-
Previous Article
Stabilization of the wave equation with interior input delay and mixed Neumann-Dirichlet boundary
- DCDS-B Home
- This Issue
-
Next Article
On stability for impulsive delay differential equations and application to a periodic Lasota-Wazewska model
Moment stability for nonlinear stochastic growth kinetics of breast cancer stem cells with time-delays
1. | School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510006, China |
2. | Center of Clinical Pharmacology, The Third Xiangya Hospital, Central South University, Changsha 410083, China |
3. | Department of Mathematics, University of South Carolina, Columbia, SC 29208, United States |
References:
[1] |
S. Bao, Q. Wu, R. E. McLendon, Y. Hao, Q. Shi, A. B. Hjelmeland, M. W. Dewhirst, D. D. Bigner and J. N. Rich, Glioma stem cells promote radioresistance by preferential activation of the DNA damage response, Nature, 444 (2006), 756-760. |
[2] |
I. Ben-Porath, M. W. Thomson, V. J. Carey, R. Ge, G. W. Bell, A. Regev and R. A. Weinberg, An embryonic stem cell-like gene expression signature in poorly differentiated aggressive human tumors, Nature genetics, 40 (2008), 499-507. |
[3] |
L. O. Chua and L. Yang, Cellular neural netork: Theory and applications, IEEE Trans Circ Syst, 35 (1988), 1257-1272.
doi: 10.1109/31.7600. |
[4] |
A. Cicalese, G. Bonizzi, C. E. Pasi, M. Faretta, S. Ronzoni, B. Giulini, C. Brisken, S. Minucci, P. P. Di Fiore and P. G. Pelicci, The Tumor Suppressor p53 Regulates Polarity of Self-Renewing Divisions in Mammary Stem Cells, Cell, 138 (2009), 1083-1095. |
[5] |
P. Dalerba, R. W. Cho and M. F. Clarke, Cancer stem cells: Models and concepts, Annu. Rev. Med., 58 (2007), 267-284. |
[6] |
C. J. Guo, D. O'Regan, F. Q. Deng and R. Agarwal, Fixed points and exponential stability for a stochastic neutral cellular neural network, Applied Mathematics Letters, 26 (2013), 849-853.
doi: 10.1016/j.aml.2013.03.011. |
[7] |
C. J. Guo, D. O'Regan, F. Q. Deng and R. Agarwal, Fixed points and exponential stability for uncertain stochastic neural networks with multiple mixed time-delays,, Applicable Analysis, ().
|
[8] |
J. K. Hale, Theory of Functional Differential Equations, Springer-Verlag, 1977. |
[9] |
R. P. Hill and R. Perris, "Destemming" Cancer Stem Cells, Journal of the National Cancer Institute, 99 (2007), 1435-1440. |
[10] |
J. Hu, S. M. Zhong and L. Liang, Exponential stability analysis of stochastic delays cellular neural network, Chaos, Solitons and Fractals, 27 (2006), 1006-1010.
doi: 10.1016/j.chaos.2005.04.067. |
[11] |
H. Huang and J. D. Cao, Exponential stability analysis of uncertain stochastic neural networks with multiple delays, Nonlinear Anal: Real World Appl, 8 (2007), 646-653.
doi: 10.1016/j.nonrwa.2006.02.003. |
[12] |
G. Joya, M. A. Atencia and F. Sandoval, Hopfield neural networks for optimization: Study of the different dynamics, Neurocomputing, 43 (2002), 219-237.
doi: 10.1016/S0925-2312(01)00337-X. |
[13] |
W. J. Li and T. Lee, Hopfield neural networks for affine invariant matching, IEEE Trans Neural Networks, 12 (2001), 1400-1410. |
[14] |
X. F. Liu, S. Johnson, S. Liu, D. Kanojia, W. Yue, U. Singn, Q. Wang, Q. Wang, Q, Nie and H. X. Chen, Nonlinear growth kinetics of breast cancer stem cells: Implications for cancer stem cell targeted therapy, Scientific reports, 3 (2013)(OI: 10.1038/srep02473). |
[15] |
N. A. Lobo, Y. Shimono, D. Qian and M. F. Clarke, The biology of cancer stem cells, Annu. Rev. Cell Dev. Biol., 23 (2007), 675-699. |
[16] |
J. W. Luo, Fixed points and exponential stability for stochastic Volterra-Levin equations, J.Comput.Appl.Math., 234 (2010), 934-940.
doi: 10.1016/j.cam.2010.02.013. |
[17] |
S. Pece, D. Tosoni, S. Confalonieri, G. Mazzarol, M. Vecchi, S. Ronzoni, L. Bernard, G. Viale, P. G. Pelicci and P. P. Di Fiore, Biological and molecular heterogeneity of breast cancers correlates with their cancer stem cell content, Cell, 140 (2010), 62-73. |
[18] |
T. Reya, S. J. Morrison, M. F. Clarke and I. L. Weissman, Stem cells, cancer, and cancer stem cells, Nature, 414 (2001), 105-111. |
[19] |
M. Shipitsin, L. L. Campbell, P. Argani, S. Weremowicz, N. Bloushtain-Qimron, J. Yao, T. Nikolskaya, T. Serebryiskaya, R. Beroukhim, M. Hu and others, Molecular definition of breast tumor heterogeneity, Cancer cell, 11 (2007), 259-273. |
[20] |
B. T. Tan, C. Y. Park, L. E. Ailles and I. L. Weissman, The cancer stem cell hypothesis: A work in progress, Laboratory Investigation, 86 (2006), 1203-1207. |
[21] |
J. E. Visvader and G. J. Lindeman, Cancer stem cells in solid tumours: Accumulating evidence and unresolved questions, Nature Reviews Cancer, 8 (2008), 755-768. |
[22] |
Z. D. Wang, S. Laura, J. A. Fang and X. H. Liu, Exponential stability analysis of uncertain stochastic neural networks with mixed time-delays, Chaos, Solitons and Fractals, 32 (2007), 62-72.
doi: 10.1016/j.chaos.2005.10.061. |
[23] |
Z. D. Wang, Y. R. Liu and X. H. Liu, On global asymptotic stability analysis of neural networks with discrete and distributed delays, Phys Lett A, 345 (2005), 299-308. |
[24] |
S. Young, P. Scott and N. Nasrabadi, Object recognition using multilayer Hopfield neural networks, IEEE Trans Image Process, 6 (1997), 357-372.
doi: 10.1109/83.557336. |
[25] |
J. H. Zhang, P. Shi and J. Q. Qiu, Novel robust stability criteria for uncertain stochastic Hopfield neural networks with time-varying delays, Nonlinear Anal: Real World Appl, 8 (2007), 1349-1357.
doi: 10.1016/j.nonrwa.2006.06.010. |
show all references
References:
[1] |
S. Bao, Q. Wu, R. E. McLendon, Y. Hao, Q. Shi, A. B. Hjelmeland, M. W. Dewhirst, D. D. Bigner and J. N. Rich, Glioma stem cells promote radioresistance by preferential activation of the DNA damage response, Nature, 444 (2006), 756-760. |
[2] |
I. Ben-Porath, M. W. Thomson, V. J. Carey, R. Ge, G. W. Bell, A. Regev and R. A. Weinberg, An embryonic stem cell-like gene expression signature in poorly differentiated aggressive human tumors, Nature genetics, 40 (2008), 499-507. |
[3] |
L. O. Chua and L. Yang, Cellular neural netork: Theory and applications, IEEE Trans Circ Syst, 35 (1988), 1257-1272.
doi: 10.1109/31.7600. |
[4] |
A. Cicalese, G. Bonizzi, C. E. Pasi, M. Faretta, S. Ronzoni, B. Giulini, C. Brisken, S. Minucci, P. P. Di Fiore and P. G. Pelicci, The Tumor Suppressor p53 Regulates Polarity of Self-Renewing Divisions in Mammary Stem Cells, Cell, 138 (2009), 1083-1095. |
[5] |
P. Dalerba, R. W. Cho and M. F. Clarke, Cancer stem cells: Models and concepts, Annu. Rev. Med., 58 (2007), 267-284. |
[6] |
C. J. Guo, D. O'Regan, F. Q. Deng and R. Agarwal, Fixed points and exponential stability for a stochastic neutral cellular neural network, Applied Mathematics Letters, 26 (2013), 849-853.
doi: 10.1016/j.aml.2013.03.011. |
[7] |
C. J. Guo, D. O'Regan, F. Q. Deng and R. Agarwal, Fixed points and exponential stability for uncertain stochastic neural networks with multiple mixed time-delays,, Applicable Analysis, ().
|
[8] |
J. K. Hale, Theory of Functional Differential Equations, Springer-Verlag, 1977. |
[9] |
R. P. Hill and R. Perris, "Destemming" Cancer Stem Cells, Journal of the National Cancer Institute, 99 (2007), 1435-1440. |
[10] |
J. Hu, S. M. Zhong and L. Liang, Exponential stability analysis of stochastic delays cellular neural network, Chaos, Solitons and Fractals, 27 (2006), 1006-1010.
doi: 10.1016/j.chaos.2005.04.067. |
[11] |
H. Huang and J. D. Cao, Exponential stability analysis of uncertain stochastic neural networks with multiple delays, Nonlinear Anal: Real World Appl, 8 (2007), 646-653.
doi: 10.1016/j.nonrwa.2006.02.003. |
[12] |
G. Joya, M. A. Atencia and F. Sandoval, Hopfield neural networks for optimization: Study of the different dynamics, Neurocomputing, 43 (2002), 219-237.
doi: 10.1016/S0925-2312(01)00337-X. |
[13] |
W. J. Li and T. Lee, Hopfield neural networks for affine invariant matching, IEEE Trans Neural Networks, 12 (2001), 1400-1410. |
[14] |
X. F. Liu, S. Johnson, S. Liu, D. Kanojia, W. Yue, U. Singn, Q. Wang, Q. Wang, Q, Nie and H. X. Chen, Nonlinear growth kinetics of breast cancer stem cells: Implications for cancer stem cell targeted therapy, Scientific reports, 3 (2013)(OI: 10.1038/srep02473). |
[15] |
N. A. Lobo, Y. Shimono, D. Qian and M. F. Clarke, The biology of cancer stem cells, Annu. Rev. Cell Dev. Biol., 23 (2007), 675-699. |
[16] |
J. W. Luo, Fixed points and exponential stability for stochastic Volterra-Levin equations, J.Comput.Appl.Math., 234 (2010), 934-940.
doi: 10.1016/j.cam.2010.02.013. |
[17] |
S. Pece, D. Tosoni, S. Confalonieri, G. Mazzarol, M. Vecchi, S. Ronzoni, L. Bernard, G. Viale, P. G. Pelicci and P. P. Di Fiore, Biological and molecular heterogeneity of breast cancers correlates with their cancer stem cell content, Cell, 140 (2010), 62-73. |
[18] |
T. Reya, S. J. Morrison, M. F. Clarke and I. L. Weissman, Stem cells, cancer, and cancer stem cells, Nature, 414 (2001), 105-111. |
[19] |
M. Shipitsin, L. L. Campbell, P. Argani, S. Weremowicz, N. Bloushtain-Qimron, J. Yao, T. Nikolskaya, T. Serebryiskaya, R. Beroukhim, M. Hu and others, Molecular definition of breast tumor heterogeneity, Cancer cell, 11 (2007), 259-273. |
[20] |
B. T. Tan, C. Y. Park, L. E. Ailles and I. L. Weissman, The cancer stem cell hypothesis: A work in progress, Laboratory Investigation, 86 (2006), 1203-1207. |
[21] |
J. E. Visvader and G. J. Lindeman, Cancer stem cells in solid tumours: Accumulating evidence and unresolved questions, Nature Reviews Cancer, 8 (2008), 755-768. |
[22] |
Z. D. Wang, S. Laura, J. A. Fang and X. H. Liu, Exponential stability analysis of uncertain stochastic neural networks with mixed time-delays, Chaos, Solitons and Fractals, 32 (2007), 62-72.
doi: 10.1016/j.chaos.2005.10.061. |
[23] |
Z. D. Wang, Y. R. Liu and X. H. Liu, On global asymptotic stability analysis of neural networks with discrete and distributed delays, Phys Lett A, 345 (2005), 299-308. |
[24] |
S. Young, P. Scott and N. Nasrabadi, Object recognition using multilayer Hopfield neural networks, IEEE Trans Image Process, 6 (1997), 357-372.
doi: 10.1109/83.557336. |
[25] |
J. H. Zhang, P. Shi and J. Q. Qiu, Novel robust stability criteria for uncertain stochastic Hopfield neural networks with time-varying delays, Nonlinear Anal: Real World Appl, 8 (2007), 1349-1357.
doi: 10.1016/j.nonrwa.2006.06.010. |
[1] |
Evelyn Buckwar, Girolama Notarangelo. A note on the analysis of asymptotic mean-square stability properties for systems of linear stochastic delay differential equations. Discrete and Continuous Dynamical Systems - B, 2013, 18 (6) : 1521-1531. doi: 10.3934/dcdsb.2013.18.1521 |
[2] |
Wei Wang, Kai Liu, Xiulian Wang. Sensitivity to small delays of mean square stability for stochastic neutral evolution equations. Communications on Pure and Applied Analysis, 2020, 19 (4) : 2403-2418. doi: 10.3934/cpaa.2020105 |
[3] |
Henri Schurz. Moment attractivity, stability and contractivity exponents of stochastic dynamical systems. Discrete and Continuous Dynamical Systems, 2001, 7 (3) : 487-515. doi: 10.3934/dcds.2001.7.487 |
[4] |
Pham Huu Anh Ngoc. New criteria for exponential stability in mean square of stochastic functional differential equations with infinite delay. Evolution Equations and Control Theory, 2021 doi: 10.3934/eect.2021040 |
[5] |
Manuel Delgado, Ítalo Bruno Mendes Duarte, Antonio Suárez Fernández. Nonlocal elliptic system arising from the growth of cancer stem cells. Discrete and Continuous Dynamical Systems - B, 2018, 23 (4) : 1767-1795. doi: 10.3934/dcdsb.2018083 |
[6] |
J. Ignacio Tello. On a mathematical model of tumor growth based on cancer stem cells. Mathematical Biosciences & Engineering, 2013, 10 (1) : 263-278. doi: 10.3934/mbe.2013.10.263 |
[7] |
Alexey G. Mazko. Positivity, robust stability and comparison of dynamic systems. Conference Publications, 2011, 2011 (Special) : 1042-1051. doi: 10.3934/proc.2011.2011.1042 |
[8] |
Giovanni Russo, Fabian Wirth. Matrix measures, stability and contraction theory for dynamical systems on time scales. Discrete and Continuous Dynamical Systems - B, 2022, 27 (6) : 3345-3374. doi: 10.3934/dcdsb.2021188 |
[9] |
Gregory Berkolaiko, Cónall Kelly, Alexandra Rodkina. Sharp pathwise asymptotic stability criteria for planar systems of linear stochastic difference equations. Conference Publications, 2011, 2011 (Special) : 163-173. doi: 10.3934/proc.2011.2011.163 |
[10] |
Yi Zhang, Yuyun Zhao, Tao Xu, Xin Liu. $p$th Moment absolute exponential stability of stochastic control system with Markovian switching. Journal of Industrial and Management Optimization, 2016, 12 (2) : 471-486. doi: 10.3934/jimo.2016.12.471 |
[11] |
Kai Du, Jianhui Huang, Zhen Wu. Linear quadratic mean-field-game of backward stochastic differential systems. Mathematical Control and Related Fields, 2018, 8 (3&4) : 653-678. doi: 10.3934/mcrf.2018028 |
[12] |
Alexander Pimenov, Dmitrii I. Rachinskii. Linear stability analysis of systems with Preisach memory. Discrete and Continuous Dynamical Systems - B, 2009, 11 (4) : 997-1018. doi: 10.3934/dcdsb.2009.11.997 |
[13] |
Arzu Ahmadova, Nazim I. Mahmudov, Juan J. Nieto. Exponential stability and stabilization of fractional stochastic degenerate evolution equations in a Hilbert space: Subordination principle. Evolution Equations and Control Theory, 2022 doi: 10.3934/eect.2022008 |
[14] |
Yuyun Zhao, Yi Zhang, Tao Xu, Ling Bai, Qian Zhang. pth moment exponential stability of hybrid stochastic functional differential equations by feedback control based on discrete-time state observations. Discrete and Continuous Dynamical Systems - B, 2017, 22 (1) : 209-226. doi: 10.3934/dcdsb.2017011 |
[15] |
Xiaowei Tang, Xilin Fu. New comparison principle with Razumikhin condition for impulsive infinite delay differential systems. Conference Publications, 2009, 2009 (Special) : 739-743. doi: 10.3934/proc.2009.2009.739 |
[16] |
Jianxun Liu, Shengjie Li, Yingrang Xu. Quantitative stability of the ERM formulation for a class of stochastic linear variational inequalities. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021083 |
[17] |
Bixiang Wang. Mean-square random invariant manifolds for stochastic differential equations. Discrete and Continuous Dynamical Systems, 2021, 41 (3) : 1449-1468. doi: 10.3934/dcds.2020324 |
[18] |
Zhen Li, Jicheng Liu. Synchronization for stochastic differential equations with nonlinear multiplicative noise in the mean square sense. Discrete and Continuous Dynamical Systems - B, 2019, 24 (10) : 5709-5736. doi: 10.3934/dcdsb.2019103 |
[19] |
Hailong Zhu, Jifeng Chu, Weinian Zhang. Mean-square almost automorphic solutions for stochastic differential equations with hyperbolicity. Discrete and Continuous Dynamical Systems, 2018, 38 (4) : 1935-1953. doi: 10.3934/dcds.2018078 |
[20] |
Huseyin Coskun. Nonlinear decomposition principle and fundamental matrix solutions for dynamic compartmental systems. Discrete and Continuous Dynamical Systems - B, 2019, 24 (12) : 6553-6605. doi: 10.3934/dcdsb.2019155 |
2020 Impact Factor: 1.327
Tools
Metrics
Other articles
by authors
[Back to Top]