin, Jingxue Yin, Zejia Wang. Positive periodic solutions to a nonlinear fourth-order differential equation. Communications on Pure and Applied Analysis, 2008, 7 (5) : 1225-1235. doi: 10.3934/cpaa.2008.7.1225 |
2021 Impact Factor: 1.497
Tools
Metrics
Other articles
by authors
[Back to Top]